Bearing Between Two Points Calculator

How to calculate the bearing between two points

1. Enter both points. Latitude first, then longitude, in decimal degrees or DMS. South and west are negative, or use S and W.
2. Click Calculate. The initial bearing is the direction to set out on from point 1. The final bearing is the direction of travel on arrival at point 2. The back bearing is the direction from point 2 back to point 1.
3. Read it in the format you need. The result is shown as an azimuth in degrees, in DMS, as a quadrant bearing such as N 51°14'28" E, as a 16-point compass direction and in NATO mils.
4. To go the other way, use the destination box. Enter a start, a bearing (an azimuth or a quadrant bearing) and a distance to get the end point.

Why the bearing changes along the way

On a sphere or ellipsoid the shortest path between two points is a curve, not a straight line on a flat map. Its direction changes continuously, so the bearing at the start (initial) and the bearing at the end (final) differ. For New York (40.7128° N, 74.0060° W) to London (51.5074° N, 0.1278° W):

initial bearing  51.2412°  (N 51°14'28" E, north-east)
final bearing   108.3690°
back bearing    288.3690°  (final bearing + 180°)

You leave New York heading north-east and arrive in London heading east-south-east. For short distances, such as a plot boundary, the two values are almost the same.

The formula behind it

On a sphere the initial bearing θ from point 1 to point 2, with latitudes φ and longitude difference Δλ, is:

θ = atan2( sin Δλ · cos φ2 ,
              cos φ1 · sin φ2 - sin φ1 · cos φ2 · cos Δλ )

This page does not stop at the spherical formula. It solves the same problem on the WGS84 ellipsoid with Vincenty's method, so the bearings stay accurate over long distances. The result is converted to a 0 to 360° azimuth measured clockwise from north.

Destination point from bearing and distance

The destination box solves the direct problem on the ellipsoid. Starting at New York and travelling 5,570 km on an azimuth of 51.2° ends at 51.5804° N, 0.3204° W, near London. The bearing can be an azimuth (51.2), DMS (51°12'00") or a quadrant bearing (N 51°12' E). Distance can be in kilometres, miles, nautical miles, metres or feet.

True north, grid north and magnetic north

• The bearings here are true bearings, measured from geographic north (the direction of the meridian).
• A compass shows magnetic north, which differs from true north by the local declination. The page does not apply declination, because it changes with place and year.
• A map grid such as UTM uses grid north, which differs from true north by the convergence angle. This page does not apply convergence either.

Common mistakes

• Using the initial bearing as the whole route. Over long distances the direction drifts. Navigation along a great circle needs repeated recalculation.
• Mixing up bearing and back bearing. The back bearing is the final bearing plus 180°, not the initial bearing plus 180°, except over short distances.
• Using a compass reading as a true bearing. Add or subtract the local declination first.
• Identical points. Two equal points have no bearing; the tool says so instead of returning 0°.

What this calculator does and does not do

• WGS84 geodesic. Bearings and the destination are computed on the ellipsoid. For points almost opposite each other on the globe, the method does not converge and the page falls back to a spherical estimate and tells you.
• True bearings only. No magnetic declination or grid convergence is applied.
• Accuracy. We compared 2,000 random pairs and 1,000 random destination problems with GeographicLib (through pyproj). Bearings agreed to better than 0.000001° and destinations to better than 0.000000001°.
• Runs in your browser. No coordinates are sent to a server.

Related calculators

To convert between azimuths and quadrant bearings use the bearing and azimuth converter. For the distance use distance between coordinates. Traverses are covered in the bearing and distance guide.