Midpoint on the geodesic

The point halfway along the shortest path between two points on the ellipsoid, and the course there.

Planning and education aid. Not for primary navigation. Full disclaimer

Computing your own values needs JavaScript and WebAssembly. The worked example below was computed when this page was built, and the documentation under "How we got this" applies.

52.2375218°

The midpoint is 52.2375218°, -41.2903387°, 2,777.454 km from each end.

Midpoint longitude
Course at the midpoint
Distance to each end

Provenance

Computed by: navigation.geodesic.midpoint 1.0.1, core 0.1.0
Model: Karney (2013) geodesic on WGS 84 (inverse, then direct to half the distance)
Accuracy: About 15 nanometers on WGS 84
Notes: None
Cites: Karney, C. F. F., Journal of Geodesy, Algorithms for geodesics

Something look off?

Your values

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Start latitude Decimal degrees, north positive, like 40.6413 · plain numbers mean degrees Start longitude Decimal degrees, east positive, like -73.7781 · plain numbers mean degrees End latitude Decimal degrees, north positive, like 40.6413 · plain numbers mean degrees End longitude Decimal degrees, east positive, like -73.7781 · plain numbers mean degrees Ellipsoidoptional wgs84 (default), grs80, clarke1866, intl1924, airy1830, bessel1841, or krassovsky1940

More options 2

Custom semi-major axisoptional With inverse flattening, like 3396190 m (Mars) · plain numbers mean m Custom inverse flatteningoptional Like 169.894; 0 for a sphere

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How we got thisFormula, worked example, sources, and proof

Model: Karney (2013) geodesic on WGS 84 (inverse, then direct to half the distance)

Accuracy: About 15 nanometers on WGS 84

When to use this: Use this for the point halfway along the shortest path between two places -- a staging point, the centre of a search area, a label position for a long route. It is halfway by distance travelled, which is not where averaging the coordinates puts it.

Limitations: Averaging latitude and longitude is not this, and is not close: for New York to London the two are more than 700 km apart, and across the antimeridian the average lands on the wrong side of the planet. Halfway by distance is also not halfway in time or in fuel, which depend on wind and on speed. For nearly antipodal points the geodesic itself is barely determined -- many paths are almost equally short -- so the midpoint moves a long way for a small change in either end.

Worked example: Midpoint of JFK to Heathrow. Source: Karney direct at half the inverse distance. It is golden test vector v006, and every build checks the tool still gives its answer within its tolerance.

You enter

Start latitude: 40.6413 deg
End latitude: 51.47 deg
Start longitude: -73.7781 deg
End longitude: -0.4543 deg

You get

Midpoint latitude: 52.2375218°
Midpoint longitude: -41.2903387°
Course at the midpoint: 75.3455671°
Distance to each end: 2,777.454 km

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 1.0.1, core 0.1.0. See this tool in the verification report.

Changes

2026-09-23, fixed: Short distances lost their meaning: a 0.859 m geodesic showed as 0.001 km. Distances in the navigation tools (version 1.0.1) still show to the meter in kilometers, but a short one now keeps three significant digits, down to the millimeter, so it shows as 0.000859 km. Differences such as the rhumb line's extra distance keep fixed decimals. Values are unchanged. Changelog

Checked against: 23 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.

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