Maps and geodesy
Destination point from bearing and distance
Find where you arrive after travelling a distance on an initial bearing from a start point, on the WGS84 ellipsoid, with the final bearing and the spherical answer for comparison.
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Showing the worked example. Results update as you type.
Result
Method and limits
This solves the direct geodesic problem: from a start point, an initial bearing and a distance along the ellipsoid, find the end point and the bearing on arrival. Distances and bearings use Karney’s algorithms for geodesics on the WGS84 ellipsoid (a = 6,378,137 m, f = 1/298.257223563), through the GeographicLib JavaScript library. They are accurate to about 15 nanometres for any pair of points, including nearly antipodal ones where Vincenty’s iteration fails to converge.
For comparison the spherical formula is shown: φ2 = asin(sin φ1 cos δ + cos φ1 sin δ cos θ), λ2 = λ1 + atan2(sin θ sin δ cos φ1, cos δ − sin φ1 sin φ2), with δ = d/R and R = 6,371.0088 km. Over long distances the two differ by kilometres.
Worked example (GeographicLib documentation): 20,000 km south-west (225°) of Perth, Australia (32.06°S, 115.74°E) is 32.11195529°N, 63.95925278°W, in the Atlantic near Bermuda.
Limits
The path is a geodesic, the shortest route, not a constant-compass-bearing rhumb line. Bearings are true, not magnetic.
References
Related tools
- Coordinate converter: decimal degrees, DMS, UTM and MGRSConvert WGS84 coordinates between decimal degrees, degrees-minutes-seconds, degrees and decimal minutes, UTM and MGRS, with grid convergence and scale factor.
- Distance and bearing between two coordinatesGeodesic distance, initial and final bearing and midpoint between two latitude/longitude points on the WGS84 ellipsoid, with the haversine great-circle result for comparison.
- Polygon area on the ellipsoid from coordinatesPaste latitude/longitude points, GeoJSON or WKT and get the area and perimeter of the polygon on the WGS84 ellipsoid, in km², hectares, acres and square miles.