Compass Bearing Calculator

The compass bearing (also called heading or azimuth) is the angle measured clockwise from true north to the direction of travel. A bearing of 0° or 360° is due north, 90° is due east, 180° is due south, and 270° is due west.

The formula for the initial bearing from point A to point B is:

θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))

This gives the initial bearing, the direction you face at the start of your journey. Because Earth is a sphere, the bearing changes continuously along a great circle route. The final bearing is the direction you are facing when you arrive at point B, and it differs from the initial bearing on long routes.

True bearing vs magnetic bearing: This calculator gives true bearing, relative to geographic north. To get the magnetic bearing for use with a compass, subtract the magnetic declination for your location. Declination runs from about -25° to +25° depending on where you are on Earth, and it drifts slowly year to year.

Rhumb line vs great circle: A rhumb line (constant bearing) is easier to navigate but covers more distance than a great circle. For short distances, under roughly 500 km, the difference is negligible. For ocean crossings a great circle route can save hundreds of kilometers.

Example: From Paris (48.86°N, 2.35°E) to Tokyo (35.68°N, 139.69°E): Initial bearing 33.5° (north-northeast). The great circle route then arcs far to the north, and the bearing on arrival into Tokyo is 153.5° (south-southeast).

That is 120 degrees of drift over one flight, and it is why the bearing on a long route is a starting heading rather than a course to hold. The great circle path curves over Siberia before descending into Japan.

The constant-bearing alternative for the same pair is a course of 097.4°, and it runs 6,116 nm against the great circle’s 5,244. That is 872 extra miles, 16.6% of the trip, bought with a heading you never have to touch. The rhumb line calculator works both figures out for any pair.