Coordinates · true bearing
Bearing between two coordinates.
Enter a start point and a destination. Get the true initial bearing to leave on, the final bearing on arrival, and the 16-point compass direction.
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Initial and final bearing on a great circle
A bearing is the angle clockwise from true north, 0° to 360°. Along a great circle the heading changes as you travel, so the bearing you leave on (the initial bearing, or forward azimuth) differs from the one you arrive on (the final bearing). The initial bearing is θ = atan2(sin Δλ × cos φ2, cos φ1 × sin φ2 − sin φ1 × cos φ2 × cos Δλ), from the Aviation Formulary's course formulas. The final bearing is the reverse bearing, from B back to A, turned through 180°.
Worked example. From Toronto (43.6532, -79.3832) to London (51.5074, -0.1278) the initial bearing is 51.51° (NE) and the final bearing is 114.51° (ESE). Flying the great circle, the heading swings by about 63° on the way.
These are true bearings, measured from geographic north. A magnetic compass reads magnetic north, so apply the local magnetic declination from a published model such as NOAA's before steering by it. The bearing is undefined when both points are the same or exactly opposite each other on the globe, and the tool says so instead of guessing.
Frequently asked questions
Which earth radius does this use?
The mean radius of the WGS 84 ellipsoid, 6371.0088 km. Treating the earth as a sphere can differ from an ellipsoidal calculation by up to about 0.3%, so it is right for planning and general use but not for surveying.
Can I type degrees, minutes and seconds?
Yes. Each box accepts decimal degrees (43.6532), degrees and decimal minutes (43 39.19 N) or degrees, minutes and seconds (43°39′11″ N). Use a minus sign or the letters S and W for south and west.
What is the difference between initial and final bearing?
The initial bearing is the direction to start out on. The final bearing is the direction you are heading when you arrive. They differ because meridians converge towards the poles.
Is this a true or magnetic bearing?
True bearing, measured from geographic north. Correct for magnetic declination before using a compass.
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Scope
True great-circle bearings on a spherical earth. Not a navigation aid. Magnetic declination, wind, currents and terrain are not applied.