Geodesic
Shortest paths on the ellipsoid.
These tools solve distance and course problems on the Earth: the shortest path between two points on the ellipsoid, the destination from a start, course, and distance, midpoints, waypoints, and where two paths cross, plus the spherical and Vincenty versions for comparison. Pilots, mariners, developers, and GIS analysts use them. Start with distance between two points, and compare it with the haversine tool to see how far the spherical shortcut drifts on your route. The pitfall is trusting the haversine formula for reported distances; it can be off by tenths of a percent.
Planning and education aid. Not for primary navigation. Full disclaimer
No tools here match . or .
I want to work on a sphere: great-circle course, destination, or a point part way
- Great-circle distance and course (spherical)
Distance and initial and final courses along the great circle on a sphere, with the difference from the ellipsoidal geodesic shown.
- Great-circle destination (spherical)
Where a great circle from a start point on a course takes you after a distance on a sphere, and how far that is from the ellipsoidal answer.
- Point part way along a great circle
The point a given fraction of the way between two points along the great circle on a sphere, beside the same fraction along the ellipsoidal geodesic.
I want to find the distance and courses between two points
- Distance between two points (geodesic)
The shortest distance and the start and end courses between two points on the WGS 84 ellipsoid (or any ellipsoid), exact to nanometers with Karney's algorithm.
- Haversine distance (spherical)
The great-circle distance on a sphere by the haversine formula, with its error against the ellipsoidal geodesic shown.
- Vincenty inverse (legacy)
Distance and courses by Vincenty's 1975 method, for checking legacy software; reports its difference from Karney and fails honestly near antipodes.
I want to find where I end up from a start, course, and distance
- 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.
- Vincenty direct (legacy)
The destination by Vincenty's 1975 method, for checking legacy software; reports how far it lands from the Karney destination.
I want to find points along the way
- Midpoint on the geodesic
The point halfway along the shortest path between two points on the ellipsoid, and the course there.
- Waypoints along a route line
Points along the geodesic (or rhumb line) from A to B at N equal intervals, a fixed spacing, or given fractions, with distance and course at each, as a table, a GPX route, and GeoJSON.
I want to check whether two lines cross, or find a route's highest point
- Where two geodesic segments cross
The crossing of the geodesics through two segments on the ellipsoid, nearest the segments' middles, and whether it falls within both segments or out on their extensions.
- Highest point of a geodesic (vertex)
The vertex of a geodesic: the northernmost point it reaches, where it runs due east or west, and how far along the line from the start it lies.
Which distance method
- The geodesic tools solve the ellipsoid exactly (Karney's method) and are the ones to use. Distance between two points (geodesic)
- Haversine treats the earth as a sphere and can be off by about 0.5%; it is here for comparison with other software. Haversine distance (spherical)
- Vincenty's method is a legacy iteration that can fail near antipodal points; it is here to check older results. Vincenty inverse (legacy)
Guides that use these tools
- VFR cross-country: Distance and true course between two airports, the heading to fly into the wind, the magnetic heading, and the time en route.