What is the Vincenty inverse problem?

The inverse problem asks: given two latitude/longitude points, what is the shortest path (geodesic) between them on Earth's surface, and what bearings does it leave and arrive at? Vincenty's 1975 formula solves this on the WGS-84 oblate spheroid with accuracy better than 0.5 mm.

How does Vincenty compare to Haversine?

Haversine treats Earth as a perfect sphere (R ≈ 6 371 km) and can have errors up to ~0.5% (several km over long distances). Vincenty uses the WGS-84 oblate spheroid (flattening ≈ 1/298.257), achieving sub-millimeter accuracy. For most navigation 0.5% is fine, 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, New York City is approximately 40.7128, -74.0060.

What is the forward vs. reverse azimuth?

The forward azimuth is the bearing (clockwise from true North) at Point 1 heading toward Point 2. The reverse azimuth is the bearing at Point 2 back toward Point 1. They differ because geodesics curve on an oblate spheroid.

What happens with identical or antipodal points?

Identical points return a distance of 0. Nearly antipodal points (roughly 180° apart) can cause slow convergence or failure in the Vincenty iteration — the tool detects this and reports a non-convergence error. For all other inputs the formula converges in fewer than 10 iterations.

Why are distances shown in three units?

Kilometers are standard in science and most navigation. Miles are used in US and UK aviation and road contexts. Nautical miles (1 nm = 1 852 m) are the standard unit in maritime and international aviation navigation.

Vincenty Inverse Calculator

Compute the precise geodesic distance and azimuths between two geographic coordinates on the WGS-84 ellipsoid using the Vincenty inverse formula.

Two-Point Coordinates

Quick Presets

Point 1 (Origin)

Latitude (°, +N/−S)

Longitude (°, +E/−W)

Point 2 (Destination)

Latitude (°, +N/−S)

Longitude (°, +E/−W)

Enter two coordinates and click Calculate Geodesic.

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Summary

The Vincenty Inverse Calculator solves the inverse geodetic problem: given two latitude/longitude coordinates, it returns the exact ellipsoidal distance (in km, miles, and nautical miles), the forward azimuth (bearing from point 1 to point 2), and the reverse azimuth. It uses Thaddeus Vincenty's 1975 iterative formula on the WGS-84 reference ellipsoid, which is accurate to sub-millimeter precision — far more precise than the spherical Haversine formula, especially over long distances. A Haversine reference value is also shown for comparison.

How it works

Enter the latitude and longitude of Point 1 in decimal degrees (negative for South/West).
Enter the latitude and longitude of Point 2 in decimal degrees.
Click Calculate to apply the Vincenty inverse formula on WGS-84 (a = 6 378 137 m, f = 1/298.257 223 563).
The tool iterates on the reduced latitude until convergence to better than 0.01 mm accuracy.
Results include distance in km, miles, and nautical miles, plus forward and reverse azimuths.
A Haversine distance is computed in parallel for direct comparison with the ellipsoidal result.

Use cases

Survey and geodesy: compute precise distances between benchmarks on the WGS-84 ellipsoid.
Aviation and maritime navigation: determine exact great-circle courses between airports or ports.
GIS analysis: measure accurate distances between geographic features.
Verify GPS device output against a reference ellipsoidal distance calculation.
Educational comparison of spherical (Haversine) vs. ellipsoidal (Vincenty) distance models.
Seismic and geophysical research requiring sub-meter distance accuracy over long baselines.

Frequently Asked Questions

Last updated: 2026-05-29 · Reviewed by Nham Vu