What is a great circle?

The shortest path between two points on a sphere. On Earth, that's the shortest route between two locations.

Why not use Euclidean distance for GPS?

Earth is curved (sphere). Euclidean distance (straight line) ignores the curvature and gives incorrect results.

Is haversine the only way to calculate geographic distance?

No, but it's accurate, numerically stable, and avoids singularity issues of other formulas.

Mathematics

Haversine Calculator

Haversine Formula — Great Circle Distance

Point 1 Latitude (°)

Point 1 Longitude (°)

Point 2 Latitude (°)

Point 2 Longitude (°)

✓Great Circle Distance

Kilometres

5570.2 km

Miles

3461.2 mi

Nautical Miles

3007.7 nm

The Haversine formula calculates the great-circle distance between two points on a sphere (like Earth) from their latitude and longitude. It is used in navigation, mapping, and GPS applications.

Symbol	Name	Unit	Description
φ₁, φ₂	latitude of points 1 and 2	radians	—
Δφ	difference in latitude	radians	—
λ₁, λ₂	longitude of points 1 and 2	radians	—
Δλ	difference in longitude	radians	—
R	Earth radius	km (≈6371)	or miles (≈3959)
d	great-circle distance	km or miles	—

From	To	Distance (km)
London	New York	5570
London	Sydney	16993
New York	Los Angeles	3940
Paris	Berlin	878

References

›Haversine formula — Wikipedia

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Haversine Calculator

Haversine Formula — Great Circle Distance

✓Great Circle Distance

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Haversine Formula — Great Circle Distance

✓Great Circle Distance