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 varies from about −25° to +25° depending on where you are on Earth, and changes slowly over time.

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 ~500 km), the difference is negligible. For ocean crossings, a great circle route can save hundreds of kilometres.

Example: From Paris (48.86°N, 2.35°E) to Tokyo (35.68°N, 139.69°E): Initial bearing ≈ 42° (northeast). But the actual great circle route arcs far to the north, and the final bearing into Tokyo is approximately 135° (southeast).

This example shows why the bearing changes so dramatically on long routes — the great circle path curves over Siberia before descending into Japan.