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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