Destination from a start, course, and distance (geodesic)
Where you end up after traveling a distance on an initial course along the ellipsoid, any length, with Karney's algorithm.
Planning and education aid. Not for primary navigation. Full disclaimer
The destination is 45.8920808°, -63.7549563°, arriving on a course of 57.8863727°.
- Destination longitude
- Final course
Provenance
- Computed by
- navigation.geodesic.direct 1.0.0, core 0.1.0
- Model
- Karney (2013) geodesic on WGS 84
- Accuracy
- About 15 nanometers on WGS 84, for any distance
- Notes
- None
- Cites
- Karney, C. F. F., Journal of Geodesy, Algorithms for geodesics; Karney, C. F. F., GeographicLib, GeographicLib geodesic test data (GeodTest.dat) and GeodSolve
Something look off?
How we got thisFormula, worked example, sources, and proof
Model: Karney (2013) geodesic on WGS 84
Accuracy: About 15 nanometers on WGS 84, for any distance
When to use this: Use this when you have a starting point, a bearing, and a distance and need the point you arrive at: laying out a leg, projecting a position from a fix, placing a point at a known range and bearing, or building a circle of points around a center. It follows the shortest path on the ellipsoid, at any distance.
Limitations: It answers geometry on an ellipsoid, not travel: the azimuth is the initial one and it changes along the path, so a course held constant on a compass is a rhumb line and belongs in that tool. Heights are not part of it, a geodesic is not a route around terrain or airspace, and the azimuth here is true rather than magnetic.
Worked example: 1,000 km from JFK on a course of 051°. Source: add-navigation-and-geometry geodesic scenario: (45.8920808°, -63.7549563°), final course 57.886373°. It is golden test vector v001, and every build checks the tool still gives its answer within its tolerance.
You enter
- Initial course
- 51 deg
- Distance
- 1000 km
- Start latitude
- 40.6413 deg
- Start longitude
- -73.7781 deg
You get
- Destination latitude
- 45.8920808°
- Destination longitude
- -63.7549563°
- Final course
- 57.8863727°
Review: Not yet independently reviewed by a geodesist.
Last verified: 2026-09-18, when a maintainer last confirmed this tool's sources at the issuer. See the sources ledger.
Status: version 1.0.0, core 0.1.0. See this tool in the verification report.
Changes
- 2026-09-22, changed: Geodesic distance and destination now work on strongly flattened ellipsoids (|f| from 0.02 up to 0.5) by the exact method, where they used to refuse. On 480 geodesics at six flattenings they match GeographicLib's GeodesicExact to rounding. Results on WGS 84 and other catalog ellipsoids are unchanged. Changelog
- 2026-09-19, changed: Five more tools passed the stable verification bar: geodesic distance and destination (checked against GeographicLib's GeodTest), UTM forward and inverse (checked against exact transverse Mercator values), and the standard atmosphere (checked against a separately written implementation). Changelog
Checked against: 28 golden test vectors (download the test vectors, each with its source and tolerance). See how results are checked and every source.
Sources
- Algorithms for geodesics, Karney, C. F. F., Journal of Geodesy, Vol. 87, No. 1. pp. 43-55.
- GeographicLib geodesic test data (GeodTest.dat) and GeodSolve, Karney, C. F. F., GeographicLib, GeographicLib 2.x. Geodesic test data, 500,000 geodesics on WGS 84. Read free.