📏 Distance on a curved Earth

Why this matters

Distance powers “near me,” service radii, route checks, field planning, clustering, and proximity alerts. The Earth is curved, while most screens are flat, so the calculation method matters.

Learn it

For two longitude/latitude positions, the Haversine formula estimates great-circle distance on a sphere. It converts angular differences into a central angle, then multiplies by an Earth radius. For higher-accuracy work, ellipsoidal geodesic methods model the Earth more precisely. The important skill is knowing what approximation you are using and whether it is good enough for the decision.

Work through an example

Two points may look close on a web map but the screen distance changes with zoom and projection. A geographic distance calculation uses their coordinates instead of measuring pixels.

a = sin²(Δφ/2) + cos φ₁ · cos φ₂ · sin²(Δλ/2)
c = 2 · atan2(√a, √(1−a))
d = R · c

Practice

1. 1Choose two positions in the distance exercise and calculate their Haversine distance.
2. 2Move one point north and predict whether the result grows or shrinks before recalculating.
3. 3Compare the result with the kind of accuracy your project actually needs.

Try it