Page "Great-circle distance" Paragraph 28

The shape of the Earth closely resembles a flattened sphere ( a spheroid ) with equatorial radius of 6, 378. 137 km ; distance 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 sphere that best approximates that part of the spheroid has a radius of, or 6, 335. 439 km, while the spheroid at the poles is best approximated by a sphere of radius, or 6, 399. 594 km, a 1 % difference.

So as long as we're assuming a spherical Earth, any single formula for distance on the Earth is only guaranteed correct within 0. 5 % ( though we can do better if our formula is only intended to apply to a limited area ).