Between two points on the globe you can draw two important lines. The great circle is the shortest path, while the rhumb line lets a ship or plane keep one constant compass bearing. Below we explain the difference and compare both lines on example routes.
A great-circle route follows part of a circle whose center is the center of the Earth. It is the shortest path between two points on the surface of a sphere. Its compass bearing, however, changes along the way, except on routes along the equator or a meridian.
A rhumb line crosses every meridian at the same angle, so you only need to hold one compass bearing. On the Mercator map it is a straight line, which made marine navigation easier for centuries. Except along the equator or a meridian, it is longer than the great circle.
The smallest difference in this set is on Santiago → Beijing (2.9%), and the largest on Reykjavík → Anchorage (20.5%). The difference grows when a route is long and runs far 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 the Mercator map the great circle between Europe and North America bends towards the pole and looks like a detour. In reality it is the shortest path, which is why many transatlantic and transpacific routes pass over Greenland, Canada or Alaska. The arc comes from the map's distortion, not from a longer route.
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 one constant bearing was enough. On long voyages navigators split the great circle 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%.
