How accurate is measuring distance on a map?

Three ways to measure, three levels of accuracy

There are three common ways a map tool can turn two clicked points into a distance. The first is to measure the straight line between them on the flat map, in projected map units. The second is to treat the Earth as a perfect sphere and use the great-circle formula, often called haversine. The third is to solve the geodesic problem on the ellipsoid that GPS uses, WGS84, which is slightly flattened at the poles. Only the third gives the true shortest distance over the Earth's surface.

The difference is easy to see with a real example. The straight-line distance from central Copenhagen to central Aalborg in Denmark is 223.85 km on the ellipsoid. The sphere formula gives 223.29 km, about 550 metres short. A ruler on a Web Mercator map, using the projection's own metres, gives 403.6 km, almost twice the real distance.

Why a flat web map exaggerates distances

Web Mercator, the projection used by nearly all online maps, enlarges everything by a factor that depends on latitude: 1 at the equator, about 1.4 at 45 degrees, 2 at 60 degrees and 3.9 at 75 degrees. That is why Greenland looks as big as Africa on a web map, although Africa is about 14 times larger. A measuring tool that ignores this factor will report distances that are too long everywhere except near the equator.

Well-made map tools correct for the scale factor, but a correction at a single latitude is still wrong for long north-south lines, which cross many latitudes. Calculating on the Earth itself avoids the problem completely.

How wrong is the sphere formula?

The Earth's radius is about 21 km larger at the equator than at the poles. A sphere cannot match that shape everywhere, so the haversine formula, with the usual mean radius of 6,371 km, is a little off. Along the equator it gives 1,111.95 km for 10 degrees of longitude instead of the true 1,113.20 km, a 0.1 percent error. Along a meridian near the equator it gives 1,111.95 km for 10 degrees of latitude instead of 1,105.86 km, an error of 0.55 percent. For New York JFK to London Heathrow it gives 5,540 km instead of 5,555 km.

For a rough idea of how far apart two cities are, 0.5 percent does not matter. For property boundaries, survey checks, flight planning or anything that is compared with official figures, it does. GeoDrafter's distance calculator uses GeographicLib, which solves the ellipsoid problem to within a few nanometres for any pair of points, including points on opposite sides of the Earth.

What limits your measurement in practice

Once the calculation is exact, the accuracy depends on the points you put in. A click on a map is as precise as one screen pixel. Zoomed out to show a whole region, a pixel covers a hundred metres or more; zoomed in to street level, it covers less than a metre. Zoom in before you place important points, and drag points to adjust them. If you have coordinates from a GPS or a survey, paste them instead of clicking.

The background map has its own errors too. OpenStreetMap and aerial imagery are usually within a few metres in towns, but can be off by ten metres or more in remote areas. Consumer GPS positions are typically within 3 to 10 metres under open sky and worse between tall buildings or under trees.

Finally, a distance on a map is a horizontal distance. Walking up and down a hill is longer than the map distance; on a 10 percent slope the difference is only 0.5 percent, but on steep mountain paths it adds up. Use the elevation finder to check the heights along the way.