Distance Between Coordinates

In short The great-circle distance is the shortest path between two points over the surface of the earth, and it is what the haversine formula computes. Two results that come with it surprise people. First, the initial and final bearings are different: a great circle is not a straight line on a flat map, so its compass heading changes continuously along the route. London to New York leaves on a bearing of 288° and arrives on one of 231° — a swing of 57° with no turn made — which is why long-haul flight paths look curved on a Mercator map. They are not detours; they are the straight line, and the projection is what is bending. Holding a single compass heading the whole way instead is a rhumb line, which is simpler to steer and measurably longer. Second, the midpoint is NOT the average of the two latitudes and longitudes. Averaging is wrong by tens of kilometres over long distances and fails outright across the antimeridian, where averaging 170° and −170° gives 0° — a point on the opposite side of the planet from the correct answer of 180°. The model here is a sphere of radius 6,371.0 km. On the WGS84 ellipsoid the answer differs by up to about 0.5%, which matters for surveying and not for anything else. And this is surface distance rather than travel distance: no road, flight corridor or terrain is involved, so it is a lower bound on any real journey.