Haversine Distance Formula

The formula: a = sin²(Δlat/2) + cos(lat1) × cos(lat2) × sin²(Δlon/2); c = 2 × atan2(√a, √(1-a)); d = R × c. Where R is Earth's mean radius (6,371 km) and lat/lon are in radians.

The Haversine distance is a straight-line 'as the crow flies' measurement. It doesn't account for roads, traffic, or routing. Road distance is typically 20–40% longer than Haversine distance in the UK, depending on the road network. In rural areas with winding roads, the multiplier can be even higher.

WorthThePump uses Haversine distance as a practical approximation for two reasons: (1) it's computationally fast — calculating road distances for 500+ stations simultaneously using a routing API would be extremely slow and expensive; (2) it's directionally correct — if Station A is 1 mile Haversine distance and Station B is 5 miles Haversine distance, Station A will almost always be closer by road too.

The practical implication is that WorthThePump's detour cost estimates are slightly optimistic (the actual road distance will be longer). The real-world detour to a station may cost 20–30% more than calculated. We apply a conservative approach: if it's a borderline case, factor in that the true road distance is probably a bit further.

For precise routing, Google Maps Directions API or HERE API would provide road distances — but these add latency, cost, and API key dependencies. Haversine distance is the right trade-off for a calculator that needs to rank hundreds of stations instantly.