Miles per degree calculator

Worked example: Denver at 39.739° N

At Denver's latitude the ellipsoid's prime vertical radius of curvature is N = 6,386,880 m. The parallel through Denver is a circle of radius N × cos(39.739°), so one degree along it is 85,718.1 m, or 53.263 miles.

North-south, the meridional radius of curvature is M = 6,361,529 m, and one degree of latitude centered on Denver is 111,029.6 m, or 68.991 miles. A 1 degree by 1 degree block of land there is therefore about 69.0 by 53.3 miles.

Why longitude shrinks and latitude does not

Lines of longitude (meridians) meet at the poles. The distance between two meridians one degree apart is widest at the equator and falls to zero at the pole, in proportion to the cosine of the latitude. Lines of latitude (parallels) stay evenly spaced, so a degree of latitude is nearly the same length everywhere.

The ellipsoid correction

The Earth bulges at the equator. WGS84, the datum GPS uses, models it as an ellipsoid with a semi-major axis of 6,378,137 m and a flattening of 1/298.257223563. Two radii of curvature follow from those constants. The meridional radius M sets the length of a degree of latitude. The prime vertical radius N sets the length of a degree of longitude.

Because the surface is flatter near the poles, M grows with latitude, and so does a degree of latitude: from 110.574 km at the equator to 111.694 km at the pole. The calculator integrates M across the degree rather than evaluating it once, and uses N × cos(latitude) for longitude.

M = a(1 − e²) / (1 − e² sin²φ)^(3/2)
N = a / √(1 − e² sin²φ)
1° longitude = (π/180) · N · cos φ
e² = f(2 − f),  a = 6,378,137 m,  1/f = 298.257223563

What decimal places mean on the ground

The precision table under the chart turns digits into distance. At 40° north, the fourth decimal place of latitude is about 11.1 m and the fifth about 1.1 m. Six decimals resolve about 11.1 cm.

The comparison rows in the readout use a sphere of radius 6,371.0088 km, the model the distance tools on this site use. The gap between sphere and ellipsoid is a fraction of a percent, which the readout lets you check at any latitude.

Minutes, seconds, and nautical miles

A degree splits into 60 minutes and each minute into 60 seconds. One minute of latitude is close to one nautical mile, which is how the nautical mile was first defined; it is now fixed at exactly 1,852 meters. At 45° north one minute of latitude is 1,852.2 meters and one second is 30.9 meters.

To turn a latitude difference into miles, multiply the degrees by the length of a degree at the middle latitude. For a longitude difference, use the longitude length at that latitude instead. For anything longer than a few degrees, or crossing a wide range of latitudes, use a great-circle distance rather than this shortcut.