How accurate is the Haversine formula?

It is accurate to within about 0.3–0.5%. The formula models the Earth as a perfect sphere of mean radius 6,371 km, whereas the real Earth is an oblate spheroid (6,378 km at the equator, 6,357 km at the poles). For cycling distances under a few hundred kilometres the spherical error is negligible — far smaller than the difference between this straight-line figure and the actual ridden route.

Is this a straight-line distance?

Yes. This is the great-circle (as-the-crow-flies) distance between two points. It is the shortest possible path over the surface of the Earth, so your actual ridden distance will always be LONGER — roads wind, switchback up climbs and rarely run dead straight. On typical UK roads the ridden route is commonly 20–40% further than the straight-line distance.

Does it account for hills and elevation?

No, and deliberately so. A point-to-point straight-line distance has no single climb to apply slope geometry to, and total elevation gain over a winding route cannot be combined with one crow-flies horizontal leg in a single Pythagoras triangle. The extra ground covered by climbing is also tiny: a 150 m gain over a 60 km route adds under 20 cm. The dominant reason your route is longer is road winding, not elevation — use a route planner (Komoot, Ride with GPS, Strava) for true ridden distance.

Where do I find GPS coordinates?

Use Google Maps (right-click any point and click the decimal coordinates to copy), your bike GPS computer, or your smartphone. Coordinates are in decimal degrees: positive north/east, negative south/west — e.g. 51.5074, -0.1278 for London (51.5° N, 0.13° W).

What is the bearing output?

It is the initial compass bearing (forward azimuth) you would set off on to head straight towards the end point, measured clockwise from true north: 0°/360° = north, 90° = east, 180° = south, 270° = west. On a great circle the bearing changes along the way, so this is the bearing at the start point only.

GPS Distance Calculator — Point-to-Point with Elevation

How We Calculate This

Haversine Formula

The Haversine formula calculates the great-circle distance — the shortest path over the surface of a sphere — between two points from their latitudes and longitudes.

a = sin²(Δlat/2) + cos(lat₁) × cos(lat₂) × sin²(Δlon/2)

distance = 2 × R × atan2(√a, √(1−a))

Where R is the Earth's mean radius, 6,371 km (the IUGG-recommended value that minimises RMS error against true geodesic distance).

Initial Bearing

The forward azimuth at the start point is found from:

θ = atan2( sin(Δlon)×cos(lat₂), cos(lat₁)×sin(lat₂) − sin(lat₁)×cos(lat₂)×cos(Δlon) )

normalised to 0–360° clockwise from true north.

Straight-line, not ridden distance

This is the as-the-crow-flies distance. Your actual ridden route will be longer because roads wind and climb — typically 20–40% further on UK roads. For true ridden distance, plan the route in a GPS route planner.

Frequently Asked Questions

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Last updated: 2025-02-20

All calculations are estimates. Always verify results and consult a professional bike fitter where appropriate.

GPS Distance Calculator — Straight-Line Distance Between Two Points

Start Point

End Point