Initial Bearing Calculator
From two pairs of coordinates, get the initial compass bearing — the direction, measured clockwise from North, you would head in to start a great-circle journey.
Two points, one direction
Enter the latitude and longitude of a start and an end point and the calculator returns the initial bearing in degrees, where 0° is North, 90° East, 180° South, and 270° West.
Initial, not constant
This is the bearing at the start. Along a great-circle route the direction changes continuously, so the final bearing on arrival is usually different.
What is an initial bearing calculator?
Coordinates in, compass direction out
An initial bearing calculator turns two pairs of geographic coordinates into the forward azimuth — the compass direction from the start point toward the end point, measured clockwise from true North. It is the heading you would dial in at the very beginning of the shortest (great-circle) path between the two places. Navigators, pilots, sailors, and mapping tools use this bearing to point themselves the right way before they set off, then adjust as the route curves over the globe.
Enter a start and an end latitude and longitude to get the initial compass bearing in degrees instantly.
The forward azimuth comes from the two latitudes and the difference in longitude, combined with the atan2 function, then normalized to a value between 0° and 360°.
y = sin(Δλ) · cos φ₂, x = cos φ₁ · sin φ₂ − sin φ₁ · cos φ₂ · cos(Δλ), bearing = atan2(y, x)Here φ₁ and φ₂ are the two latitudes in radians and Δλ is the longitude difference. The atan2 function returns an angle from −180° to +180°, so the result is normalized by adding a full turn where needed, leaving a clean compass bearing in [0°, 360°). Because longitude is negative in the west and latitude is negative in the south, the formula handles every hemisphere without special cases.
Take Berlin at latitude 52.52, longitude 13.405 and Munich at latitude 48.1351, longitude 11.582.
Longitude gap
Δλ = 11.582 − 13.405 = −1.823° — Munich is slightly west of Berlin; convert this and the two latitudes to radians.
Components
y = sin(Δλ) · cos φ₂, x = cos φ₁ · sin φ₂ − sin φ₁ · cos φ₂ · cos(Δλ) — the east-west and north-south parts of the direction.
Bearing
atan2(y, x) normalized = 195.57° — a south-southwest heading, since Munich is south and a touch west of Berlin.
The number you get is the initial bearing — the compass direction to head in at the start of the journey, measured clockwise from true North. Read it against the cardinal points: 0° or 360° is due North, 90° is East, 180° is South, and 270° is West, with everything in between (45° is northeast, 225° southwest, and so on). For Berlin to Munich the bearing is about 195.57°, just west of due South, which matches Munich sitting south and slightly west of Berlin. The single most important caveat is the word "initial": on a great-circle route — the genuinely shortest path over the curved Earth — the bearing changes the whole way, so the direction you arrive on usually differs from the one you left on. The effect is small over short hops but large on intercontinental routes, which is why a flight from London to Tokyo seems to curve far north on a flat map. Use this bearing to point yourself the right way at the outset, not as a single fixed heading to hold for the entire trip.
The bearing formula is exact for a sphere, but a couple of practical points are worth keeping in mind.
Initial bearing, true North, spherical model
This is the bearing only at the start of a great-circle path; the direction changes continuously along the route, so do not hold it as a constant heading. The result is measured from true (geographic) North, not magnetic North — to steer by a magnetic compass, apply the local magnetic declination. The formula also treats the Earth as a sphere, so it differs marginally from an ellipsoidal calculation. Enter latitudes between −90 and 90 and longitudes between −180 and 180, in decimal degrees, for a meaningful answer.