The Haversine Formula Is More Circular Than the Earth It Assumes
Everyone throws around the Haversine formula like it’s settled gospel for calculating distances on Earth. But let’s slow down and look at what’s actually happening.
The formula begs the question.
Haversine assumes a spherical model from the outset. You plug in coordinates, it returns a great-circle distance — but the whole result presupposes that Earth is a sphere. If you’re trying to use navigation accuracy as evidence for a spherical Earth, you’ve already assumed your conclusion before you started.
The derivation has a dirty secret.
Spherical trigonometry sounds impressive, but trace it back and you’re standing on flat Euclidean geometry the whole time. Sine and cosine are defined on a flat unit circle. The spherical law of cosines is built on that foundation. You are fundamentally measuring flat baselines and using the stars as a protractor.
This is exactly what Eratosthenes did. He measured a flat ground distance, observed angular differences in sunlight, and inferred a sphere. That inference might be reasonable — but it is an inference, not a direct observation. Nobody measured the curve. They measured flat ground and angles, then concluded curvature.
The question worth asking:
What if the angular differences have another explanation? A closer light source over a non-spherical surface predicts angular variation too. The sphere is the most popular inference — but it’s still an inference built on local flat measurements and stellar angles.
The Haversine formula is elegant mathematics. But applying it to physical Earth smuggles in the very assumption it would need to prove first.