Methodology and sources

The short version

• Open, official data We use public sources that allow reuse, including on a site with ads, as long as they’re credited: the U.S. Census Bureau, the U.S. Geological Survey (USGS), Spain’s Instituto Geográfico Nacional (IGN) and statistics office (INE), OpenStreetMap, Natural Earth and the World Bank, among others. The full list with licenses is at the end.
• The math runs in your browser Distances, areas, coordinates, datum shifts, the county or municipality of a point and the population inside a radius are calculated on your own device, with the boundaries and figures the page downloads. All Map Tools has no server that receives what you look up: when outside data is needed (an elevation, an address, a route), your browser asks the public service that provides it directly, and each section below names it.
• How accurate to expect It depends on the tool. The table below sums it up, and each section explains it with numbers.
• Found a mistake? Tell us through the contact page, with the link to the tool and what you expected to see. We review every report and log each fix, with its date, on the Corrections page.

How accurate each number is

Base map

Almost every tool shares the same map. MapLibre GL JS, an open-source library, draws it in your browser from OpenFreeMap tiles, which are built from OpenStreetMap. We use its “Positron” style recolored to our palette, with place names in the page’s language. When a tool needs it, hillshading goes underneath, computed by MapLibre from the Terrain Tiles elevation data (the same as in elevation).

Sources

• Tiles: OpenFreeMap, free, with no API key, and commercial use allowed with credit. The map shows “OpenFreeMap © OpenMapTiles Data from OpenStreetMap.”
• Map data: © OpenStreetMap contributors, under the ODbL 1.0 license.
• Aerial imagery: each country’s or region’s official orthophotos where they’re openly licensed and, everywhere else, EOX’s Sentinel-2 cloudless 2016 satellite imagery. The list is right below.

Aerial imagery

The area calculator, measure distance, the Spanish cadastral parcel tool and the radius map can show aerial imagery under your drawing. Your browser requests it live from each official service: the country’s or region’s orthophotos, at 8 to 50 cm (3 to 20 in) per pixel, and, where there are none openly licensed, EOX’s satellite imagery at about 10 m (33 ft) per pixel, fine for fields and woods but not for exact property lines. We only use imagery whose license allows commercial use, from services with no API key or account. It’s picked by bounding boxes: each service has its own, and the ones in view are switched on. The map credits only the imagery in view, and the radius map’s PNG image has it written on it.

• Austria: basemap.at · Orthofoto · CC BY 4.0
• Brussels (Belgium): Paradigm · UrbIS Ortho · CC0
• Flanders (Belgium): Digitaal Vlaanderen · Orthofotomozaïek · Modellicentie gratis hergebruik
• Wallonia (Belgium): SPW · Orthophotos · CC BY 4.0
• Czechia: ČÚZK · Ortofoto ČR · CC BY 4.0
• Estonia: Maa- ja Ruumiamet · Ortofoto · Maa- ja Ruumiameti avaandmete litsents
• France, with Corsica and the overseas departments: IGN France · BD ORTHO® · Licence Ouverte 2.0 (Etalab)
• Baden-Württemberg (Germany): LGL-BW · DOP20 · dl-de/by-2.0
• Bavaria (Germany): Bayerische Vermessungsverwaltung · DOP20 · CC BY 4.0
• Berlin and Brandenburg (Germany): LGB · Geoportal Berlin · DOP20 · dl-de/by-2.0
• Hamburg (Germany): LGV Hamburg · DOP · dl-de/by-2.0
• Hesse (Germany): HVBG · DOP20 · Free use, commercial too (§ 24 HVGG)
• Lower Saxony (Germany): LGLN · DOP20 · CC BY 4.0
• Mecklenburg-Western Pomerania (Germany): LAiV M-V · DOP20 · CC BY 4.0
• North Rhine-Westphalia (Germany): Geobasis NRW · DOP · dl-de/zero-2.0
• Rhineland-Palatinate (Germany): LVermGeoRP · DOP20 · dl-de/by-2.0
• Saarland (Germany): LVGL Saarland · DOP20 · dl-de/by-2.0
• Saxony (Germany): GeoSN · DOP20 · dl-de/by-2.0
• Thuringia (Germany): GDI-Th · DOP20 · CC BY 4.0
• Japan, from zoom 14: 国土地理院 (GSI) · 全国最新写真 · Public Data License 1.0 (compatible with CC BY 4.0)
• Luxembourg: ACT Luxembourg · Orthophoto · CC0
• Mainland Portugal: DGT · Ortos 2025 · CC BY 4.0
• Netherlands: Beeldmateriaal Nederland (PDOK) · Luchtfoto 8 cm · CC BY 4.0
• Poland: GUGiK (Geoportal) · Ortofotomapa · Free for any use, with credit
• Spain, with the Balearic and Canary Islands, Ceuta and Melilla: IGN · Ortofoto PNOA · CC BY 4.0 ign.es
• Switzerland and Liechtenstein: swisstopo · SWISSIMAGE · swisstopo open data, commercial use allowed
• US: the lower 48, Alaska, Hawaii and Puerto Rico: USGS · The National Map, Imagery Only · Public domain
• Everywhere else, about 10 m per pixel: EOX · Sentinel-2 cloudless 2016 (EOxCloudless) · CC BY 4.0

We don’t use aerial imagery for Italy, the UK, Ireland, Denmark, Sweden, Norway, Finland, Canada, Australia or New Zealand: either it isn’t openly licensed, or the service needs an API key or account (Denmark, Sweden, Finland and LINZ in New Zealand), or it mixes in commercial imagery under a closed license (New South Wales and Queensland), or it’s paid (Victoria). Nor do we use the 2018 and later editions of Sentinel-2 cloudless, which don’t allow commercial use. In Germany, Schleswig-Holstein and Saxony-Anhalt are missing, because their services don’t let other websites load the imagery, and so is Bremen. In Hamburg we use the 2026 series: the 2023 one is commercial imagery under a closed license.

Known limitations

• The base map is there to help you find your way. Each tool’s numbers come from its own sources, listed below: if the base map and a tool disagree (a boundary, a town name), go with the tool’s source.
• The map uses web Mercator, which stretches areas far from the equator, so a circle looks slightly elongated toward the poles. Measurements are never taken on the flat map: they’re calculated on the Earth.
• Outside the countries listed, the aerial view is satellite imagery at about 10 m (33 ft) per pixel. Each orthophoto is from a different year, and along a border you may see a white strip or the neighboring country’s imagery.

Elevation and profiles

Sources

• Terrain Tiles, everywhere except Spain (and in Spain wherever the IGN has no data, such as the sea, or doesn’t respond): a worldwide elevation model published in the Amazon Web Services open data registry. For each area it uses the best public source available: the USGS 3D Elevation Program (3DEP) in the US (10 m), Copernicus EU-DEM across most of Europe (30 m), NASA’s SRTM in most other places (30 m), national models in a few countries and NOAA’s ETOPO1 for the ocean floor. Almost all of it is public domain or openly licensed; the attribution list is below.
• In Spain, the IGN’s MDT05: the national terrain model, with a value every 5 meters, made from airborne laser (lidar) surveys. Licensed CC BY 4.0 ign.es and queried live from the IGN’s WCS service (servicios.idee.es, coverage Elevacion4258_5). Profiles also use the MDT25 (coverage Elevacion4258_25) on long routes.

How it’s calculated

A single point. We download the zoom-14 Terrain Tiles tile that contains it. Each pixel stores the height in its three color channels (the Terrarium format) and is decoded with the formula below. Then we interpolate between the four nearest pixels (bilinear interpolation, the standard method for terrain models).

In Spain (the mainland, the Balearic and Canary Islands, Ceuta and Melilla), we first ask the IGN for a 2 × 2 cell window around the point and apply the same interpolation. If the IGN has no value there (it returns zeros in Portugal, France or at sea) or doesn’t answer within 8 seconds, we fall back to Terrain Tiles.

A profile. The line is split into evenly spaced samples, at least one every 5 m and at most 1,000 (2,000 in the GPX route profile). In Spain, each sample takes its elevation from the MDT05, but not point by point: we ask the IGN’s WCS service for 256 × 256-cell clips of the grid (about 1.15 × 1.15 km), aligned with it so the service doesn’t resample, with an extra row and column so any sample’s interpolation falls inside a single clip, and read them in the browser. They arrive as 16-bit integer GeoTIFFs (the service rounds to the meter), DEFLATE-compressed: 7 to 25 KB each. Only the clips the line crosses are requested, four at a time at most and each only once, after checking a mask of Spain (0.05° cells with a 5 km margin) so clips of France, Portugal or the sea, which would come back empty, aren’t requested. If the line needs more than 24 clips (routes longer than about 20 km), we use the MDT25, which covers 25 times more per clip: with a sample every 10 or 20 m the climb barely changes (Sarria–Portomarín, 21.6 km: 546 m of climb with the MDT05 and 555 with the MDT25) and the IGN gets four times fewer requests; if it would still need more than 40, the whole line comes from Terrain Tiles. Anything left without data (outside Spain, at sea, a clip that doesn’t arrive) comes from Terrain Tiles, at a zoom level that depends on the length: 14 up to 5 km, 13 up to 30 km, 12 up to 120 km, 11 up to 400 km, 10 up to 1,500 km and 9 beyond, dropping if more than 48 tiles would be needed. Below the figures, the profile says which model it came from and, if it mixes two, how much of each. Distance along the profile is measured on a sphere with a radius of 6,371,008.8 m (the haversine formula).

Climb and grade. Total climb adds up every ascent and total descent every descent. To avoid counting noise, a change of direction only counts once the route has climbed or dropped more than 3 m on the terrain model, or more than 5 m with a GPX file’s own elevation, which is noisier. Maximum grade is the steepest over a 100 m stretch (or a fifth of the route if it’s under 500 m), so a single glitch in the model can’t inflate it.

Time. The English version uses Naismith’s rule, with no breaks. The Spanish version uses the MIDE method common on Spanish trail signs.

Accuracy

With Terrain Tiles, the real detail is that of each area’s source, not the pixel: 10 m in most of the US and about 30 m in Europe and most of the world. At that scale the terrain gets smoothed: peaks come out a little lower and canyon floors a little higher.

We compared the two models on three real routes, traced along OpenStreetMap paths, with 2,000 samples and the 3 m threshold:

Total climb and descent with the IGN model and with Terrain Tiles

In the mountains, the 30 m Terrain Tiles grid smooths the slope and mixes the trail with what’s next to it: on the Veleta it adds 7% more climb, and on the Cares, a trail cut into the walls of a gorge, 36% more. There not even the MDT05 is exact, since 5 m also takes in some of the wall. On gentle hills like Sarria’s, both models give almost the same.

For single points in Spain, the MDT05 gives a value every 5 m. As a check, at 39 of the 43 Spanish provincial capitals whose reference point matches the IGN gazetteer, the MDT05 and the official elevation differ by 1 m or less.

In What is my elevation?, where your device places you matters most: a few meters with GPS, but tens or hundreds of meters with Wi-Fi or a cell network, which in the mountains changes the elevation a lot. That’s why we show the accuracy your browser reports.

Known limitations

• On profiles, the MDT05 arrives rounded to the meter (the WCS service only serves it that way as GeoTIFF), so a profile and the point elevation tool, which reads it with decimals, can differ by half a meter: Mount Teide comes out at 3,712 m on the sample profile. The terrain model gives the height of the ground, not of the path: in a tunnel you get the mountain above, on a bridge the valley floor, and on a trail cut into a cliff some of the wall creeps in.
• It’s the height of the ground above mean sea level. Buildings, trees and the floor you’re on don’t count.
• It isn’t your GPS altitude: GPS measures height above an ellipsoid, a mathematical shape that doesn’t follow sea level, and the difference can be tens of meters.
• At sea, the global source gives the depth of the ocean floor, as a negative number.

Where am I and addresses

Sources

• Your location: provided by your browser (GPS, Wi-Fi or cell network), with an accuracy radius we show next to the result.
• United States: the Census Bureau’s TIGERweb, queried live for the state, county, city or census-designated place (CDP) and ZCTA. Public domain.
• Spain: municipalities, provinces and regions from the IGN’s administrative boundaries database (BDDAE), data as of August 10, 2026 (CC BY 4.0 ign.es, simplified); addresses, building numbers and postal codes from CartoCiudad, the IGN’s official street directory (CC BY 4.0).
• Place search: our own gazetteer of 219,441 places worldwide (towns and cities, countries, regions, provinces, counties, peaks, volcanoes, islands and mountain ranges), searched in your browser. Sources: GeoNames (CC BY 4.0: cities1000, allCountries and alternateNamesV2, which also provide the English, Spanish and local names); in Spain, the 8,132 municipalities with their population from the INE municipal register and the point of their main town, plus IGN population centers of 100 people or more (IGR Poblaciones, CC BY 4.0 ign.es); in the US, counties, cities, towns and census-designated places (CDPs) from the Census Bureau (public domain). Results are ranked by how well they match, population and in how many languages the place has a name, and it tolerates missing accents and small typos. If nothing matches, Photon is asked instead.
• Rest of the world: Photon, Komoot’s search engine on OpenStreetMap data, and countries from Natural Earth 1:10m, version 5.1.2 (public domain). Vatican City and Monaco, which Natural Earth draws badly, come from OpenStreetMap (© OpenStreetMap contributors, ODbL).

How it works

The country. If the point falls in a Spanish municipality, it’s Spain; if TIGERweb returns a state, it’s the US. Otherwise it’s the country of the nearest OpenStreetMap address, if it’s within 300 m; failing that, the Natural Earth country that contains the point (or one within 1 km, on the coast). If there’s none, we tell you you’re at sea.

A municipality in Spain. A point-in-polygon test. The province file picks the candidates (the province containing the point and any whose boundary is within 210 m), only their municipalities are loaded, and we find the one that contains the point. If the point falls in none but is within 30 m of one (on the shore, where simplification trims a few meters), we return that one. Within 100 m of another municipality, we warn you.

Address to coordinates. Each address is looked up in Photon (the tools for Spain, in either language, also check CartoCiudad), and we keep the result that best matches what you typed, house number and town included, not just the first one. For the reverse, the address of a point, Spain uses CartoCiudad and everywhere else uses Photon. Each result says how precise it is: building, street, town, municipality, postal code or named place. Batches go one address at a time, about one per second, up to 100 per batch.

Accuracy

The Spanish boundaries are simplified to 10 m so they load fast on a phone. Measured over the 4.37 million vertices of every unit 150 m or larger, the error is 2.4 m on average, 1.3 m at the median and 10.7 m at most. That’s far less than the source’s own uncertainty: the IGN says most boundary lines are accurate to about 40 m, and some stretches are provisional. That’s why the “near the boundary” warning kicks in at 100 m.

Known limitations

• ZIP codes are delivery routes, not areas, and the Postal Service doesn’t publish boundaries. We use the Census Bureau’s ZIP Code Tabulation Areas (ZCTAs), which match them almost everywhere; P.O. box and single-building ZIP codes have no ZCTA.
• Natural Earth borders can be off by hundreds of meters: the bridge at Irún, on the Spain–France border, shows up in France. In Spain, the IGN municipality takes precedence.
• Kosovo, Taiwan and Western Sahara appear separately: we generally follow Natural Earth, which shows who controls each territory in practice, and Western Sahara is shown whole and separate, as in Natural Earth’s Spain view. That’s not a position on who they should belong to.
• At sea there’s no county or country: boundaries stop at the coast and we don’t draw territorial waters.
• Spanish postal code boundaries belong to Correos: CartoCiudad shows them on its map, but a 2023 agreement with the IGN doesn’t allow downloading them. We give the postal code of the nearest building without drawing its area (see postal codes).

Coordinates and national grids

No outside data here: it’s all formulas running in your browser. We wrote them ourselves, without libraries, and test them against 501 reference cases computed with PROJ 9.8.1, the coordinate transformation software behind QGIS and most GIS programs, plus, for State Plane, 693 PROJ cases and 205 from NCAT, the NGS’s coordinate conversion tool; and for Great Britain and the Netherlands, 521 PROJ cases and the official test points: Ordnance Survey’s 40, both ways, and the 9,758 from NSGI, the Dutch geodetic agency; for Ireland, the worked example of the official polynomial in EPSG Guidance Note 7-2, plus PROJ.

How it’s calculated

Formats. Decimal degrees, degrees-minutes-seconds (DMS), degrees and decimal minutes, UTM, MGRS, geohash and Plus Codes. The reader detects the format on its own, with N, S, E and W letters, and tells you if it swapped latitude and longitude or assumed the northern hemisphere.

UTM. Transverse Mercator with the Krüger series up to the sixth power (n⁶), in Karney’s 2011 form, accurate to the millimeter thousands of kilometers from the central meridian. We use the GRS80 ellipsoid (less than 0.1 mm from WGS84), a scale factor k₀ = 0.9996 and a false easting of 500,000 m, with the Norway and Svalbard zone exceptions.

National grids. Each has its own projection (transverse Mercator, Lambert conformal conic, Swiss oblique Mercator or the Dutch oblique stereographic), using the formulas in EPSG Guidance Note 7-2 and from swisstopo, plus its datum shift:

• None when the system is already on ETRS89: UTM ETRS89, Lambert-93 (France), Irish Transverse Mercator and PT-TM06 (Portugal).
• Official grid file (interpolated bilinearly): for OSGB36 to ETRS89 in Great Britain, OSTN15, the Ordnance Survey transformation that defines the National Grid, in the NTv2 version Ordnance Survey itself publishes (EPSG:7709), with a node every 30″ × 60″ (about 0.9 × 1.1 km); Spain’s IGN SPED2ETV2 grid from 2009 for ED50 to ETRS89 (EPSG:15932); and Germany’s BeTA2007 for DHDN to ETRS89 (EPSG:15948). We take them from the PROJ network (cdn.proj.org) and convert them to a lightweight format for the browser, downloaded only when needed; the British one comes in 18 pieces of about 25 KB, and only the ones around your points are fetched.
• 3D similarity plus correction grid in the Netherlands, following NSGI’s official 2018 procedure (variant 1): a 7-parameter similarity with exact rotations (EPSG:9281) and a fixed height (43 m in ETRS89, 0 m on Bessel), then the rdcorr2018 grid, which corrects up to 0.25 m of distortion in the old network. Positions only: NAP heights aren’t converted.
• 3-parameter shift from the EPSG registry: CH1903+ in Switzerland (EPSG:1647).
• Official polynomial on the island of Ireland, for the older Irish Grid (TM75, EPSG:29903): OSi and OSNI’s transformation (EPSG:1041), a third-degree polynomial in each coordinate with 32 coefficients that shifts TM75 latitude and longitude to ETRS89. The reverse is solved by iteration, as EPSG specifies. It’s only valid on land and along the island’s coast.

Lettered grid references. The British National Grid names each 100 km square with two letters (from SV, at the origin, to HP, in Shetland), and the Irish Grid with one, A to Z without I (V at the origin). Then come the easting and northing figures within the square, cut off, not rounded: “TQ 302 796” is the 100 m square whose south-west corner is at 530,200 E, 179,600 N. In the OS grid reference finder, a point goes to the Irish Grid if it’s on the island of Ireland (Northern Ireland included, where OSNI maps use it) and to the British National Grid if it’s in Great Britain or on the Isle of Man; the line between them runs through the Irish Sea and the North Channel, leaving Kintyre, Islay and the Isle of Man in Great Britain and Rathlin and the Copeland Islands in Ireland.

WGS84 (what GPS uses) and ETRS89 are treated as the same: in Europe they’re a little under 1 m apart today.

US State Plane. All 124 current SPCS83 zones, on NAD83, with the EPSG registry’s parameters: 231 systems, every zone in meters and, where EPSG defines them, in US survey feet or international feet (Arizona, Michigan, Montana, North Dakota, Oregon, South Carolina and, alongside the others, Utah). The false origin in feet is EPSG’s, which isn’t always the meter value converted to feet (North Carolina: exactly 2,000,000 ft). Projections: transverse Mercator, Lambert conformal conic and, in Alaska zone 1, Hotine oblique Mercator (variant A). A point’s zone comes from its county, since zones are defined by county: we use Census county boundaries (1:5,000,000) and a county-to-zone table built by intersecting them with Esri’s zone polygons. Alaska goes by meridians, Niihau is Hawaii zone 5, Washington, D.C. uses Maryland’s, and in Kentucky, as NCAT does, the single zone (1600), with North or South as an alternative. It’s in the coordinate converter, for any point in the US, and in the national grid converter, as source or target, with each point’s zone or one you pick.

Accuracy

The projections match PROJ within 1 mm for UTM and 1 cm for national grids; for State Plane, within 0.05 mm across all 124 zones and their 231 systems, and NCAT to the millimeter (NCAT rounds to the millimeter). The detected zone matches NCAT’s at all 205 test points (two random counties per zone plus twelve special cases). Converting back lands within a ten-millionth of a degree (about 1 cm) of the start. In Great Britain we match PROJ within 1.4 mm (264 points) and Ordnance Survey’s 40 test points within 7 mm both ways: that’s how far the NTv2 version of OSTN15 strays from the original (PROJ also lands within 7 mm). In the Netherlands we match all 9,758 of NSGI’s test points within 0.6 mm in RD and a hundred-millionth of a degree (about 1 mm) back to ETRS89; inside the correction grid, within 0.3 mm. The datum shift is what limits accuracy, as rated by the EPSG registry:

Datum shift for each system and its accuracy

Decimal places matter too: 5 decimal places of a degree get you to about 1 m, and 6 to about 11 cm. More adds nothing, since not even a phone’s GPS is that precise.

Known limitations

• State Plane treats NAD83 as WGS84, as PROJ does by default: today they’re 1 to 2 m (3 to 7 ft) apart in the lower 48, so for survey work use the NGS’s NAD83(2011) tools. The zone comes from simplified county boundaries: within about 100 m (330 ft) of a zone line, double-check it. Alaska zones follow meridians and are approximate near their edges (the tool warns you).
• In the Netherlands we convert positions (RD), not NAP heights; outside the correction grid (50° to 56° N, 2° to 8° E) the correction is zero, as the procedure specifies. In Great Britain we use the NTv2 version of OSTN15, which strays up to about 7 mm from the original, and don’t convert heights either (OSGM15). In both cases the reference is ETRS89: GPS and Google Maps (WGS84) are a little under 1 m from it today.
• There’s no NAD27 conversion: older USGS topo maps in NAD27 can be off by tens of meters, up to about 100 m. US data in NAD83 is read as WGS84; today the two are within about 1 to 2 m, which matters only for survey work.
• UTM only exists between 80° S and 84° N; near the poles another projection (UPS) is used, which we don’t provide.
• The Irish Grid is only worked out on the island of Ireland and its coast, where the official polynomial is valid: far from the points it was fitted to, a polynomial goes wild. Lettered references for the Channel Islands (Jersey and Guernsey have their own grids) aren’t given.

Distances, routes, drive-time zones and areas

Sources

• Geodesy: GeographicLib, Charles F. F. Karney’s library (MIT license), on the WGS84 ellipsoid.
• Routes, distance matrices and stop ordering: OSRM, on the public FOSSGIS server (routing.openstreetmap.de). Drive-time zones: Valhalla, also run by FOSSGIS. Both use the OpenStreetMap road network (ODbL).
• FOSSGIS offers them for free on three conditions: one request per second at most, no heavy use, and credit with a link to fix the map. They keep route requests in their server logs, as their site says.

How it’s calculated

As the crow flies. The geodesic, the shortest path on the WGS84 ellipsoid (semi-major axis a = 6,378,137 m, flattening f = 1/298.257223563), solved with Karney’s 2013 method, accurate to nanometers. The haversine formula does the same on a sphere and can be off by up to 0.5%; we show it to explain the idea, but we don’t measure with it.

The halfway point is halfway along the geodesic (not the average of the coordinates), and the bearing is the compass direction you leave in. Between cities, each city is a single point: in the US, its interior point from the Census Gazetteer, except San Francisco, Anchorage and Juneau, where we use the OpenStreetMap city center; in Spain, the town seat in the IGN gazetteer. ZIP codes use their ZCTA interior point.

Radius map. The circle is drawn on the Earth: 128 points at the same true distance from the center (up to 512 for very large ones). Its area and perimeter come from the spherical formula, because that’s the circle you see. To find which states, counties or ZIP areas it touches, the circle and the boundaries are projected onto a Lambert azimuthal equal-area projection centered on the circle (it preserves areas) and clipped; a unit counts if more than 1,000 m² of it is inside.

The radius goes up to 20,000 km (12,427 miles). To paint on the flat map a circle that crosses the 180th meridian, the edge longitudes simply carry on past 180°; if it surrounds a pole, the fill is closed by running up the meridian to that pole; and if it holds both poles (radii of more than a quarter of the way around), the whole world is filled except the cap around the center’s antipode. What’s inside (population, municipalities, ZIP codes and cities) is worked out with the same method as “Population in a radius”, only once the panel is in view and, for radii over 500 miles, when you ask for it. When loading a list, coordinates and gazetteer places are found in the browser and addresses are looked up with Photon or CartoCiudad, at most one per second.

Area. The polygon is measured on the WGS84 ellipsoid with GeographicLib, as it lies on the Earth, without flattening it onto a map first. The perimeter is the sum of its sides, each along the shortest path. It’s the horizontal (plan) area: slope isn’t counted.

Units. Tools for a single country start in that country’s units, whatever the language of the page: miles in the US tools and kilometers in the Spain tools. Worldwide tools start in miles in English and in kilometers in Spanish. Once you pick other units (in a tool or in the map settings at the top), every tool uses yours.

Routes. OSRM finds the fastest route by car, bike or on foot along the roads you can use, at each road’s normal speed, with no traffic. The distance matrix takes up to 50 places (1,225 pairs, each in both directions, because the trip there and back can differ). The multi-stop route takes up to 25 stops: with fewer than 10 it tries every possible order; with more, it uses a fast method that gives a very good order, though not always the best one.

Measuring distance. Each leg of the line is its geodesic and the total is the sum of the legs, with the running total at each point; legs longer than 50 km (31 miles) are drawn and exported with a point every 25 km along their geodesic. The units are exact: 1 mi = 1,609.344 m, 1 yd = 0.9144 m, 1 ft = 0.3048 m and 1 nautical mile = 1,852 m. The time is the distance divided by the speed, with no stops or hills, at these speeds for each mode: walking, 3 mph (5 km/h); running, 6 mph (10 km/h); cycling, 11 mph (18 km/h); driving, 55 mph (90 km/h); by boat, 20 knots, and flying, 530 mph (850 km/h). A pace in minutes per mile or per kilometer is turned into a speed.

Distances from one point to many, and in bulk. Each place in the list is looked up only once: coordinates are read as they are; US ZIP codes go to the point of their Census ZCTA; names without digits, to our own gazetteer if a place has that name (if several equally well-known places share it, the row is flagged to check), and the rest (addresses and Spanish postal codes), to Photon and CartoCiudad, one request per second. The straight line and the initial bearing are the geodesic’s. By road, the OSRM one-to-many table is used: one request for every 50 destinations; in bulk, rows with the same origin go together and requests wait at least one second between them, with two retries if the service is busy.

Drive-time zones. Valhalla walks the roads and paths you can use from the starting point and draws the outline of what’s within each time or distance: up to 4 zones, 60 minutes or 100 km (62 miles) at most. By car it uses each road’s normal speed; by bike, about 18 km/h (11 mph); on foot, about 5 km/h (3 mph). Each zone’s area is measured with GeographicLib, and its reach is the longest straight line from the start to its edge.

The population inside each zone uses the same data as Population in a radius (Census ZCTAs in the US, the municipal register in Spain, the GHS-POP grid everywhere else). Each row of 30″ grid cells is cut by the zone at four latitudes and, in longitude, exactly, as with the circle: each cell (and, in Spain, each municipality’s populated cells) counts by the share inside, and each ZIP area, treated as a circle of its land area, by the share of that circle inside. A zone shaped like a circle gives the circle’s figure within 1.5%. The comparison circle has the same center and a radius equal to the zone’s reach, and its population is exactly what Population in a radius gives.

Accuracy

For straight-line distances and areas the math adds no error: what counts is where you put the points (and that a city is a single point). On a hillside the ground has more surface than its plan area: 2% more on a 20% slope and 12% more on a 50% slope.

Routes are only as good as the OpenStreetMap road network in the area. There’s no traffic: at rush hour you’ll take longer and get less far.

Known limitations

• OSRM doesn’t say when a point has no road nearby: it snaps it to the closest road, even on another continent (New York to London by car came back as a 2,150 km route, because it moved New York to Portugal). So if a point is more than 30 km from its road and more than a quarter of the route, we show “no route”; in the distance matrix, beyond 30 km. For drive-time zones, if the start is more than 2 km from any road or path, we show “no route” too.
• By car, routes use ferries where there’s no other way, and the crossing counts toward the distance and time. When a route includes a ferry (the route’s steps say so), we tell you how far and how long the crossing is.
• The routing services are free and public: if they’re busy, wait a moment and try again.

Spain maps, blank maps, worksheets and quizzes

Sources

• US states: the us-atlas 3.0.1 package, built from Census Bureau cartographic boundary files (public domain).
• Countries and capitals of the world: Natural Earth 1:10m, version 5.1.2 (public domain).
• Continents and 53 countries by state, province or region: Natural Earth 1:10m Admin 0 and Admin 1 (version 5.1.2, public domain). Neighbors, coastlines and areas of each division are calculated from those boundaries, so areas are approximate. Where Natural Earth lacks a regional capital or misplaces it, we use the city-center coordinates from OpenStreetMap (ODbL) or Wikidata (CC0). We fixed its outdated names (Mexico City, not Distrito Federal; La Guaira, not Vargas; Costa Caribe Norte and Sur in Nicaragua; Elías Piña; Eswatini) and moved the Amami Islands from Okinawa to Kagoshima, where they belong. Italy is shown by its 20 regions and the UK by its 4 countries. Kenya is shown by its 47 counties with geoBoundaries boundaries (RCMRD data, public domain), and Egypt and Cuba, which Natural Earth has outdated, with geoBoundaries boundaries from OpenStreetMap (ODbL). South Korea, Norway, Ireland, Hungary, Panama, Vietnam, Indonesia, the Philippines and New Zealand, whose divisions are outdated or mixed in Natural Earth, use OpenStreetMap boundaries as of October 31, 2026 (© OpenStreetMap contributors, ODbL): each division’s relation, pinned one by one and clipped to Natural Earth coastlines and borders so they fit the rest of the maps. That gives the current 15 counties of Norway (2024), Vietnam’s 34 provinces and cities (2025 reform), Indonesia’s 38 provinces, Panamá Oeste, the Philippines’ Negros Island Region (2024) and South Korea’s Jeonnam-Gwangju (2026). We don’t mark division capitals for Vietnam (after the reform, the seats are new wards Wikidata doesn’t have yet), Indonesia (three Papuan provinces have capitals under construction) or the Philippines (its regions have no capital), nor for Jeonnam-Gwangju and Tipperary, which have two seats. Morocco is left out (two of its 12 regions lie in Western Sahara, which we draw separately), as are Russia and Ukraine. We compared the areas of the divisions that have one in Wikidata, and the capitals, against Natural Earth and Wikidata, and fixed the wrong ones.
• Regional capitals for France, Greece, Japan, South Korea, Thailand, Turkey and Egypt: Wikidata (CC0), checked one by one; France’s are cross-checked against INSEE’s 2025 Code officiel géographique.
• The 50 US states by county: the Census Bureau’s 2025 Cartographic Boundary Files at 1:500,000 (public domain), in an Albers equal-area projection fitted to each state (Alaska uses the official Alaska Albers). Land and water area and population (July 1, 2025 estimates) are the Census Bureau’s. Which states, countries and coastline each county touches is calculated from those boundaries and checked against the Census county adjacency file.
• Spanish provinces and regions: the IGN’s BDDAE (CC BY 4.0), the same used in Where am I.
• Country areas: the World Bank (indicator AG.SRF.TOTL.K2, latest year 2024, CC BY 4.0), with the ±10% rule below.

How they’re made

These maps don’t use the base map: they’re drawings (SVG) that are projected and simplified in advance. The US uses the Albers projection with Alaska and Hawaii in insets; the world, Equal Earth; Europe, an azimuthal equal-area projection centered on 12° E, 52° N; and Spain, a conformal conic projection with the Canary Islands in an inset. Each border between two regions is simplified only once (Douglas-Peucker, about half a pixel), so neighbors fit with no gaps or overlaps. Each region’s area is measured on the unsimplified shape.

In the quizzes, the 193 UN member states and Vatican City count as countries. Kosovo, Taiwan, Palestine, Western Sahara and other countries’ territories appear in gray but aren’t asked. Worksheet answers (which state is smallest, which country is largest) come from this same data, not from memory.

The data maps split values into six shades by rounded quantiles (each shade holds about the same number of counties, with breaks at easy-to-read numbers). Population change uses fixed breaks: gray between −1% and +1%, and darker green or brown beyond 5% and 10%. Every scale runs light to dark, so it still reads in grayscale or printed in black and white.

Physical maps: rivers and mountains

• Spain. The 35 rivers and their lengths come from the IGN’s table of main rivers (Información Geográfica Destacada, revised December 18, 2025; CC BY 4.0 ign.es): the total length (in Spain, along the border and in Portugal) and the Spanish part. Courses come from the IGN reference hydrography (IGR Hidrografía, IDEE download service; CC BY 4.0 scne.es); the Portuguese stretches of the Douro, Tagus and Guadiana from Natural Earth (public domain). The map has the IGN’s 8 first-order rivers, the second-order rivers over 200 km that Spanish textbooks cover, and the shorter tributaries and coastal rivers taught in school for each drainage slope.
• The 11 mountain ranges are the IGN’s nine first-category systems plus the Basque Mountains and the Serra de Tramuntana. Since there are no official outlines, they are traced from the IGN’s 1 km digital terrain model: an area is mountainous if it meets the UNEP-WCMC world mountain criterion (Kapos et al., 2000), based on elevation, slope and relief within 7 km, and each area goes to the system of the summits and ranges the IGN assigns to it. They are approximate outlines for a school map. Each system’s highest peak and its elevation come from the IGN’s table of summits (revised October 10, 2025). Capes and gulfs: IGN Concise Gazetteer of Spain.
• United States, Europe and the world. Rivers and mountain ranges: Natural Earth 1:10m (public domain). US river lengths: the USGS table “Largest rivers in the United States” (Kammerer, 1990; public domain), in miles; other rivers, Wikidata (CC0, retrieved October 31, 2026), except Spanish rivers, which use the IGN figure. Each range’s highest peak and its elevation: Wikidata; Spanish peaks, the IGN.
• No length or elevation is measured on the map: they all come from their source, and the tests check them against a copy of those sources. In the quiz, tapping a river means tapping on its line or within 16 pixels of it.

Accuracy and known limitations

• These maps are for viewing, playing and printing, not measuring: simplification is a fraction of a pixel at their size.
• Country areas: we use the World Bank’s figure only if it’s within ±10% of what we measure on the map. Natural Earth alone would give Algeria 2.31 million km² and Libya 1.63 million (officially 2.38 and 1.76), changing the order. But the World Bank has errors too: it has listed Canada at 15.6 million km² since 2018, sometimes includes territorial waters (Croatia, Dominican Republic, Sweden) and for Greenland counts only ice-free land. Where we don’t use it, we give the map measurement as approximate (“about … km²”).
• Some capitals have more than one answer, and all of them are accepted when typing (Pretoria, Cape Town or Bloemfontein for South Africa; Sucre or La Paz for Bolivia).
• River lengths vary a lot between sources (where the source is placed, how meanders are measured): each page says where its figures come from. Mountain range outlines are approximate: there are no official ones.

Size comparisons

How the map is made

Each map is a drawing (SVG) built at compile time with a Lambert azimuthal equal-area projection, on the sphere of mean radius (6,371.0088 km), centered on one of the two shapes: it preserves areas, so both appear in their true proportion. The other shape is rotated across the globe until its center sits on the same point, using the same function as the true size map, without changing its shape or area. Faraway parts (Alaska and Hawaii, the Canary Islands, the Azores and Madeira, overseas territories) are not drawn, but they count in the figures, and the map caption says how much they represent.

Sources and figures

• Areas: the same as in the true size map. For countries, the World Bank (AG.SRF.TOTL.K2, CC BY 4.0) when it is within 10% of the area measured on the map; otherwise that measured area, marked “about”. For Spain’s autonomous communities, the IGN; for US states, the Census Bureau (Gazetteer 2025, land and water). Europe (excluding Russia) and Africa are the sum of their countries according to Natural Earth.
• “Fits N times” is one area divided by the other.
• Population: the World Bank (SP.POP.TOTL, 2025), Spain’s INE (population register on January 1, 2025, summing each community’s provinces) and the Census Bureau (Vintage 2025 estimates, July 1); continents are the sum of their countries with data. Density is population divided by total area.
• “End to end” is the longest great-circle distance between two points of the drawn outline; “Mercator enlarges it” is the area of its outline on Mercator divided by its real area.

Accuracy and known limits

• Outlines are simplified, so measurements taken on the outline (end to end, Mercator) have a margin of about 1–2%. Areas and population are not measured on the drawing: they come from the sources.

Distances between cities

How it’s calculated

Straight-line distance, bearings and the midpoint are geodesics on the WGS84 ellipsoid computed with GeographicLib (Karney) between each city’s point: the one on its place page (the USGS GNIS “Populated Place”, the city center, in the US; Spain’s IGN gazetteer in Spain) and, outside both countries, the GeoNames point in our gazetteer.

Driving distance and time come from the fastest car route on the public FOSSGIS OSRM server, using OpenStreetMap data (ODbL). They were requested once, on October 31 and November 1, 2026, never more than one request every 2.1 seconds, and are stored with the site: pages make no requests when they load. Times assume no traffic and no stops, at OSRM’s speeds, which are somewhat below the limits. For London to Paris, Madrid to London and Barcelona to London the route is pinned to the Channel Tunnel (Le Shuttle), because without it OSRM chose a six-hour ferry. The main roads, the states, Spanish regions or countries the route crosses (boundaries from the Census Bureau, IGN and Natural Earth) and the halfway point on the road all come from that route’s line. The places near both midpoints are the nearest Census place, Spanish municipality (INE) or GeoNames town, with its population.

Pairs with no road (the Balearic and Canary Islands, Hawaii and the pairs on different continents) request no route: the page gives the straight line as the flight path, the countries and sea beneath it (Natural Earth countries, in 5 km steps), the line’s northernmost or southernmost point, and the rhumb line (the constant-bearing route, straight on a Mercator map), computed on the WGS84 ellipsoid from the isometric latitude and the meridian arc. Their midpoint often falls at sea, so the nearest town is searched up to 3,000 km (1,860 miles) away.

Flight time is a simple estimate, only from 500 km (310 miles) up when there’s a road: 30 minutes plus the straight line at 800 km/h (about 500 mph). The arrival time adds the flight and the time difference to a 10:00 departure. The time difference comes from each city’s time zone (timezone-boundary-builder outlines and the IANA database) in mid-January and mid-July. Elevation and population are those on the place pages (USGS 3DEP and Census Bureau Vintage 2025 estimates; IGN and the INE population register) and, elsewhere, GeoNames population.

Known limits

• Driving routes are from one particular day: roadwork, a closure or a new road can change them. For today’s drive, use the tool, which asks live.

Flight distances between airports

Sources

• Airports: OurAirports (its airports.csv and countries.csv files, in the public domain), an open, community-maintained database of the world’s airports. It includes those with an IATA code that are large or medium-sized or have scheduled service: more than 5,000 in about 230 countries and territories, with their name, city, country, IATA and ICAO codes, type and coordinates (to 4 decimals, about 36 ft). Country names are the ones on our maps (Natural Earth). The file is rebuilt with data/aeropuertos/generar.mjs.

How it’s calculated

Distance and heading. The geodesic on the WGS84 ellipsoid between the two airports’ points, with GeographicLib (Karney, 2013), in kilometers, miles (1,609.344 m) and nautical miles (1,852 m), with the initial and final headings of that same geodesic. The “straight line on a flat map” you can compare it with is the rhumb line (constant heading), the one that’s straight on Mercator, calculated with the isometric latitude.

Flight time. A fixed 30 minutes per flight (taxi, takeoff, climb, descent and landing) plus the distance at 800 km/h (497 mph), rounded to 5 minutes: the same rule as the estimated flight on the city distance pages. A route with stopovers adds up its flights, without layovers.

Map and downloads. Each flight is drawn along the geodesic with points no more than 40 km (25 miles) apart and continuous longitudes, so it crosses the antimeridian on the right side; the map is framed on the narrower side of the globe (the Pacific, when needed). In GeoJSON and KML the lines are split exactly at ±180° (a MultiLineString or several LineStrings), as the GeoJSON standard (RFC 7946) requires, with the latitude of the split interpolated between the two neighboring points.

Accuracy

GeographicLib computes the distance between two points to within nanometers. Against the published distances of well-known routes (7,488 miles from Los Angeles to Sydney, 9,009 miles from Perth to London), the difference is under 0.1%, and it comes from each source using a slightly different point for the airport: OurAirports’ point can be a mile or so from the official airport reference point, which changes a flight of more than 3,000 miles by less than 0.05%.

Known limits

• It’s the minimum distance. Planes follow airways, ride or avoid the wind and detour around closed airspace, so they fly a few percent more.
• The time is an estimate for jets with no wind: scheduled times change with the direction of the flight and the aircraft.
• Airfields without an IATA code and small ones without scheduled service aren’t included. City codes (NYC, LON) don’t belong to one airport and can’t be measured.

Data studies

Our studies compute original figures from official data and publish the results as CSV under a CC BY 4.0 license. Provincial capital elevations are those of the IGN populated place (IGR Poblaciones), checked against the MDT05 terrain model (for 11 capitals, the MDT05 value at the official gazetteer point); US state capital elevations come from the USGS 3D Elevation Program at each city’s GNIS point.

The geographic center is the area centroid, computed on the GRS80 ellipsoid in a Lambert azimuthal equal-area projection centered on the result, from full-resolution IGN municipal boundaries (BDDAE, August 10, 2026) and the Census Bureau’s 2025 Cartographic Boundary Files (counties, 1:500,000). The main center excludes islands (only land connected by land to the continent); where there are islands we also give the center including them, and for archipelagos the center of the whole chain and of its largest island. Every center is checked against an independent calculation (the center of gravity on the sphere with the site’s simplified boundaries) and compared with published centers: the Cerro de los Ángeles (IGN geodetic marker 58258), the centers of Andalusia (CNIG), Galicia and Catalonia, and the USGS “Geographic Centers” table (Bulletin 689, 1923; Bulletin 1212, 1966; Elevations and Distances in the United States).

The population within 1, 3, 5, 10, 25 and 50 miles of the 100 largest US cities (from their GNIS point) and within 1, 5, 10, 25 and 50 km of Spain’s provincial capitals (from their gazetteer point) is computed with Population in a radius’s own code and data (see “Population in a radius” below), with low and high figures; an automated test checks that the tool gives the same result for every circle.

Sources: IGN (CC BY 4.0 ign.es), INE, USGS and Census Bureau (public domain), JRC (GHS-POP, CC BY 4.0), Natural Earth (public domain) and OpenStreetMap (ODbL).

What’s within a radius of each city

Each city page draws four circles (5, 10, 25 and 50 miles in the US and the UK; 5, 10, 25 and 50 km elsewhere) around the city’s point: the GNIS point for US cities (the 100 largest, the same as the study), the official gazetteer point for Spain’s provincial capitals, Ceuta and Melilla, and the GeoNames point for 33 big cities elsewhere. Only cities where GeoNames covers the surrounding towns well are included.

People in each circle come from Population in a radius’s own code (with low and high figures), and the counts of municipalities, ZIP codes and Census places from the radius map’s “What’s inside” panel; an automated test checks both against the tools for the same circles. Towns are Spain’s municipalities by their main town, Census places (cities, towns and CDPs) by their interior point and, outside both countries, GeoNames places of 1,000+ people without neighborhoods, with straight-line distances and bearings on the WGS84 ellipsoid. The 30-minute drive area is a FOSSGIS Valhalla isochrone (typical speeds, no traffic), requested once when the data is built, with its area, reach and population computed like the drive time map does.

Population and other data (Census, INE, World Bank)

Sources

• U.S. Census Bureau (public domain): Vintage 2025 population estimates (July 1, 2025, with the April 1, 2020 estimates base) for counties, states, cities and towns; the 2020–2024 American Community Survey 5-year estimates for census-designated places, ZCTAs and county median household income (in 2024 dollars); and the 2025 Gazetteer and cartographic boundary files.
• Spain’s INE: official population figures from the municipal register (table 29005) as of January 1 of 2025, 2020 and 2015, published December 11, 2025. INE allows reuse, including commercial reuse, with credit.
• Spain’s IGN: the area of each municipality and the location of its seat, from the national gazetteer (CC BY 4.0).
• World Bank: country areas (CC BY 4.0), with the ±10% rule described under maps.
• JRC (European Commission): the GHS-POP R2023A population grid, 2025 estimate, one cell every 30″ (about 1 km) worldwide (Schiavina et al., 2023; CC BY 4.0, commercial use allowed). Outside the US and Spain it gives the population; in Spain it also tells where people live within each municipality (427,555 populated cells in 8,128 municipalities). The country of each cell comes from Natural Earth (public domain) and the US border from the Census Bureau’s 2025 Cartographic Boundary Files at 1:500,000.

How it’s calculated

Population in a radius (US). Population is published per ZIP area (ZCTA), with no detail on where people live inside each one. So we work out what share of each ZCTA’s area falls inside the circle and count that same share of its population. This is areal interpolation, the standard method when data only exists by area. We don’t have ZCTA shapes, so each ZCTA is treated as a circle with the same land area around its interior point. The range goes from counting only the ZCTAs entirely inside to counting every ZCTA the circle touches, in full.

Population in a radius (Spain). The municipal register gives each municipality’s population but not where people live within it. Municipalities entirely inside the circle count in full and those outside don’t count. For those the circle cuts, we use the GHS-POP 2025 grid, which spreads people over 30″ (about 1 km) cells according to what’s built, and count the share of the register population living in cells inside the circle. Each municipality’s total stays the INE figure; the grid only decides how it’s spread. Each cell belongs to the municipality its center falls in, and shoreline cells to the nearest one. The few municipalities with nobody in the grid are still split by land area. Range: municipalities entirely inside count in full; for the cut ones, we add and subtract the error that 8 out of 10 circles stay within against the 2021 census: ±60% at 1 km, ±38% at 2, ±21% at 5, ±11% at 10, ±8% at 25 and ±6% from 50 km.

Counties and states. Population change compares the July 1, 2025 estimate with the April 1, 2020 estimates base. Density is population divided by land area. Connecticut shows its nine planning regions, which replaced its counties in Census data in 2022.

Outside the US and Spain. Population comes from GHS-POP, which spreads each country’s census population over 30″ cells according to what’s built there (as seen from satellites) and projects it to 2025 with UN figures. We add up the cells inside the circle and, for the cells the edge cuts through, the share that falls inside. The circle is measured on a sphere with the Gaussian radius at its latitude, within 0.35% of the geodesic distance. When the circle crosses the US or Spanish border, each side is counted with its own data: ZCTAs or the municipal register on one side, the grid on the other. The grid has no cells in those two countries, so nobody is counted twice. The grid comes in 8 × 8-cell blocks (4′), with the 64-cell detail only where it matters: 23 MB in 1,468 files, and each circle downloads 20 to 200 KB.

Grid figures come with a rough range that depends on the radius: ±30% at 1 km, ±16% at 5, ±11% at 10, ±9% at 25 and ±7% from 50 km. In 8 out of 10 circles, the error against Eurostat’s official 2021 census grid (1 km² counts from EU and EFTA statistics offices) stays below that range.

Rings. With several circles around the same center (1, 3 and 5 miles; 1, 5 and 10 km, or any radii you choose, up to 6), the cumulative population up to each radius is exactly what a single circle of that radius gives, low and high figures included, and each band is the difference. A band’s range isn’t a difference: ZIP areas or municipalities entirely inside the band count in full; those cut by either of its two edges carry their uncertainty (from none to all, or ± the register spread’s margin), and the grid’s share gets the margin of a circle as wide as the band, which has as much edge per square mile.

Accuracy

Population figures are the official ones, untouched. For Spain we publish the IGN’s municipal areas; as a check we also calculate them from the boundaries, and for municipalities over 1 km² the difference is 0.01% at the median and 1.4% at the 99th percentile.

Storing the grid in blocks moves the figure by less than 0.8% in 9 out of 10 circles of 1 km, and by less than 0.1% from 25 km. Against Eurostat’s 2021 census grid, the grid itself has a median error of 14% at 1 km, 7% at 5 km, 4.6% at 10 km, 3.8% at 25 km and 2.4% at 50 km. At 25 km: Paris +0.1%, Berlin +1.0%, Rome +2.0%. At 50 km the median error is 4.7% against the Census ACS and 7% against Spain’s register. Whole units: Île-de-France −1.3%, Tokyo −6.5%, Greater London +11% (2021 census), Mexico City −15%.

In Spain we measured it against Eurostat’s 2021 census grid (1 km², made in Spain by the INE), with 150 to 300 random circles per radius, using the 2020 register. Median error before (land area) → now (grid): 1 km 79% → 22%; 2 km 68% → 14%; 5 km 41% → 6.1%; 10 km 22% → 3.0%; 25 km 4.7% → 1.1%; 50 km 1.2% → 0.7%; 100 km 0.6% → 0.5%. There’s little gain at large radii, where almost everyone lives in municipalities entirely inside. Puerta del Sol in Madrid, 10 km: 1.71 million before, 3.34 million now (2021 census: 3.26 million). With this range, the register spread the way the census says falls between the low and high figures in 81–83% of circles at every radius.

Known limitations

• In the US, population in a radius assumes people are spread evenly within each ZIP area: with a small circle the range is wide. In Spain, people are placed within each municipality with the GHS-POP grid, which knows where buildings are but not how many people live in each; at 1–2 km it still runs low in the densest spots (−16% median at 1 km).
• In Spain the low and high figures only cover where people live within the municipalities the circle cuts; each municipality’s register figure is taken as given, so at large radii the range is narrow and doesn’t reflect differences between the register and the census.
• Outside the US and Spain, population is an estimate (GHS-POP), not a count. It tends to run high in very dense and business districts and low in fast-growing cities and informal neighborhoods. Where the last census is old (much of Africa; Nigeria hasn’t held one since 2006) it can be off by more than the range. It has nobody in Svalbard.
• The country of each part is decided by blocks of about 7 km, so in a city split by a border part of it may be counted on the wrong side. The total doesn’t change.
• Census-designated places have no annual estimate, so they use the ACS figure; 33 places have neither. ZIP codes without a ZCTA (P.O. boxes, single buildings) have no population. There’s no data for Puerto Rico or the territories.
• One county, De Baca County, New Mexico, has no published median household income.

Postal codes and ZIP codes in an area

Sources

• US: the Census Bureau’s ZCTAs (the same as for population: interior point, land area, ACS 2020–2024 population, city and county). Their outlines, and which areas touch a circle or a polygon, come live from TIGERweb (public domain). ZIP codes with no ZCTA (7,335: P.O. boxes, single buildings or created after 2020) come from GeoNames Postal Codes (CC BY 4.0), as a point only. Counties come from the 2025 Cartographic Boundary Files.
• Spain: the INE electoral roll street list as of June 30, 2025, which gives the postal code of every street segment (1.52 million segments); the INE’s 2025 census tract boundaries; and the IGN’s population centers (IGR Poblaciones, CC BY 4.0). All Map Tools with data from the INE website: www.ine.es.
• Spanish postal code boundaries belong to Correos. The IGN shows them on CartoCiudad (the WMS “codigo-postal” layer, which states “CC BY 4.0 scne.es”), but the 2023 agreement between the IGN and Correos (BOE-A-2023-11522) only allows viewing and querying them: the vector layer can’t be downloaded or passed on, and the CNIG download center doesn’t offer it. So we don’t calculate with it; the tool only shows it, live from CartoCiudad, if you turn it on.
• United Kingdom: Ordnance Survey’s Code-Point Open (Open Government Licence v3), with Royal Mail postcodes as of July 17, 2026: 1,748,230 full postcodes in Great Britain with their point on the British National Grid and the ONS codes of their ward and local authority; names from its codelist (Boundary-Line). The licence requires these three lines, which appear in the tool and here: “Contains OS data © Crown copyright and database right 2026”, “Contains Royal Mail data © Royal Mail copyright and database right 2026” and “Contains National Statistics data © Crown copyright and database right 2026”.
• Canada: Statistics Canada, 2021 Census. Forward sortation area (FSA) and dissemination area boundaries, from the ArcGIS REST service of its 2021 cartographic boundary files (Open Government Licence – Canada: “Contains information licensed under the Open Government Licence – Canada”); population by FSA (table 98-10-0019-01) and by dissemination area, with its municipality (table 98-10-0015-01), under the Statistics Canada Open Licence. Adapted by All Map Tools; this does not constitute an endorsement by Statistics Canada. Full postal codes (M5V 3L9) belong to Canada Post and aren’t open.
• Australia: Australian Bureau of Statistics (CC BY 4.0): the 2021 Postal Areas (ASGS Edition 3), the allocation files that put each mesh block in its Postal Area and its Suburb and Locality, the 2021 Census person counts by mesh block, and table G01 by Postal Area (ABS Data API).
• Mexico, no data: Correos de México’s national postal code catalog is free, but its page says it may not be commercialized, and GeoNames MX is derived from it; on top of that, in GeoNames many codes in the same city share one point (93 in Ciudad Juárez), so it’s no use for a radius. We haven’t found another open source with the codes and their location.

How it’s calculated

ZIP codes in a radius or an area. With “Center inside”, a ZIP code counts when its interior point falls in the circle (geodesic distance) or in the polygon (point in polygon, holes included). With “Any part inside”, we ask TIGERweb which ZCTAs intersect the area (a spatial “intersects” query with the 64-sided circle or the polygon, thinned to 2,000 vertices at most). In a circle, the Inside column is the share of each ZIP’s area inside, clipped like the municipalities; anything under 0.05% is a simplification artifact and doesn’t count. Outlines are requested simplified (about 3 m per km of radius) and only up to 1,500 ZIP codes. ZIP codes with no area always count by their point.

One point per Spanish postal code. Each street segment is placed at its population center (if that center has a single postal code, or if its census tract is larger than 10 km²), at the main center of its locality (scattered houses in a large tract) or at the interior point of its census tract (in cities, where tracts are small). Each segment weighs the house numbers it spans. The code’s point is the place of its own closest to its center of gravity, so it lands where it has streets even if the area is horseshoe-shaped. Errors in the street list are removed: codes ending in 000, codes with fewer than 5 segments all in another province, and municipalities with one or two segments of a code that has 50 or more. That leaves 10,782 codes; the main municipality is the one with the most segments.

United Kingdom. Code-Point Open’s point (the building of the address closest to the middle of the postcode’s addresses, on the British National Grid) is converted to latitude and longitude with Ordnance Survey’s transverse Mercator and the Helmert transformation from its guide (3 to 5 m out) and stored to 5 decimals. The 879 postcodes with no point (quality 90) are left out. A postcode counts when its point is in the circle. Sectors (SW3 6) and districts (SW3) are placed at their postcode closest to the average of all of theirs and count by that point; their local authority is the one with the most postcodes. Full postcodes go up to a 25 km radius; beyond that the list shows sectors.

Canada and Australia. Outlines are simplified with mapshaper, with detail that grows with each area’s size (60 m in cities, up to 1.5 km in the Arctic), and stored as TopoJSON. With “Center inside”, each area’s point counts: in Canada, the dissemination area closest to the center of gravity of its people (so an FSA with a neighborhood and a stretch of countryside, like T2P in Calgary, isn’t placed in the countryside); in Australia, an interior point of its outline. With “Any part inside”, the outline is clipped by the circle like the municipalities, and the Inside column is the share of the area inside. Each FSA’s municipality is the one with the most people in it; each Australian postcode’s suburbs are the Suburbs and Localities with people in it, from most to fewest.

Accuracy

We checked 160 postal code points picked at random (two samples, of 60 and 100) with a query of the CartoCiudad layer (GetFeatureInfo, without storing any geometry): 153 fall inside their own code; the other 7, all rural, in the neighboring code. A ZIP or postal code is an area reduced here to a point, so “Center inside” leaves out large ones whose edge crosses the circle.

Known limitations

• Spain: P.O. box codes and codes for post offices and organizations (ending in 070, 071 or 080) have no streets and don’t appear. “Any part inside” isn’t possible because the boundaries can’t be used.
• The street list is published twice a year, so a new code can take up to six months to appear. The INE and Correos don’t always agree on the code of a street on a boundary.
• US: the point of a ZIP code with no area is its town’s point in GeoNames, not the post office, and GeoNames doesn’t say whether it’s a P.O. box or a single address.
• “Any part inside” needs TIGERweb: if it doesn’t answer, the list goes by center and the tool says so.
• UK: Great Britain only. Northern Ireland (BT) isn’t in Code-Point Open and its open data doesn’t allow commercial use; the Channel Islands and the Isle of Man aren’t included either. Postcode boundaries aren’t open, so there’s no “Any part inside”.
• Canada: census FSAs approximate Canada Post’s, and those created after 2021 may be missing. A cut FSA’s population counts in full.
• Australia: PO box-only and large-user postcodes have no Postal Area and don’t appear.

ZIP codes by state, county and city

Sources

• Which ZIP codes (ZCTAs) touch each county and each city, town or CDP, and how much land they share: the Census Bureau’s 2020 ZCTA to County and ZCTA to Place relationship files. Connecticut replaced its counties with nine planning regions in 2022, so there we use the 2022 County Subdivision to ZCTA file: each town lies entirely in one region.
• Population of each ZIP code, census tract and Connecticut town: American Community Survey 2020–2024 five-year estimates (table B01003). County population: Vintage 2025 estimates. ZCTA land area and interior point: 2025 Gazetteer Files.
• Maps on the county pages: Cartographic Boundary Files (ZCTAs 2020 and counties 2025, 1:500,000) and the 2025 county adjacency file. In the tool, the outlines come live from TIGERweb. All public domain.

How it’s calculated

Share inside. For each ZIP code, the land it shares with the county or city divided by its total land, straight from the relationship files (water doesn’t count). A ZIP code belongs to a county when at least 1% of its land is inside; below that it’s usually the two boundaries not quite matching, so it’s listed apart as “touching the border”. With 99% or more inside, it counts as entirely inside; otherwise it’s shared.

Residents inside a county. The Census doesn’t publish the population of each piece of a ZIP code, so we estimate it with census tracts, which never cross county lines: each tract’s people are spread evenly over its land, each piece of the ZIP code takes the share of the tract it covers, and the result is scaled so the pieces add up to the ZIP code’s ACS population. In Connecticut we do the same with its towns. A ZIP code entirely inside keeps its whole population. The map class (entirely inside, shared mostly inside, shared mostly outside) goes by land.

Which counties have a page. Those with at least 120,000 people in the 2025 estimates; any other county or city opens in the tool. The District of Columbia has no counties, so its state page lists its ZIP codes directly. On the county maps, the ZIP areas and the county outline are simplified to well under a pixel and cut to the county’s frame; a ZIP number is written only where it fits.

Accuracy and known limitations

• ZCTAs are the 2020 census ones and are only redrawn every ten years: a ZIP code created since then isn’t there, and one the Postal Service changed keeps its 2020 shape. ZIP codes with no area (P.O. boxes, single buildings) aren’t included.
• Residents inside a county are an estimate for shared ZIP codes: it assumes people are spread evenly within each census tract. Added up, the residents in the ZIP codes of each county with a page come within 6% of its ACS population; in small rural counties the gap can be wider, because ACS figures for small ZIP codes and tracts have wide margins. They also fall short of the 2025 county estimate in fast-growing counties, which have grown since the survey.
• Cities use the 2020 boundaries in the relationship file; a city that has annexed land since then may be missing a ZIP code at its edge. A few places renamed or recoded since 2020 keep their 2020 name.

Place pages

There are 465 place pages, in English and Spanish: Spain’s 52 provincial capitals and autonomous cities, the 380 other municipalities with more than 20,000 people (INE municipal register, January 1, 2025: 103 above 50,000 and 277 with 20,000 to 50,000) and 33 peaks. Each one gives the elevation (in meters and feet; your chosen unit wins), the coordinates and the UTM. There’s also a page for every province (all 50 plus Ceuta and Melilla; for the 7 single-province regions it doubles as the region’s page), one for each of the 10 multi-province regions and one for Spain, with register population, IGN area, a map of the municipalities and the highest point.

Sources and method

• Capital and municipality elevations come from the IGN’s population centers (IGR Poblaciones), at each town’s reference point, rounded to the meter. Which municipalities pass 20,000 people, and their population, come from the INE municipal register (January 1, 2025).
• Each Catalan municipality’s comarca comes from Idescat’s municipality code table (CC BY 4.0); each Balearic and Canary municipality’s island, from the NUTS 3 code in the IGN’s administrative units. Municipalities in Catalonia are compared with their comarca and those on the islands with their island; the rest of Spain has no common official comarca division, so those pages don’t mention one.
• Which peaks get a page, their elevation, range and provinces, and each province’s highest point come from the IGN’s summit table; peak positions come from the summit node in OpenStreetMap (ODbL), 0 to 17 m from the IGN’s point (90 m for Puig Major).
• Every capital is checked against the MDT05 terrain model at the same point. We don’t use the IGR figure if its point is more than 200 m from the town seat in the national gazetteer or its elevation is more than 30 m off the MDT05; we publish the gazetteer point and the MDT05 elevation instead, and the page says so. That happens for 11 capitals (Ávila, Burgos, Albacete, Vitoria-Gasteiz, Huesca, Badajoz, Almería, Palma, Barcelona, San Sebastián, and Alicante) and 87 other municipalities (30 above 50,000 and 57 with 20,000 to 50,000), almost all in provinces 02, 03, 04, 06, 07, 08 and 09, where IGR Poblaciones gives the center of the built-up area instead of the gazetteer point; outside them, Culleredo, Cangas, Galdakao and Erandio. In Galdakao and Erandio IGR Poblaciones flags two population centers as the seat: we check the one nearest the gazetteer point, which is more than 200 m away in both. 98 pages in all. Of the 293 municipalities that keep the IGR figure, 274 are within 1 m of the MDT05; the largest gaps are Hernani (+15.0 m), Errenteria (−14.7 m) and Eibar (−11.7 m), all within the threshold. Municipalities are compared with the 153 over 50,000 people or the 279 with 20,000 to 50,000, capitals included.
• Peaks with a page are, from the IGN’s summit table, the 8 first-category summits plus, in each region, the highest one and the next one of first or second category; a summit on a border counts for both regions. The page goes in the province of the municipality that contains the point. We drop a peak if its OSM node is more than 150 m from the IGN’s point or its official elevation is more than 30 m off the MDT05 there; none was dropped (the biggest gap is Puig Major, −12.3 m). Each province’s highest point is the one the IGN marks as “techo provincial”; in three cases it’s a named area, not a peak: El Telégrafo (Ciudad Real), Campo Cuchillejo (Valladolid) and Rostrogordo (Melilla).
• UTM coordinates use the Krüger series to n⁶, the GRS80 ellipsoid and k₀ = 0.9996, in the official datum: REGCAN95 in the Canary Islands and ETRS89 elsewhere.

Known limits

• Since 2015, Torrenueva Costa split from Motril, El Palmar de Troya from Utrera and Usansolo from Galdakao. On those three pages the 2015 population is compared with today’s plus the new municipality’s, so both figures cover the same territory.

United States

There are 407 pages, in English and Spanish and in feet first, the country’s own units (the unit you pick always wins): the 50 state capitals, the 91 cities with more than 250,000 people according to the Census Bureau’s 2025 estimates (Washington, D.C. included; 14 of them are also capitals), the 249 with 100,000 to 250,000 (17 of them capitals) and the highest point of 47 states and the District of Columbia. There’s also a page for each state (the 50 and the District of Columbia), with a map of its counties, its highest and lowest points and its most populous places, and one for the United States.

Sources

• Each city’s point: its “Populated Place” in GNIS, the USGS official gazetteer. It has to fall inside that same Census city according to TIGERweb.
• City elevations: the USGS 3DEP at that point, through its EPQS service, with the grid and date of the model behind it (almost always 1-meter lidar).
• Each state’s highest and lowest points: the USGS table “Elevations and Distances in the United States”; Denali, from the 2015 USGS survey (20,310 ft; the table still says 20,320). Each summit’s position: its “Summit” in GNIS.
• Population, land area and counties: U.S. Census Bureau (Vintage 2025 estimates and 2025 Gazetteer; Honolulu, a CDP with no annual estimate, from the 2020–2024 ACS). Time zone: timezone-boundary-builder (ODbL). All USGS and Census data is public domain.

How it’s calculated

There’s no official published elevation for US cities: GNIS stopped publishing it in 2021, and the one it gave also came from the USGS model at the same point. So we publish the 3DEP elevation at the city’s reference point and check it against the last GNIS figure: for all 359 cities the point hasn’t moved since 2021, and the difference is 1 m (3 ft) or less for 318 and 7.3 m (24 ft) at most (for the 232 added on November 1, 2026, 205 are within 1 m and all within 5 m). We don’t use the Census interior point because in sprawling cities it lands far from downtown: in the ocean for San Francisco (54 km away), in the mountains for Anchorage and Juneau.

Of the 251 cities with 100,000 to 250,000 people and a Census estimate, two have no page: Jurupa Valley, California, which has no “Populated Place” in GNIS, and Centennial, Colorado, whose GNIS point falls outside the city according to TIGERweb. Lee’s Summit is looked up as “Lees Summit”, the GNIS form, which drops apostrophes. The 15 census-designated places of that size, such as Enterprise, Arlington (Virginia) or Metairie, have no annual estimate and are left out, as Honolulu is among the big cities. When two cities with a page share a name (Springfield, Columbus, Augusta…), the title includes the state.

For summits we publish the official USGS figure and check it against 3DEP at the GNIS point. We’d drop any that differs by more than 30 m (98 ft), the same threshold as in Spain; none does. The largest gap is Denali’s (−25 m, because in Alaska 3DEP is a 5-meter model that rounds off the summit); all others are within 8 m. The USGS table is largely referenced to the NGVD29 datum and 3DEP to NAVD88: in the West they differ by 1–2 m. Three high points have no page because GNIS has no point for them: Connecticut’s (on the south slope of Mount Frissell, whose summit is in Massachusetts), Delaware’s (Ebright Azimuth) and Oklahoma’s (Black Mesa, which spans three states and whose GNIS point is in Colorado). Their state page gives the table’s elevation and explains why.

Each page is compared with its group: capitals with the 50, cities over 250,000 with the 91, cities of 100,000 to 250,000 with the 249 and summits with the 50 state high points; distances are in a straight line. Pages of cities that have distance pages link to them under “Distances from…”. UTM uses NAD83 (GRS80 ellipsoid), with the same Krüger series as for Spain. Summit names are today’s official GNIS names (Black Elk Peak since 2016, Kuwohi since 2024), with the former name as an alternate; Denali goes by that name on its page, which explains that its federal name has been Mount McKinley since 2025.

Known limits

• A city’s elevation is the elevation of one point: the city rises and falls from one neighborhood to another. New Orleans gives 0 ft at its reference point, and its page says “at sea level”.

Make maps: coloring, drawing, pins, data maps and viewers

Sources

• Outlines: US states and counties and ZIP Code Tabulation Areas from the U.S. Census Bureau (public domain), countries from Natural Earth 1:10m and Spain’s provinces and regions from its national mapping agency (IGN, CC BY 4.0), all simplified. Sample figures from Census estimates.
• Addresses in a list or table: Photon (with OpenStreetMap data), and CartoCiudad (IGN) for Spain.
• Areas in the true size map: the World Bank (with the ±10% rule described under population), the Census 2025 Gazetteer and the IGN.

How it’s calculated

Everything happens in your browser: what you color, draw or pin, and the files you open in the viewers, are never sent anywhere. Only the addresses you ask us to look up leave your device. The viewers read KML, KMZ, GeoJSON and GPX; if a GeoJSON file is in meters in another system (UTM, for example), they convert it to latitude and longitude with the same formulas as the coordinate converter. Lengths and areas of what you draw or open are measured on the WGS84 ellipsoid with GeographicLib. Icons packed inside a KMZ are read from the file itself, downscaled to 64 px and drawn at 32 px times the KML scale, like Google Earth, with their tint, rotation and anchor point (hotSpot). When you save back to KMZ, the images go back inside.

In data maps, numeric colors use five classes with roughly the same number of items each (quantiles) and rounded breaks; categories get one color for each of the nine most common. The color-blind-safe palette is Okabe and Ito’s.

True size. The Mercator map enlarges everything 1/cos(latitude) times in both directions: twice as big at 60°. When you move a country, we redraw it point by point at the scale of its new latitude, so its real area never changes.

Known limits

• Simplified outlines lose islets and inlets: for official work, use the original files.
• A misspelled or ambiguous address can land in the wrong place: check the points on the map.
• Icons that point to the internet (almost always the case with Google Earth and Google My Maps) show up as circles in their color until you press “Load icons”: opening a file never makes requests to third parties without you knowing. When you load them, your browser requests them without cookies or referrer; sites that don’t allow that (My Maps icons, on gstatic.com) stay as circles. Icons in a standalone KML that point to files not included with it also show as circles, with a notice.

Photo locations

Sources

• The data stored in each photo, read according to Exif 3.0 (CIPA DC-008-2023), JPEG (ITU-T T.81), HEIF (ISO/IEC 23008-12), PNG (W3C, Third Edition), the WebP container (RFC 9649) and XMP (ISO 16684-1).
• Time zones, to convert to UTC the time of photos that don’t store their offset: the same boundaries as in the time zone tools (timezone-boundary-builder, ODbL).

How it’s calculated

Everything happens in your browser, with no third-party libraries: photos aren’t uploaded anywhere. The tool reads the EXIF data of JPEGs (the APP1 segment), HEIC, HEIF and AVIF files (the “Exif” item in the “meta” box), PNGs (the eXIf chunk), WebPs (the EXIF chunk) and TIFF and DNG files, plus the XMP when it carries the location. Latitude and longitude come as degrees, minutes and seconds (rationals) with the hemisphere letter and are converted to decimal degrees without rounding. It also reads the elevation (above or below sea level), the camera direction (relative to true or magnetic north), the estimated horizontal error, the GPS time in UTC, the photo’s date and offset, the camera, the lens and the orientation. Coordinates of 0, 0 are treated as an empty location.

Only JPEGs are edited, and the image is never recompressed: the EXIF segment is rebuilt (and the XMP, if it holds GPS data) and everything else is copied byte for byte, including whatever follows the image (extra MPF images or the video of motion photos). Nothing moves inside the EXIF either: the new GPS block is appended and the old one is overwritten with zeros, because maker notes point to fixed positions. If the photo had no GPS, the main directory is copied to the end with the new entry. Seconds are written to a ten-thousandth (about 3 mm or 1/8 in). Changing the location keeps the GPS time and the direction; the elevation and estimated error are removed. “Remove all metadata” keeps only the orientation, the color profile (ICC) and the JFIF, Adobe and MPF segments needed to display the image correctly.

In KML and GPX files, times are in UTC: using the photo’s offset if it has one; otherwise, the GPS time; and otherwise, the time zone at the photo’s location on that date. The tests read photos written with macOS ImageIO and with Pillow, add and remove locations while checking that the image comes out identical byte for byte, and read the result back with Pillow.

Known limits

• HEIC, PNG, WebP, AVIF, TIFF and DNG files are read-only. To edit them, convert them to JPEG first.
• A photo with no location can’t be placed: the tool doesn’t guess the spot from what’s in the picture.
• On phones, the system photo picker can strip the location before passing the photo to the browser.
• “Remove location” doesn’t erase place names (city, country) that some apps write in the IPTC or XMP data: use “Remove all metadata” for that.
• HEIC thumbnails only show in Safari, which can open them; other browsers show an icon unless the EXIF has its own thumbnail.
• If a photo’s EXIF already fills almost the 64 KB its segment allows, the new location may not fit: the tool tells you and leaves it untouched.

Sun and moon

Sources

• Sun and moon positions, phases and eclipses: Astronomy Engine 2.1.19 by Don Cross (MIT license), with the VSOP87 models for the sun and an abridged ELP model for the moon. It’s accurate to one arcminute.
• Local time at each place: time zone boundaries and the IANA time zone database (see Time zones).
• To check it: tables from the U.S. Naval Observatory (USNO), Spain’s national astronomical observatory (OAN) and NASA’s eclipse catalogs (F. Espenak).

How it’s calculated

Sunrise and sunset. The moment the sun’s upper edge touches a sea-level horizon, allowing for 34′ of refraction and its apparent radius: the same definition the USNO uses. Civil, nautical and astronomical twilight start and end with the sun’s center at −6°, −12° and −18°. Golden hour runs from +6° to −4° and blue hour from −4° to −6°. Everything is worked out for the day from midnight to midnight in local time.

Sun and moon position. Azimuth and apparent elevation, with average refraction; for the moon, also from your exact spot (its parallax). An object’s shadow is its height divided by the tangent of the sun’s elevation, on flat ground. The moon’s illumination comes from Sun–Earth–Moon geometry. In the calendar, a supermoon is a full moon less than 360,000 km away, and a blue moon is the second full moon in a calendar month.

Day and night map. Night is drawn from the point where the sun is straight overhead: caps around the opposite point for sun elevations of −0.83° (sunrise and sunset), −6°, −12° and −18°. In live mode it updates once a minute and pauses when the tab is hidden.

Accuracy

Against 4,878 USNO sunrise and sunset times for 2026 in seven places, 1,460 for 1900 and 2100, 1,460 OAN times, 3,816 twilight times and 1,409 moonrise and moonset times, we’re never more than one minute off. All 50 moon phases of 2026 match the USNO to within a minute, and the four eclipses of 2026 match NASA: peak time within 1–4 seconds and each stage’s duration within 1.1 minutes. The sun’s position is within 0.16′ of USNO celestial navigation data, and the edge of night on the map within 0.3 km.

Known limits

• The horizon is a sea-level one: mountains and buildings aren’t included. Behind a ridge, the sun rises later and sets earlier.
• Refraction changes with temperature and pressure, and can shift the real sunrise and sunset by a minute or two.

Time zones

Sources

• Time zone boundaries: timezone-boundary-builder 2026e by Evan Siroky, the variant with oceans and full IANA names (America/Denver, America/Phoenix, America/Indiana/Indianapolis). They come from OpenStreetMap and carry its license, the ODbL (© OpenStreetMap contributors). The simplified boundaries the site downloads, in the /datos/husos/ folder, are offered under the same license.
• Times, UTC offsets and daylight saving changes: the IANA time zone database built into your own browser.

How it’s calculated

The boundaries are simplified to 50 m and split into 430 tiles: to find a point’s zone, your browser downloads only its tile (a few KB) and looks it up in under a millisecond. The time, the UTC offset and the dates of clock changes aren’t stored in any table of ours: your browser computes them with the IANA database. The world map uses the same boundaries simplified to 3 km, and the US and Europe maps, to 400 m.

States split between two zones are found by checking a point every 0.015° inside each Census county, leaving out a 1.5 km strip along the edge. The meeting planner counts working hours Monday to Friday, and handles the 23- and 25-hour days when clocks change.

To convert an exact time from one place to others (in the time zone converter and in the time difference calculator), we find the instant when the first place reads that date and time, trying the offsets half a day before and half a day after, and then each place’s time at that instant. If neither offset gives that clock time, it’s the hour skipped when clocks spring forward (you get the time just after the jump, which is what clocks will read); if both do, it’s the hour that happens twice when clocks fall back (you get the first one, with a warning). The 12- or 24-hour clock follows the language unless you pick the other one: the choice is saved in your browser, never on a server.

Accuracy

Against the original boundaries, with 20,000 test points near borders, the ones that land in the wrong zone are at most 46 m from the line. Times are only as good as your browser’s database: if a country changes its clocks at short notice, an out-of-date browser may lag behind.

Known limits

• In Xinjiang and some disputed territories (Abkhazia, the West Bank, Aksai Chin…) two times are used side by side. We give the official one and the page mentions the other.
• The US map leaves out the Aleutian Islands west of the 180th meridian.

Map lines

Sources

• Countries, lakes, seas, populated places and the date line: Natural Earth 1:10m, version 5.1.2 (public domain).
• Towns near the prime meridian and places on each side of the date line: GeoNames cities1000 (CC BY 4.0).

How it’s calculated

The latitude of the tropics and polar circles depends on the tilt of Earth’s axis. We compute it for January 1 of the current year (when the page is built and, on the map, in your browser) with the IAU 2006 formula for the mean obliquity of the ecliptic (Capitaine et al. 2003; IERS Conventions 2010), leaving out nutation, which moves it by ±9.2″ (about 280 m). The tilt shrinks by about 0.47″ a year, so the lines shift 14–15 m every year. Crossings, distances and the area of the polar caps were calculated with the latitude on January 1, 2026: the gap grows by about 15 m a year, far below the accuracy of the crossings.

Crossings come from cutting each line against the unsimplified Natural Earth polygons, and lengths and distances are measured on the WGS84 ellipsoid with GeographicLib. A line counts as passing through a country’s waters when it comes within 12 nautical miles of its coast (territorial waters) plus a 3 km margin, because those miles are measured from the baseline, not the shoreline.

Accuracy

Natural Earth borders can be a few hundred meters off and some islets are missing, so entry and exit points are good to about a kilometer. Each line’s list of countries matches the reference sources.

Known limits

• The International Date Line has no legal definition: its course at sea is approximate.
• With Natural Earth outlines, the Arctic Circle barely touches Grímsey, and Mirny Station in Antarctica falls 1.3 km south of the Antarctic Circle (other sources put it north).
• Natural Earth lacks Rolas islet, where the equator crosses São Tomé and Príncipe, so the country shows up “through its waters”.

Bearings, horizon and other whole-Earth math

Sources

• Magnetic declination: the World Magnetic Model WMM2025 from NOAA (NCEI) and the British Geological Survey (public domain), valid 2025–2030, with the coefficients from its official file.
• Earth’s layers and density: the Preliminary Reference Earth Model (PREM; Dziewonski and Anderson, 1981).
• Land or sea and countries: Natural Earth 1:10m; Census states and Spain’s IGN provinces for random points. Ground elevation: AWS Terrain Tiles, and the IGN MDT05 model in Spain.

How it’s calculated

Bearings. Start and arrival bearings of the shortest route are computed on the WGS84 ellipsoid with GeographicLib; the rhumb line (constant bearing) uses the isometric latitude and the exact meridian arc. Declination comes from WMM2025: a degree-12 spherical harmonic sum with the yearly change up to the chosen date. Magnetic bearing = true bearing − declination (east declination is positive).

Horizon. A sphere of 6,371 km. The distance to the horizon over the ground is R′·acos(R′/(R′+h)), and the part of a distant object hidden by the curve is R′(1/cos((D−d)/R′)−1). Refraction uses an effective radius R′ = R/(1−k) with the standard coefficient k = 0.13 used in surveying; near the ground it can range from −4 to +16 (Hirt et al., 2010).

Antipode and tunnel. The antipode of (φ, λ) is (−φ, λ±180°), which is exact. Land or sea is tested against Natural Earth countries, with a 1 km coastal margin. The figure on the page (13.1% of land has land at its antipode, ±0.03%) comes from a grid of 20 million evenly spaced points. The tunnel is the chord between the two points: its length, depth and dip are plain geometry; the layers it crosses and the frictionless fall time come from PREM. Through the center it takes 38 min 11 s, matching Klotz (2015); with uniform density, 42 min 10 s for any tunnel.

Random location. Uniform on the sphere: longitude 360u − 180 and latitude asin(2v − 1), so every square mile is equally likely (picking latitude evenly would crowd the poles). Inside a country, state or province, points are drawn in its bounding box until one falls inside.

Geographic center. Three centers on the sphere: the center of gravity (the mean of 3D vectors, weighted if you add weights), the point of least total distance (the geometric median, by Weiszfeld’s method) and the simple average of latitudes and longitudes, shown so you can see how it fails. An area’s center is its spherical centroid, from the exact first-moment formula of a spherical polygon.

Accuracy

Our WMM2025 code matches the official test values: the 12 points of the technical report’s table to the published rounding, and the 100 points of the long table to within 0.001 nT. The model itself has a global average declination error of 0.36° in 2025 (0.40° in 2030). The tunnel and horizon use a sphere: against the ellipsoid, the tunnel’s length changes by 0.6% at most.

Known limits

• Near the magnetic poles a compass can’t be trusted: we warn when the horizontal field drops below 6,000 nT (caution) and 2,000 nT (blackout). Nearby iron, cars or magnetic rocks also pull the needle.
• The horizon ignores any terrain in between, and real refraction changes day to day.
• There’s no single accepted definition of a geographic center (as the USGS points out): the result depends on the method and the outlines used.

National parks and map embeds

Sources

• US national parks: boundaries from the National Park Service Land Resources Division (public domain), official areas from the NPS Listing of Acreage of September 30, 2026 (gross acres), and the date each park was established from the NPS’s official index (The National Parks: Index 2012–2016) and its Recent Changes to the National Park System page (updated October 26, 2026), checked against the laws.
• Driving distance and time: OSRM on the FOSSGIS server, with OpenStreetMap data.

How it’s calculated

We measure the shortest geodesic on the WGS84 ellipsoid (GeographicLib) from your point to the nearest point of each park boundary (zero if you’re inside) and to a point inside the park. On request, OSRM routes to the road closest to that boundary point, assuming clear roads, for the 15 nearest parks you can drive to. Parks with no road access (from each park’s NPS directions page) and parks on other islands are flagged instead of routed.

Google Maps embed code. The code is built in your browser in one of three forms: the maps.google.com/maps?…&output=embed address, widely used though not in Google’s documentation; Google’s Maps Embed API with your own key, which never leaves your browser; or the OpenStreetMap embed, with its box worked out from the zoom and size. Nothing loads from Google or OpenStreetMap until you ask for the preview.

Accuracy

Park boundaries are simplified to 200 m, so the distance to a boundary can be off by about 200 m.

Meet in the middle, thematic maps, widgets and posters

Sources

• Travel times for meeting points: OSRM on the FOSSGIS public server, with OpenStreetMap data (ODbL). Places to meet (cafés, restaurants, parks, towns…): OpenStreetMap, read from the same OpenFreeMap tiles that draw the map.
• US thematic maps: median household income and median age from the American Community Survey 2020–2024 5-year estimates (tables B19013 and B01002), with their 90% margins of error, and population from the Census Vintage 2025 estimates (public domain).
• Spain thematic maps: mean net income per person and per household (2024) and mean age (people in private households on January 1, 2025) from INE’s Household Income Distribution Atlas (ADRH 2024, released October 19, 2026), and population from the municipal register as of January 1, 2025.
• Posters: OpenStreetMap data (ODbL) through OpenFreeMap vector tiles, with our own styles.

How it’s calculated

Meet in the middle. We try about 80 spots in two rounds: first a grid around the geodesic midpoint and along the line between people, then towns or places near the best one. For each spot OSRM gives the travel time from each person, and we pick the one with the smallest gap between the longest and shortest trip, as long as the longest trip is no more than 5% (or 2 minutes) over the shortest possible longest trip; if several have a similar gap, the one with the least total time wins. Times assume clear roads, with no traffic or public transit; bikes at about 9 mph and walking at about 3 mph.

Thematic maps. Each map sorts values into six classes by rounded quantiles on a light-to-dark green ramp. Counties and municipalities use the same simplified Census and IGN boundaries as the rest of the site’s maps.

Widgets. They use the same math as the full tools: the circle’s area on a sphere and distances on the WGS84 ellipsoid with GeographicLib. The distance widget gives the straight-line distance only. Blank-map widgets are pre-drawn SVGs from the printable blank maps.

Posters. To download one, a second, hidden map redraws the same framing at 300 DPI in pieces that line up to the pixel, and the tool itself writes a lossless PNG and PDF. On phones, A2 and 50 × 70 cm come out at a lower DPI to avoid running out of memory. Every poster carries the OpenStreetMap credit.

Known limits

• Meeting points take a few seconds: the public routing server handles one table of travel times about every 10 seconds.
• ACS figures are estimates with a margin of error, which is wide in small counties: the map shows it.

Places within a radius

Sources

• Places: OpenStreetMap (ODbL), queried live from the visitor’s browser through Overpass API on the server run by Private.coffee, an Austrian non-profit whose terms allow any project, commercial ones included, with no fixed rate limit. We don’t use the main overpass-api.de server, whose rules ask commercial sites to run their own instance or pay for one.
• Fallback when Overpass doesn’t respond: the “poi” layer of the same OpenFreeMap vector tiles that draw the map (OpenMapTiles schema, OpenStreetMap data).
• The 30 categories are OpenStreetMap tags (for example amenity=pharmacy, shop=supermarket, railway=station); public parking excludes access=private and access=no.

How it’s calculated

One Overpass QL query per search: a union with one nwr[tag](around:r,lat,lon) statement per tag of each category, then out count for the total and out tags center 2000 for up to 2,000 places with their tags and, for buildings and grounds, the center of their outline. Each query declares a 25-second time limit and 64 MiB of memory, small enough for the server to admit it sooner when it’s busy. A name or brand is matched as a regular expression that ignores capitals and accents, against name and brand; with no category, only against name, among places tagged amenity, shop, tourism, leisure, healthcare, office or craft, within 3 km at most. The name is checked only on the places already found in the circle (nwr.s[name~…]), so the server doesn’t compare it with every name in the world.

We measure each distance in the browser from the center to the place’s point with GeographicLib on the WGS84 ellipsoid, plus the initial bearing to 8 compass points, and drop anything farther than the radius (a large park can touch the circle with its center outside). When the total is over 2,000, we suggest the radius r′ = 0.9 · r · √(2,000 / N), rounded down to a handy value, assuming places are spread evenly.

Usage rules: one query at a time per page, at least one second apart, and only when the visitor presses “Find places” or opens a link with a search. After an HTTP 429 we wait 30 seconds before asking again. The browser waits up to 75 seconds, because a request can queue for 15 seconds before it starts. If the radius is 2 km or less, after 12 seconds without an answer the named places from the map tiles are shown in the meantime, without address, hours, website or phone (gyms aren’t in those tiles); the full list replaces them when it arrives, and if it never does, they stay.

Known limits

• OpenStreetMap is volunteer-made: completeness varies by country and by town, and details such as opening hours or phone numbers are often missing.
• Opening hours are shown as tagged; we don’t work out whether a place is open now, and OpenStreetMap has no pharmacy duty rotas.
• On November 1, 2026 the public Overpass servers were overloaded: small queries took 30 to 40 seconds or failed, and the Private.coffee server didn’t respond.

Towns within a radius (worldwide)

Sources

• Places: GeoNames cities500 (CC BY 4.0), downloaded November 1, 2026: every populated place with 500 people or more, plus the seats of administrative divisions down to the fourth level, with its name, country, first-level division, population, coordinates and feature code.
• Region names: GeoNames admin1CodesASCII. Spanish names of places and regions: GeoNames alternateNamesV2, Spanish only.

How it’s calculated

Preparation (data/pueblos-mundo/generar.py): we drop places that no longer exist (feature codes PPLH, PPLCH, PPLQ and PPLW) and duplicates, meaning the same name without accents in the same country less than 3 km apart, keeping the one with more people (130 removed). The Spanish name is kept when GeoNames marks it as preferred or, for cities of 100,000 or more and national capitals, when it’s the first non-abbreviated one; it’s dropped when it only strips accents or uses letters Spanish doesn’t have. Coordinates are rounded to 4 decimals (about 11 m). The result is 236,659 places.

Tiles: a quadtree over the square from −180° to 180°. It starts with 45° tiles and splits any tile with more than 2,400 places into four, down to 1.4° in the densest areas, which gives 272 files of 31 KB on median (109 KB at most, 3.9 MB in all with gzip). In the browser, the circle’s bounding box, taken from the same geodesic ring that’s drawn and covering every longitude when the circle goes around a pole, picks the tiles it overlaps, also shifted by ±360° so circles across the date line load both sides.

Each place in those tiles is first checked on the sphere with a 0.6% margin, more than the gap between sphere and ellipsoid, and then measured with GeographicLib on the WGS84 ellipsoid: distance and initial bearing, shown as 8 compass points. A place counts when its point is within the radius. The minimum population hides places with no figure; neighborhoods (PPLX) can be hidden too. The total adds up the listed places without neighborhoods, which are already part of their city; it isn’t the population of the area, which Population in a radius estimates. When the list includes places in Spain or the United States, the tool links to the Spanish and US tools, which use official figures.

Known limits

• GeoNames coverage and population years vary by country: some figures are recent estimates and others come from old censuses.
• About 30,500 seats have no population. They’re listed with a dash and drop out as soon as a minimum population is chosen.
• Each place is a single point: a big city counts by its center, and a town whose point is just outside the circle isn’t listed even if part of it is inside.
• Neighborhoods are listed only where GeoNames has them, which is often in Australia, Canada and large cities, and rarely elsewhere.
• Only about 700 places and 900 regions have a Spanish name; the rest keep the GeoNames name.

Terrain Tiles attribution

Terrain Tiles provide elevation outside Spain (on profiles too) and the map’s hillshading. They were produced by Mapzen with its open-source Joerd software and are now published in the Amazon Web Services open data registry. They combine elevation models from many countries, and several of those licenses require showing this attribution list. Here it is, word for word:

Terrain Tiles sources, the area they cover and their license

Sources and licenses

Every data source and third-party program All Map Tools uses, with its license and the date or version of the data. Each name links to the source.

Data sources and software All Map Tools uses, with their licenses

How to cite us

If you use a number from All Map Tools in a paper, a class or an article, cite the tool and the date, for example: “All Map Tools, Distance between two points, allmaptools.com, accessed November 1, 2026.” Please also credit the original source named in each section, such as “U.S. Census Bureau,” “Data: IGN (CC BY 4.0)” or “© OpenStreetMap contributors.”

Something doesn’t add up? Let us know and we’ll look into it. Changes are logged on the Corrections page.

This page was last reviewed on November 1, 2026.