Bearing & Midpoint Calculator
Find the initial and final great-circle bearings between two coordinates, the back bearing and the midpoint, with the compass point.
Bearings on a sphere change along the way
A bearing is the direction from one point to another, measured clockwise from true north in degrees: 0° is north, 90° east, 180° south and 270° west. On a small area map you can measure it with a protractor and it stays the same along the line. Over long distances it does not, because the shortest path is a great circle and a great circle crosses each meridian at a different angle. The initial bearing is the heading at the start; the final bearing is the heading on arrival. Only routes along a meridian or the equator keep a constant bearing.
A worked example
From central London (51.5074, −0.1278) to New York (40.7128, −74.0060), the initial bearing is 288.3°, west-north-west, even though New York is further south than London. Along the way the heading swings left, and the final bearing on arrival is 231.2°, south-west. The bearing back from New York to London is 51.2°, not 288.3° − 180° = 108.3°, which surprises people used to flat maps. The midpoint of the great circle is at 52.37° N, 41.29° W, further north than either city, in the North Atlantic south of Greenland. The great-circle distance on a sphere is 5,570 km.
Rhumb lines and compass headings
A path that keeps a constant compass bearing is a rhumb line, or loxodrome, which appears as a straight line on a Mercator chart. It is longer than the great circle except along meridians and the equator; for London to New York the difference is a few hundred kilometres. Sailors historically followed rhumb lines because they are easy to steer, breaking a great-circle route into several rhumb-line legs. For walking or hiking distances of a few kilometres, the difference between great-circle and rhumb-line bearings is a small fraction of a degree, smaller than you can steer with a hand compass.
True, grid and magnetic north
The bearings here are true bearings, relative to the geographic North Pole. A magnetic compass points to magnetic north, which differs by the local magnetic declination: in 2026 about 13° W in New York, roughly 1° E in London and over 15° E in Seattle, and it changes by up to a few tenths of a degree a year. To steer a true bearing with a compass, add an east declination or subtract a west one from the magnetic reading in the other direction, and check the current declination on an up-to-date map or a geomagnetic model. Grid north on a UTM map differs from true north by the grid convergence, up to a few degrees at a zone edge.
How to use it
- Enter the start point as A and the destination as B.
- Read the initial bearing and its compass point, the heading to set off on.
- Check the final bearing to see how much the heading turns on a long route.
- Convert to a magnetic bearing with the local declination before using a compass.
Questions from the map table
How do you calculate the bearing between two coordinates?
The initial bearing is atan2(sin Δλ × cos φ₂, cos φ₁ × sin φ₂ − sin φ₁ × cos φ₂ × cos Δλ), where φ is latitude and Δλ the difference in longitude, converted to degrees and normalised to 0–360°. From London to New York it gives 288.3°.
Why is the bearing back not 180° different?
Because on a great circle the direction changes along the path. The bearing from London to New York starts at 288.3°, but the bearing from New York back to London is 51.2°. The final bearing on arrival in New York is 231.2°, which is exactly 180° from 51.2°.
What is the difference between a great circle and a rhumb line?
A great circle is the shortest path between two points on the globe, with a heading that changes along the way. A rhumb line keeps a constant compass bearing and appears straight on a Mercator chart, but it is longer except along a meridian or the equator.
Do I need to correct the bearing for magnetic declination?
Yes, if you will follow it with a magnetic compass. The calculator gives true bearings. Magnetic north differs by the local declination, about 13° west in New York in 2026, so check the current value on a recent map or a geomagnetic model before converting.
Disclaimer: Map results are calculations on the WGS84 datum from the coordinates and measurements you enter. They are not a navigation device, a land survey or a safety assessment. Carry a map and compass outdoors, check the datum of your map, apply the current magnetic declination, and rely on deeds and licensed surveyors for property boundaries and areas.