Vincenty direct (legacy)

The destination by Vincenty's 1975 method, for checking legacy software; reports how far it lands from the Karney destination.

Go the other way: Vincenty inverse (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.

45.8920808°

Vincenty lands at 45.8920808°, -63.7549563°, 0.00249 mm from the Karney destination.

Destination longitude
Final course
Distance from the Karney destination

Provenance

Computed by: navigation.geodesic.vincenty-direct 1.0.0, core 0.1.0
Model: Vincenty (1975) direct on WGS 84, tolerance 1e-12 rad, at most 200 iterations
Accuracy: About 0.5 mm
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

Something look off?

Your values

Showing an example. Change anything.

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 Initial course Degrees clockwise from true north, like 51 · plain numbers mean degrees Distance Like 1000 km · plain numbers mean km 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

Run many at once from a CSV

Loading…

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

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

Accuracy: About 0.5 mm

When to use this: Use this to reproduce a destination computed by Vincenty's 1975 direct method -- from a point, an azimuth and a distance -- when matching older surveying software or a published traverse. The gap from the exact answer is reported with it.

Limitations: The same truncated series as the inverse, about half a millimetre on a long line, which is reported beside the answer rather than left to be assumed. Unlike the inverse there is no convergence problem: nothing about going a given way for a given distance is antipodal, so the iteration on sigma always settles, usually in three or four passes. For new work use the geodesic direct tool, which is exact to about fifteen nanometres and has no series to truncate; this one exists to agree with what came before, and agreeing with it is the only reason to reach for it.

Worked example: 1,000 km from JFK on a course of 051°. Source: Compared with the Karney direct solution for the same inputs. 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°
Distance from the Karney destination: 0.00249 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.

Your values

You enter

You get

Sources

Related tools