What is the Vincenty direct problem?

The direct problem asks: starting at a given latitude and longitude, traveling a specified distance along a given initial bearing (azimuth), where do you end up? Vincenty's 1975 formula solves this iteratively on an oblate spheroid such as WGS-84, with sub-millimeter accuracy.

How accurate is Vincenty compared to Haversine?

Haversine treats Earth as a perfect sphere (R ≈ 6 371 km) and can have errors up to ~0.5%. Vincenty uses the WGS-84 oblate spheroid (flattening ≈ 1/298.257), achieving accuracy better than 0.5 mm over any distance. For most practical navigation 0.5% is acceptable, but surveying and geodesy require Vincenty precision.

What coordinate format should I use?

Decimal degrees. Positive values are North latitude and East longitude; negative values are South latitude and West longitude. For example, Sydney is approximately −33.8688, 151.2093.

What bearing convention does this tool use?

Bearings are true (not magnetic) azimuths measured clockwise from geographic North: 0° = North, 90° = East, 180° = South, 270° = West.

Can this tool handle antipodal points?

Nearly antipodal routes (very close to 180° apart) can cause slow convergence or failure in the Vincenty iteration. The tool detects non-convergence and shows an error. For such routes, the result would be on the opposite side of Earth and is rarely needed in practice.

What is the final bearing?

Because Earth is an oblate spheroid, the geodesic curves — it does not keep a constant compass heading. The final bearing is the azimuth of the geodesic at the destination point, which will differ from the initial bearing for long routes.

Vincenty Direct Calculator

Name: Vincenty Direct Calculator
Availability: InStock
Author: Nham Vu

Compute the geodesic endpoint (latitude/longitude) and final bearing reached by traveling a given distance and azimuth from a starting point using the Vincenty direct formula on the WGS-84 ellipsoid.

Starting Point & Course

Quick Presets

Origin Coordinates

Latitude (°, +N/−S)

Longitude (°, +E/−W)

Initial Bearing (Azimuth)

Bearing (0–360°, clockwise from N)

Distance

Unit

Enter a starting point, bearing, and distance, then click Calculate Endpoint.

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Summary

Compute the geodesic endpoint (latitude/longitude) and final bearing reached by traveling a given distance and azimuth from a starting point using the Vincenty direct formula on the WGS-84 ellipsoid.

How it works

Enter the starting latitude and longitude in decimal degrees (negative for South/West).
Enter the initial bearing in decimal degrees measured clockwise from true North (0–360).
Enter the distance to travel in meters or kilometers.
Click Calculate to apply the Vincenty direct formula on the WGS-84 ellipsoid (a = 6 378 137 m, f = 1/298.257 223 563).
The tool returns the destination latitude, longitude, and the final bearing at the endpoint.
Copy individual results or the full coordinate pair with one click.

Use cases

Survey and geodesy: project a point at a precise distance and azimuth from a known benchmark.
Navigation: compute a waypoint given a course heading and distance traveled.
Aviation and maritime route planning requiring ellipsoidal accuracy.
GIS analysis: buffer points or generate radial transects on the WGS-84 ellipsoid.
Verify geodetic software output against a reference implementation.
Educational demonstrations of ellipsoidal vs. spherical distance differences.

Frequently Asked Questions

Last updated: 2026-06-24 · Reviewed by Nham Vu