Vincenty Ellipsoidal Distance Calculator
Calculate the high-accuracy geodesic distance between two latitude/longitude points using Vincenty's ellipsoidal formula on the WGS84 ellipsoid.
Inputs
Ellipsoidal distance and azimuths between two points (inverse), or the end point from a start, azimuth and distance (direct). Vincenty, with a robust fallback near antipodes.
Enter the values and press Calculate.
Or load an example to see a worked result.
Batch from CSV
One row per calculation, with a header row. Values use the units currently selected in the form above. Up to 10,000 rows; nothing is uploaded.
How the method works
A fixed worked example to explain the method — it is not your result.
Before you rely on this: First-pass guide only. Verify safety-critical or regulated work against the relevant standards, your project requirements and a qualified professional.
How to use this calculator
- Choose Inverse (two points → distance and azimuths) or Direct (start point, azimuth and distance → end point).
- Enter the coordinates in decimal degrees, DMS or DDM, and choose WGS84, GRS80 or a custom ellipsoid.
- Press Calculate. Read the distance, the method that produced it, and the azimuths.
How it works
Vincenty's inverse formula iterates on the longitude on an auxiliary sphere, capped at 200 iterations with a 1×10⁻¹² rad tolerance. It is used whenever it converges and the points are not within 1° of antipodal.
Near antipodes Vincenty can fail to converge or lose accuracy. There the tool switches to a robust geodesic solver — the geodesic integrals evaluated exactly, with a bracketed search on the starting azimuth that cannot diverge — and tells you why. It never substitutes a spherical answer.
Both methods were checked against GeographicLib on 36 reference lines, including near-antipodal, polar and equatorial cases: the robust solver agrees to 1 µm, and the tool to 0.1 mm whichever method runs.
Azimuths: the forward azimuth at point 2 is the direction of travel on arrival; the back azimuth (2 → 1) is that plus 180°. For coincident points the azimuth is undefined, and for antipodal points the shortest route is not unique.
Worked example
Perth (−31.95°, 115.86°) → Melbourne (−37.81°, 144.96°), WGS84. Vincenty converges in 5 iterations: 2,726,613.856 m, forward azimuth 111.894064° at Perth and 94.986079° on arrival (back azimuth 274.986079°). The 6,371,008.8 m sphere gives 2,721,289.302 m for comparison — 5.3 km shorter.
Common mistakes
- Taking the back azimuth to be the forward azimuth at point 2. They differ by exactly 180°.
- Reading millimetre agreement between algorithms as millimetre accuracy of your coordinates.
- Swapping to a haversine result when Vincenty fails — that changes the Earth model, not just the method.
Frequently asked questions
Vincenty or haversine?
Vincenty works on the ellipsoid; haversine works on a sphere and can differ from it by several kilometres over long routes. Use the ellipsoidal value whenever the distance matters.
What happens with antipodal points?
The robust solver gives the distance (20,003,931.459 m for exactly opposite points on the equator on WGS84). Because many equally short routes exist, no single azimuth is shown.
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- Lat/Long/Height to ECEF Converter
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Cite this tool
Zerdly. (2026). Vincenty Ellipsoidal Distance Calculator. Retrieved from https://www.zerdly.com/tools/vincenty-ellipsoidal-distance-calculator-high-accuracy/
Tip: Enter any known values to calculate the remaining results.
Designed to run locally in your browser. Tool inputs are not intentionally stored by Zerdly unless stated otherwise.