Click two points on the map to draw a route.Tap two points on the map to draw a route.
Between two points on the globe you can draw two important lines. The great-circle route is the shortest path, while the rhumb line maintains a constant bearing relative to geographic north. Below we explain the difference and compare both lines on example routes.
A great-circle route follows the shorter arc of a circle whose centre is the centre of the sphere. It is the shortest path between two points on that surface. Its bearing relative to geographic north changes along the way, except on routes along the equator or a meridian.
A rhumb line maintains a constant angle to geographic north. This does not mean a fixed magnetic compass reading, because the difference between magnetic and geographic north varies with location. On a Mercator map the rhumb line is straight. Except along the equator or a meridian, it is longer than the great-circle route.
The smallest difference in this set is on Santiago → Beijing (2.9%), and the largest on Reykjavík → Anchorage (20.5%). The size of the difference depends on both endpoints and the route direction, not just distance from the equator.
| Route | Great circle | Rhumb line | Difference |
|---|---|---|---|
| Warsaw → New York | 6,854 km | 7,349 km | 495 km (7.2%) |
| London → Tokyo | 9,558 km | 11,295 km | 1,737 km (18.2%) |
| Los Angeles → London | 8,755 km | 9,733 km | 978 km (11.2%) |
| Santiago → Beijing | 19,061 km | 19,605 km | 544 km (2.9%) |
| Sydney → Santiago | 11,346 km | 12,783 km | 1,437 km (12.7%) |
| Reykjavík → Anchorage | 5,418 km | 6,531 km | 1,113 km (20.5%) |
Calculated on a sphere with a radius of 6,371 km, as in the tool above. Real flight paths depart from the great circle because of winds, air corridors and regulations.
On a Mercator map the great-circle route between Warsaw and New York bends north and can look like a detour. In the spherical model, however, it is the shortest path over the surface. An actual plane may follow a different route because of wind, weather, available airspace and air traffic control requirements. The appearance of an arc alone is not enough to judge the distance or flight time.
It is never longer. Both lines have the same length only on routes along the equator or a meridian. In every other case the great circle is shorter.
Because a constant bearing relative to geographic north was enough on each leg. On long voyages navigators split the great-circle route into shorter legs and sailed a rhumb line on each, combining the strengths of both lines.
The great-circle length uses the haversine formula and the rhumb-line length follows its path on the Mercator map, both on a sphere with a radius of 6,371 km. On the Earth's ellipsoid the results would usually differ by less than 1%.
