Longitude - Length of A Degree of Longitude

Length of A Degree of Longitude

The length of a degree of longitude depends only on the radius of a circle of latitude. For a sphere of radius a the value of the radius at a latitude φ is acosφ and the length of arc for a one degree (or π/180 radians) increment is

\Delta^1_{\rm LONG}= \frac{\pi}{180}a \cos \phi. \,\!

When the Earth is modelled by an ellipsoid this result must be modified to

\Delta^1_{\rm LONG}= \frac{\pi a\cos\phi}{180(1 - e^2 \sin^2 \phi)^{1/2}}\,,

where e, the eccentricity of the ellipsoid, is related to the major and minor axes (the equatorial and polar radii respectively) by

0° 110.574 km 111.320 km
15° 110.649 km 107.551 km
30° 110.852 km 96.486 km
45° 111.132 km 78.847 km
60° 111.412 km 55.800 km
75° 111.618 km 28.902 km
90° 111.694 km 0.000 km
e^2=\frac{a^2-b^2}{a^2}.

Cos φ decreases from 1 at the equator to zero at the poles, so the length of a degree of longitude decreases likewise. This contrasts with the small (1%) increase in the length of a degree of latitude. The table shows values of both for the WGS84 ellipsoid, where a=6,378,137.0 m and b=6,356,752.3142 m. Note that the distance between two points 1 degree apart on the same circle of latitude, measured along that circle of latitude, is not the shortest (geodesic) distance between those points; the difference is less than 0.6 m. A calculator for any latitude is provided by the U.S. government's National Geospatial-Intelligence Agency (NGA).

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