Great circle distance and bearings between any two positions, with the rhumb line alongside so you can see what the shorter track actually saves. Paste positions in decimal degrees, degrees and decimal minutes, or degrees, minutes and seconds. Add waypoints to build a multi-leg passage, and take the route away as a GPX file.
Enter positions in any common format — 51 55.4 N, 51°55'21"N or 51.9225. Add waypoints to build a multi-leg passage.
Distance between positions on a sphere, not a sailing distance: it takes no account of land, traffic separation, canals or ice. Ellipsoidal (Vincenty) calculation differs by up to about half a per cent on long passages.
Why the shortest route looks like a curve
A Mercator chart stretches the higher latitudes so that a course of constant heading draws as a straight line. That is what makes it the chart you steer on. The price is that the genuinely shortest path over the earth — the great circle — appears as a curve bowing towards the nearer pole. The straight line you rule on the chart is the rhumb line, and it is longer.
How much longer depends on the passage. North-south, or over a short distance, the difference is negligible. On a high-latitude ocean crossing it is substantial: Yokohama to San Francisco is about 4,487 nautical miles on the great circle against 4,730 on the rhumb line, a saving of roughly 243 miles. At twelve knots that is the better part of a day.
Why the bearing keeps changing
A great circle crosses every meridian at a different angle, so the heading changes continuously along the track. That is why a great circle cannot be steered as one course. In practice it is broken into a series of rhumb line legs between waypoints, each steered on a constant heading, with the track stepping along the great circle. Adding waypoints in the calculator above builds exactly that, and gives the initial and final bearing for each leg.
Coordinate formats
All of these read correctly, with or without symbols, and the hemisphere letter can go before or after the figures: 51.9225, 51 55.35 N, 51°55'21"N, N51 55.35. A negative number is taken as south or west. The position as understood is echoed under each waypoint, so a mistyped hemisphere is obvious before it reaches the arithmetic.
What this does not do
It gives the distance between positions on a sphere. It knows nothing about land, traffic separation schemes, canals, ice or weather routeing, so a port-to-port figure will be short wherever the direct path crosses a continent. Use it for ocean legs and for checking a passage plan, not as a substitute for one.
Distances use the navigational convention that one minute of arc is one nautical mile, so one degree of longitude on the equator reads exactly 60.0 miles. A full ellipsoidal calculation differs by up to about half a per cent on a long passage.
From distance to arrival time
Once you have the distance, the voyage and ETA calculator turns it into an arrival time, or tells you the speed needed to make a laycan — the button in the results carries the total across. From there the fuel consumption calculator gives the bunkers and the carbon dioxide for the passage.
Great circle calculator FAQs
Why is the great circle shorter than a straight line on a chart?
A Mercator chart stretches the higher latitudes so that a course of constant heading draws as a straight line, which is what makes it so useful for steering. The price is that the shortest path on the globe — the great circle — appears as a curve bowing towards the nearer pole. The straight line you draw on the chart is the rhumb line, and on an east-west passage in high latitudes it can be materially longer.
How much distance does a great circle actually save?
It depends entirely on the latitude and the east-west extent of the passage. On a short leg, or one running mainly north-south, the saving is negligible. On a high-latitude ocean crossing it can be hundreds of miles — Yokohama to San Francisco saves in the order of 240 nautical miles. This calculator shows both distances side by side so the difference is visible before you commit to a track.
Why does the initial bearing differ from the final bearing?
On a great circle the track crosses each meridian at a different angle, so the heading changes continuously along the route. That is precisely why a great circle cannot be steered as a single course: in practice it is broken into a series of rhumb line legs between waypoints, each steered on a constant heading, which is what the waypoint list here lets you build.
What coordinate formats can I paste in?
Decimal degrees such as 51.9225, degrees and decimal minutes such as 51 55.35 N, and degrees, minutes and seconds such as 51°55'21"N are all read correctly, with or without symbols, and the hemisphere letter can come before or after the figures. A negative number is treated as south or west.
Is this the distance my ship will actually steam?
No. It is the distance between positions on a sphere. It takes no account of land, traffic separation schemes, canals, ice or weather routeing, so a port-to-port figure from it will be short wherever the direct path crosses a continent. Use it for ocean legs and for checking a passage plan, not as a substitute for one. It also assumes a sphere: an ellipsoidal calculation differs by up to about half a per cent on a long passage.
Part of the marine engineering calculators on this site.