How many miles are in a degree?

Degree lengths every 5 degrees

Computed on the WGS84 ellipsoid. Latitude values are the length of the degree centered on the listed latitude.

Why longitude shrinks with the cosine

Meridians meet at the poles. The parallel at latitude φ is a circle whose radius is the Earth's radius times cos φ, so its length, and the length of each of its 360 degrees, scales with cos φ. At 60° the cosine is 0.5, and a degree of longitude is roughly half its equatorial length.

Why latitude grows toward the poles

On a perfect sphere every degree of latitude would be the same. The Earth is flattened, so the surface curves less near the poles, and one degree of arc covers more ground there: from 110.574 km at the equator to 111.694 km near the pole, a difference of 1.12 km.

Checking against the USGS figures

The US Geological Survey gives rule-of-thumb values at 38° north, the latitude of Stockton, California and Charlottesville, Virginia: one degree of latitude is about 69 miles, one minute about 1.15 miles and one second about 101 feet. One degree of longitude there is about 54.6 miles, one minute 0.91 mile and one second 80 feet.

The ellipsoid formula on this page gives 68.97 miles per degree of latitude and 54.58 miles per degree of longitude at 38°. Divide by 3,600 for seconds: 101 feet and 80 feet. Both match the USGS rounding.

Minutes and seconds of arc

A degree splits into 60 minutes, and a minute into 60 seconds. So a minute of latitude is about 1.15 miles and a second about 101 feet at 45°. A minute of latitude is close to one nautical mile, which is why sea charts measure distance along their side margins.

For longitude, multiply the equator value by the cosine of your latitude. The DMS conversion guide shows how to move between degrees, minutes and seconds and the decimal form that GPS apps use.

Worked example: a degree at every state capital

The capitals span from 21.3° to 58.3° north, so a degree of longitude ranges widely across them:

Using degree lengths for quick estimates

Degree lengths turn coordinate differences into distances without the full haversine formula. Near Denver, at 39.74° N, a step of 0.01° north is 1,110 meters and a step of 0.01° east is 857 meters. So a point 0.05° north and 0.05° east of the capitol is about 7.01 km away, by Pythagoras on the two ground distances.

The shortcut holds for a few tens of miles. Beyond that the degree length changes across the distance and the flat approximation drifts. Use the haversine formula for anything longer.

The range across the US

Across the contiguous states, from Austin at 30.3° to Olympia at 47.0°, a degree of longitude shrinks from 59.8 to 47.2 miles. Add Juneau and Honolulu and the range runs from 36.4 to 64.5 miles. That is why a map grid of equal degrees looks squashed in Alaska and nearly square in Hawaii.

Degrees, minutes and nautical miles

Sea and air navigation measure distance in nautical miles because a nautical mile is close to one minute of latitude. On this page's ellipsoid a minute of latitude runs from 1,843 meters at the equator to 1,862 meters near the pole, so a chart's latitude scale doubles as a distance scale. A minute of longitude is shorter everywhere except on the equator, so never measure distance off the top or bottom edge of a chart.