Great Circle Distance Calculator
On a Mercator chart the straight line is the long one.
Work out Great Circle Distance. On a Mercator chart the straight line is the long one. Counts the thing everyone forgets to count.
Great circle distance
5,540 km
2,991.4 nm · 3,442.4 miles · initial bearing 287.9°
A great circle is the shortest path over a sphere; a rhumb line holds a constant bearing and is always at least as long. On a Mercator chart the rhumb line is the straight one, which is exactly backwards from what the eye expects. The great circle bearing changes continuously along the route — that is why the initial and final bearings differ, sometimes by tens of degrees on a long flight. Following a single bearing means flying a rhumb line by definition. Haversine on a sphere is accurate to about 0.3% against the real ellipsoid. That is a few kilometres on a transatlantic route: fine for planning, not for surveying, where Vincenty's method on the ellipsoid is used instead.
How the Great Circle Distance Calculator works
Great circle and rhumb line distance between two coordinates, with initial and final bearings, the midpoint, the highest latitude reached, and how much the shorter route actually saves.
Also known as: distance between two coordinates · haversine distance calculator · why do flights go over the pole · great circle versus rhumb line
Frequently asked questions
What is a great circle?
The shortest path between two points on a sphere — the intersection of the sphere with a plane through its centre. On a globe it looks straight; on a Mercator chart it looks curved.
What is a rhumb line?
A path of constant bearing. It is straight on a Mercator chart and always at least as long as the great circle, which is exactly backwards from what the eye expects.
Why does the bearing change along a great circle?
Because the meridians converge. Following a single bearing means flying a rhumb line by definition, which is why the initial and final bearings can differ by tens of degrees.
How accurate is the haversine formula?
About 0.3% against the real ellipsoid, since it assumes a sphere. That is a few kilometres transatlantic — fine for planning, not for surveying, where Vincenty's method is used.
Why do flights go near the pole?
Because that is the short way. London to Tokyo over the Arctic is several hundred kilometres shorter than the route across Asia that a flat map makes look direct.
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