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For K-12 Students · Great-Circle Distance

Great-Circle Distance for a cell-tower map

Built for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework. Simulate a cell-tower map live below — adjust the inputs and watch it respond, right in your browser.

Great-Circle Distance (Haversine)Live

shortest path on a sphere

Controls

Presets

Point A latitude

Point A longitude

Point B latitude

Point B longitude

The shortest route between two points on Earth is a great-circle arc, not a straight line on a flat map. The haversine formula computes that distance from latitude and longitude, staying accurate even for nearly antipodal points. It powers flight planning, GPS, and every "distance between" feature — and explains why polar routes look curved on a Mercator map.

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Data Inspector

Distance5579 km

In miles3465 mi

Initial bearing51°

Governing equation

d = 2 R arcsin sin^{2} \frac{Δ φ}{2} + cos φ_{1} cos φ_{2} sin^{2} \frac{Δ λ}{2} = 5579 km

Reading this result: A great circle changes heading as you travel, so the 51-degree initial bearing is not the heading you keep — that constant-heading path (a rhumb line) would be longer.

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Frequently asked questions

Is this good for k-12 students?: Yes — this version of "Great-Circle Distance for a cell-tower map" is framed for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.