Geodetic Distance Calculator (Vincenty's Formulae)

Calculate geodetic distances with precision using Vincenty's formulae. Perfect for advanced earth science studies and applications.

Coordinates

How to use

Enter both point coordinates in decimal degrees, keeping latitudes between -90° and 90° and longitudes between -180° and 180°. Click Calculate or let the inputs auto-update.

The resulting values reflect the shortest path over the WGS84 ellipsoid, suitable for navigation, surveying, and scientific analysis.

Methodology

This tool uses Vincenty's inverse formula, which iteratively solves the geodesic problem on an oblate ellipsoid. The method accounts for Earth's flattening and converges to sub-meter accuracy.

Full original guide (expanded)

This calculator is designed for scientists and engineers needing precise geodetic distance calculations. It uses Vincenty's formulae, which are highly accurate for ellipsoidal models of the Earth.

Data Source and Methodology: All calculations draw on Vincenty's iteration for the WGS84 ellipsoid, matching the approach documented in NOAA's Geodetic Calculation documentation.

The Formula Explained: Vincenty's inverse solution iteratively computes azimuths and reduces the ellipsoid to an auxiliary sphere to find the true geodesic distance between the two points.

Glossary

  • Latitude: North–south angular coordinate of a point.
  • Longitude: East–west angular coordinate of a point.
  • Distance: Shortest path following the ellipsoidal surface.

Example

Assume Point 1 is at 34.05° N, 118.25° W, and Point 2 is at 40.71° N, 74.01° W. The calculator iteratively converges on the distance by solving Vincenty's inverse equations and returns the geodesic length.

Frequently Asked Questions

What is Vincenty's Formulae?

Vincenty's formulae solve for the distance between two points on a spheroid using iterative methods.

How accurate is this calculator?

It delivers sub-meter accuracy for most distances by modeling Earth as an ellipsoid.

Can this calculator be used for air navigation?

Yes, the precision is suitable for flight planning where accurate great-circle distances are required.

How do I convert geographic coordinates to decimal?

Use Degrees + (Minutes/60) + (Seconds/3600) to convert from DMS to decimal degrees.

Why are ellipsoids used instead of spheres?

Ellipsoids account for Earth's flattening and provide more accurate measurements than simple spherical models.

Formulas

Vincenty's inverse formula snippet:

\[\sigma = \arctan2\left(\sqrt{(\cos U_2 \sin \lambda)^2 + (\cos U_1 \sin U_2 - \sin U_1 \cos U_2 \cos \lambda)^2}, \sin U_1 \sin U_2 + \cos U_1 \cos U_2 \cos \lambda\right)\]

Distance:

\[s = b \cdot A \cdot (\sigma - \Delta\sigma)\]

  • $U_i$: reduced latitude for each point.
  • $\lambda$: difference in longitude on the auxiliary sphere.
  • $b$: semi-minor axis of the ellipsoid, $A$ and $\Delta\sigma$ correct for ellipsoidal shape.
Citations

NOAA explainer: Geodetic Calculation documentation

Changelog
  • 0.1.0-draft — 2026-01-19: Initial audit spec draft generated from the original extractor.
  • Verified the data sources (NOAA) and refactored the calculator UI into the canonical layout.
Verified by Ugo Candido
Last Updated: 2026-01-19
Version 0.1.0-draft