Bearing Between Coordinates Calculator
The bearing from one point on the Earth to another is the compass direction you would set off in to travel the shortest (great-circle) path between them. Because meridians converge toward the poles, this initial bearing generally changes along the route, so it is the heading at the start. This tool computes the initial bearing, also called the forward azimuth, from a start latitude and longitude to a destination, in degrees true measured clockwise from north. Enter both coordinates in decimal degrees, using negative values for south latitude and west longitude. The result is the true bearing to steer or plot.
Initial bearing formula
y = sin(dLon) * cos(lat2)
x = cos(lat1) * sin(lat2) - sin(lat1) * cos(lat2) * cos(dLon)
bearing = atan2(y, x), converted to degrees and normalised to 0 to 360
where dLon = lon2 - lon1, all angles in radians
The forward azimuth is found by spherical trigonometry. The components x and y are formed from the latitudes and the longitude difference, and atan2 returns the angle in the correct quadrant. Converting from radians to degrees and adding 360 then taking the remainder normalises the result to the 0 to 360 range measured clockwise from true north. The bearing is the heading at the start of the great-circle path.
Worked example
From New York (40.7128, -74.0060) to London (51.5074, -0.1278): the longitude difference is about 73.878 degrees. Working through the formula gives an initial bearing of 51.21 degrees true, a north-easterly heading. This is why great-circle flights from New York to London curve up over the North Atlantic rather than heading due east, even though London is at a similar latitude.
Frequently asked questions
What is an initial bearing?
The initial bearing, or forward azimuth, is the compass direction at the start of the shortest great-circle route between two points. Along a great circle the bearing changes continuously because the meridians converge, so the heading you begin with is not the heading you finish with. To follow the route exactly you adjust course as you go.
How does this differ from a rhumb-line bearing?
A rhumb line crosses every meridian at the same angle, giving a single constant bearing, but it is not the shortest path. A great-circle route is shortest but its bearing varies. This calculator gives the initial great-circle bearing; for a constant heading you would use a rhumb-line bearing instead, which is slightly different over long distances.
What sign convention do the coordinates use?
Latitudes are positive north of the equator and negative south of it; longitudes are positive east of the prime meridian and negative west of it. So New York's longitude is entered as -74.0060. Enter all four values in decimal degrees with the correct sign to get the right bearing.
Is the result a true or magnetic bearing?
It is a true bearing, measured from geographic (true) north. To steer it by a magnetic compass you must apply the local magnetic declination (variation), which differs by location and changes slowly over time. Charts and the NOAA magnetic-declination service give the current value for your area.
Official sources
- NOAA National Geodetic Survey: geodetic computations and azimuths.
- NOAA National Centers for Environmental Information: magnetic declination.
Reviewed by the CalculatorHub team, edited by James Graham, 19 June 2026. See our methodology.