Great Circle Calculator

Great Circle Distance Calculator

Measure the shortest surface distance between two latitude/longitude points on Earth.

Last updated: June 2026 | By Patchworkr Team

Enter a real number.

Great Circle Distance
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Enter two coordinates to calculate
Central Angle
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Radius Used
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Cosine of Angle
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Formula

This calculator uses the spherical law of cosines, not the haversine formula.

d = R arccos(sin φ1 sin φ2 + cos φ1 cos φ2 cos Δλ)

Angles are converted from degrees to radians first, and the cosine input is clamped to keep `Math.acos` numerically stable.

How to Use

Enter both latitude and longitude pairs in degrees, choose the output unit, and read the surface distance on the sphere.

  1. Enter point 1 latitude and longitude.
  2. Enter point 2 latitude and longitude.
  3. Choose kilometers or miles.

Example

New York City to London is a classic great-circle pair: the shortest surface route is about 5,570 km.

That is the distance along Earth’s surface, not a straight line through space.

Notes

The old copy said haversine, but the implementation was actually the spherical law of cosines. This version aligns the text with the code.

Latitudes outside -90 to 90 and longitudes outside -180 to 180 are rejected before the distance is computed.

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