Bearing Calculator

What this bearing calculator does

A bearing is the direction from one point to another, measured clockwise from true north: 0° is north, 90° east, 180° south and 270° west. Enter two latitude/longitude points and the calculator gives:

• Initial bearing — the direction to set off in from point A.
• Final bearing — the direction you're heading when you arrive at point B.
• Return bearing — the initial bearing for the trip from B back to A.
• A 16-point compass direction for each (such as NE or WNW), the great-circle distance and the midpoint.

All bearings follow the great circle, the shortest route over the Earth's surface.

Example: New York to London

From 40.7128, -74.0060 (New York) to 51.5074, -0.1278 (London):

Notice that the heading turns from 51° to 108° along the way, and the return bearing (288°) isn't simply the initial bearing plus 180° (231°). On a great circle your direction changes continuously, except when travelling due north, due south or along the equator.

How to use it

1. Enter point A (your start) as latitude and longitude in decimal degrees, using minus signs for south and west. You can add an optional name, or use one of the city buttons.
2. Enter point B (your destination) the same way. Use the swap button to reverse the route.
3. Select Calculate Bearing.

Have coordinates in degrees, minutes and seconds, UTM or MGRS? Convert them to decimal degrees first with the coordinate converter.

How the bearing is calculated

The initial bearing θ from point 1 to point 2 uses the standard great-circle formula, where φ is latitude, λ is longitude and Δλ is the difference in longitude:

The result is converted to degrees and normalized to 0–360°. The final bearing is the bearing from B back to A, turned around by 180°. Distance uses the Haversine formula with a mean Earth radius of 6,371 km. Each of the 16 compass points covers 22.5°; for example, N is 348.75° to 11.25°.

Things to know before you navigate with it

• These are true bearings, not magnetic. A magnetic compass points to magnetic north, which differs from true north by the local magnetic declination. To get a compass bearing, subtract an easterly declination or add a westerly one. Declination depends on where you are and changes over time; you can look it up with NOAA's magnetic field calculator.
• Great circle, not rhumb line. To follow the great circle you must keep adjusting your heading. A rhumb line keeps one constant bearing but is longer over long distances; this calculator doesn't compute rhumb lines.
• The Earth is treated as a sphere. Results can differ slightly from ellipsoidal (WGS 84) calculations used in survey and professional navigation software.
• Special cases. At the North or South Pole every direction is south or north, so a bearing from a pole isn't meaningful. For two points on exactly opposite sides of the Earth, every great circle is equally short, so the bearing shown is just one of many.

Frequently asked questions