Destination Point from Bearing Calculator
Starting from a known latitude and longitude, heading on a fixed initial bearing, and travelling a set distance along the great circle, where do you end up? This calculator solves that direct geodesic problem on a spherical Earth of mean radius 6,371 kilometers. Enter your start coordinates in decimal degrees, the initial compass bearing clockwise from true north, and the distance in kilometers. It returns the destination latitude and longitude, normalized to the standard -180 to 180 longitude range.
Destination point formula
d = distance / R, R = 6,371 km (angular distance)
lat2 = asin( sin(lat1) * cos(d) + cos(lat1) * sin(d) * cos(brg) )
lon2 = lon1 + atan2( sin(brg) * sin(d) * cos(lat1),
cos(d) - sin(lat1) * sin(lat2) )
Normalize lon2 to -180..180
All angles are computed in radians. The bearing is clockwise from true north; the longitude is normalized so it falls within the standard range.
Destination point context
- This solves the direct geodesic problem on a sphere of mean radius 6,371 km.
- Bearing is the initial heading; on a great circle the heading changes along the route.
- North and east are positive decimal degrees; south and west are negative.
- The spherical result is typically within about 0.3 percent of the ellipsoidal answer.
- For survey precision over long distances use an ellipsoidal method such as Vincenty's.
Destination point: frequently asked questions
What does this destination point calculator do?
Given a starting latitude and longitude, an initial compass bearing, and a distance, it computes the destination point you reach by travelling along the great circle (the shortest path on a sphere). This is the direct geodesic problem solved on a spherical Earth.
What is the formula used?
It uses the spherical direct formula. The destination latitude comes from asin combining the start latitude, the angular distance (distance divided by Earth radius), and the bearing. The destination longitude is found with atan2 and then normalized to the range -180 to 180 degrees.
What Earth radius does it assume?
It uses the mean spherical Earth radius of 6,371 kilometers, the standard value recommended by the International Union of Geodesy and Geophysics. You can enter distance in kilometers; the angular distance is the distance divided by this radius.
What is an initial bearing?
The initial bearing (or forward azimuth) is the compass direction measured clockwise from true north at the start point, from 0 to 360 degrees. On a great circle the bearing changes continuously along the path, so this is only the heading at the very start.
How accurate is the spherical result?
For most navigation and planning the spherical great-circle result is accurate to within about 0.3 percent of the ellipsoidal (geodesic) answer. For survey-grade precision over long distances, an ellipsoidal method such as Vincenty's is preferred.
Official sources
- NOAA National Geodetic Survey: National Geodetic Survey.
- U.S. Geological Survey: U.S. Geological Survey.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.