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Haversine Great-Circle Distance Calculator

Computes the great-circle distance, bearings and midpoint between two coordinates on a sphere (IUGG mean radius by default), in kilometres, metres or nautical miles.

100% FreeRuns in your browserIntermediate
How to use this calculator

Inputs

Spherical great-circle distance, central angle, bearings and midpoint between two latitude/longitude points.

Point 1

Decimal degrees (−31.95), DMS (31 57 0 S) or DDM (31° 57.0′ S).

Decimal degrees (115.86), DMS (115 51 36 E) or DDM (115° 51.6′ E).

Point 2

Decimal degrees (−31.95), DMS (31 57 0 S) or DDM (31° 57.0′ S).

Decimal degrees (115.86), DMS (115 51 36 E) or DDM (115° 51.6′ E).

More options

Blank uses the IUGG mean Earth radius, 6,371,008.8 m.

Enter the values and press Calculate.

Or load an example to see a worked result.

The great-circle arc (map-free sketch)
Schematic — no basemap
The great-circle arc (map-free sketch)Locally drawn route sketch on a latitude/longitude grid with the two endpoints and each route model.100°E120°E140°E160°E12Great circle (not unique)
The shortest path on a sphere between two points, drawn locally — no basemap.

Batch from CSV

One row per calculation, with a header row. Values use the units currently selected in the form above. Up to 10,000 rows; nothing is uploaded.

How the method works

A fixed worked example to explain the method — it is not your result.

Great-circle and rhumb-line routes use different heading rules
Illustrative method
Great-circle and rhumb-line routes use different heading rulesLocally drawn route sketch on a latitude/longitude grid with the two endpoints and each route model.75°W45°W15°W12Great circleRhumb line
Example on one sphere (R = 6,371,008.8 m) from 50°N 5°W to 40.7°N 74°W: great circle 5,294.0 km with a changing heading; rhumb line 5,472.5 km on a constant 259.1°. Compare routes on the same sphere before comparing distances.

Before you rely on this: First-pass guide only. Verify safety-critical or regulated work against the relevant standards, your project requirements and a qualified professional.

How to use this calculator

  1. Enter both points' latitude and longitude.
  2. Leave the radius blank for the IUGG mean Earth radius (6,371,008.8 m), or enter your own.
  3. Press Calculate. Read the distance, the central angle, the initial and final bearings and the midpoint.

How it works

a = sin²(Δφ/2) + cos φ₁ cos φ₂ sin²(Δλ/2) and d = R·c, where c is the central angle.

c is evaluated as atan2(|v₁ × v₂|, v₁ · v₂). It is mathematically identical to 2·atan2(√a, √(1 − a)), but stays exact near antipodes, where the textbook form loses about 0.1 m.

Longitude differences are wrapped, so routes across the date line take the shorter crossing and reversing the points never changes the distance.

The initial bearing is undefined for coincident points; for antipodal points neither the bearing nor the midpoint is unique.

Worked example

Perth (−31.95°, 115.86°) → Melbourne (−37.81°, 144.96°). Central angle 24.473109°, distance 2,721.289 km (1,469.379 nmi), initial bearing 111.95°, final bearing 95.05°, midpoint −35.759822°, 129.879430°. The WGS84 ellipsoid gives 2,726.614 km for the same pair.

Common mistakes

  • Treating the result as a road, terrain or grid distance. It is the surface distance on a sphere.
  • Using it where survey accuracy matters. The gap to the ellipsoid depends on the route — about 5 km on the Perth–Melbourne line — so use the Vincenty tool there.
  • Mixing a 6,371 km radius with a 6,371,008.8 m one when comparing results; the radius changes every distance in proportion.

Frequently asked questions

How accurate is haversine?

It is exact for a sphere. Its difference from the real (ellipsoidal) Earth depends on where and in which direction the route runs, so there is no single accuracy figure; for survey-grade distances use the Vincenty ellipsoidal tool.

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Cite this tool

Zerdly. (2026). Haversine Great-Circle Distance Calculator. Retrieved from https://www.zerdly.com/tools/haversine-great-circle-distance-calculator/

Tip: Enter any known values to calculate the remaining results.

Designed to run locally in your browser. Tool inputs are not intentionally stored by Zerdly unless stated otherwise.