Final Bearing Calculator
On a great-circle route the compass heading changes as you travel, so the bearing you arrive on differs from the one you departed on. This calculator returns both the initial bearing at the start and the final bearing at the destination for a route between two coordinates, along with the change between them. Enter the start and end latitude and longitude to plan an arrival heading or to understand great-circle drift.
Final bearing formula
bearing(A to B) = atan2( sin(dLon) * cos(lat2),
cos(lat1) * sin(lat2) - sin(lat1) * cos(lat2) * cos(dLon) )
initial = bearing(start to end)
final = (bearing(end to start) + 180) mod 360
The initial bearing is the forward azimuth from start to end. The final bearing is the back-azimuth from end to start, reversed by adding 180 degrees, which gives the heading you are travelling as you reach the destination.
Worked example
London (51.5 N, -0.1 E) to New York (40.7 N, -74.0 E). The initial bearing is about 288.1 degrees (west-northwest). The final bearing on arrival is about 250.9 degrees, a swing of roughly -37.2 degrees as the great circle curves over the North Atlantic.
Final bearing: frequently asked questions
What is the final bearing?
The final bearing is the compass direction of travel as you arrive at the destination on a great-circle route. Because great-circle paths curve relative to the meridians, the final bearing differs from the initial bearing you set out on.
How is the final bearing calculated?
Compute the initial bearing from the destination back to the start, then add 180 degrees and normalise to 0 to 360. Equivalently, final bearing = (initial bearing from B to A + 180) mod 360. The initial bearing uses theta = atan2( sin(dLon) * cos(lat2), cos(lat1) * sin(lat2) - sin(lat1) * cos(lat2) * cos(dLon) ).
Why does the bearing change along a great circle?
A great circle is the shortest path on a sphere, but it crosses each meridian at a different angle. Only due-north/south and equatorial routes keep a constant bearing. On all other routes the heading drifts, so the arrival bearing differs from the departure bearing.
Is this a rhumb line bearing?
No. A rhumb line holds a constant bearing but is longer than the great circle. This calculator gives great-circle bearings, where the initial and final headings differ.
Sources and references
- National Geospatial-Intelligence Agency: geodesy and azimuth reference.
- National Oceanic and Atmospheric Administration, National Geodetic Survey: forward and inverse problem fundamentals.
- Formula: standard spherical great-circle azimuth (Ed Williams, Aviation Formulary).
Reviewed by the CalculatorHub team, edited by James Graham, 19 June 2026. See our methodology.