<Dl> <Dd> d = r Δ σ . (\ displaystyle d = r \ Delta \ sigma .) </Dd> </Dl> <Dd> d = r Δ σ . (\ displaystyle d = r \ Delta \ sigma .) </Dd> <P> The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial radius a (\ displaystyle a) of 6378.137 km; distance b (\ displaystyle b) from the center of the spheroid to each pole is 6356.752 km . When calculating the length of a short north - south line at the equator, the circle that best approximates that line has a radius of b 2 / a (\ displaystyle b ^ (2) / a) (which equals the meridian's semi-latus rectum), or 6335.439 km, while the spheroid at the poles is best approximated by a sphere of radius a 2 / b (\ displaystyle a ^ (2) / b), or 6399.594 km, a 1% difference . So long as a spherical Earth is assumed, any single formula for distance on the Earth is only guaranteed correct within 0.5% (though better accuracy is possible if the formula is only intended to apply to a limited area). A good choice for the radius is the mean earth radius, R 1 = 1 3 (2 a + b) ≈ 6371 k m (\ displaystyle R_ (1) = (\ frac (1) (3)) (2a + b) \ approx 6371 \, \ mathrm (km)) (for the WGS84 ellipsoid); in the limit of small flattening, this choice minimizes the mean square relative error in the estimates for distance . </P>

The distance from around the earth along a given latitude can be found using the formula