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.

Go the other way: Vincenty direct (legacy) →

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.

5,554.908791km

Vincenty gives 5,554.908791 km, 0.0118 mm from the Karney geodesic.

Initial course
Final course
Difference from Karney

Provenance

Computed by: navigation.geodesic.vincenty-inverse 1.0.0, core 0.1.0
Model: Vincenty (1975) inverse on WGS 84, tolerance 1e-12 rad, at most 200 iterations
Accuracy: About 0.5 mm where it converges; fails to converge for nearly antipodal points
Notes: None
Cites: Vincenty, T., Survey Review, Direct and inverse solutions of geodesics on the ellipsoid with application of nested equations; Karney, C. F. F., Journal of Geodesy, Algorithms for geodesics

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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: Vincenty (1975) inverse, tolerance 1e-12 rad, at most 200 iterations

Accuracy: About 0.5 mm where it converges; fails to converge for nearly antipodal points

When to use this: Use this when the answer has to be Vincenty's: checking surveying software, a GIS library or a published figure from the last forty years, all of which use his 1975 method. The difference from the exact modern answer is reported alongside, so you can tell whether a discrepancy is the algorithm or an error.

Limitations: Vincenty's inverse does not converge for nearly antipodal points -- a known property of the method, not of this implementation -- and the tool says so rather than returning a plausible number from a truncated loop. Its series is truncated, so it carries about half a millimetre against the exact answer. For new work use the geodesic inverse, which converges everywhere and is exact to fifteen nanometres; this one is for agreeing with the past.

Worked example: JFK to Heathrow. Source: add-navigation-and-geometry scenario: sub-millimeter from Karney. It is golden test vector v001, 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

Distance: 5,554.908791 km
Initial course: 51.3816479°
Final course: 107.9828291°
Difference from Karney: 0.0118 mm

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.

Checked against: 21 golden test vectors (download the test vectors, each with its source and tolerance). See how results are checked and every source.

Sources

Direct and inverse solutions of geodesics on the ellipsoid with application of nested equations, Vincenty, T., Survey Review, Vol. 23, No. 176. pp. 88-93.
Algorithms for geodesics, Karney, C. F. F., Journal of Geodesy, Vol. 87, No. 1. pp. 43-55.

Learn the concept: Haversine vs. geodesic distance explained

Your values

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Sources

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