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Shortest arc on a sphere
We use the reviewed haversine relation, converting signed decimal degrees to radians. The central angle is multiplied by a sphere radius of 6,371 km.
a = sin²(Δφ / 2) + cos(φ₁) cos(φ₂) sin²(Δλ / 2) c = 2 atan2(√a, √(1 − a)) distance = 6371 × c kilometres
φ is latitude; λ is longitude. The intermediate value a is clamped to [0, 1] to guard floating-point rounding near coincident or opposite points.
Units and display
The same underlying kilometre result is divided by 1.609344 for miles, or 1.852 for nautical miles. These conversion constants are explicit implementation settings. Display is rounded to one decimal place; it is not an accuracy guarantee.
What this cannot tell you
No terrain, Earth ellipsoid, road network, border restrictions or transport choices are modelled. Do not use the result as a safe navigation route or a travel estimate.
Evidence boundary
The canonical supported claim covers the haversine spherical method, reviewed against the existing Movable Type Scripts reference on 7 October 2026. No claims about market demand, search volume or commercial performance follow from that review.
Reproducibility checks
Identical inputs return zero. Separation is symmetric when points are swapped. Synthetic equatorial quarter-sphere inputs return approximately 10,007.5 km. Opposite inputs return approximately 20,015.1 km.