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Great-Circle vs Rhumb Line Distance Comparison

Compare great-circle and rhumb-line distance and bearing between two coordinates, side by side, for navigation planning.

100% FreeRuns in your browserIntermediate
How to use this calculator

Inputs

The shortest route and the constant-bearing route between two points on the same sphere — distances, bearings and the extra distance.

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.

Both routes on the same sphere
Schematic — no basemap
Both routes on the same sphereLocally drawn route sketch on a latitude/longitude grid with the two endpoints and each route model.100°E120°E140°E160°E12Great circle (not unique)Rhumb line (not unique)
Great circle (solid) and rhumb line (dashed) between two points, drawn locally on a latitude/longitude grid.

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. Choose the rhumb direction: the shorter way round (default), or eastward or westward.
  3. Optionally change the sphere radius, or add the WGS84 geodesic as a separate reference.
  4. Press Calculate and compare the two routes, their bearings and the extra distance.

How it works

Great circle: the shortest route on the sphere, d = R·c, with the central angle from the stable atan2 form. Its heading changes along the way, so it has an initial and a final bearing.

Rhumb line: one constant bearing. Δψ = ln(tan(π/4 + φ₂/2) / tan(π/4 + φ₁/2)), q = Δφ/Δψ (or cos φ on an east–west line), d = R·√(Δφ² + q²Δλ²), with Δλ wrapped to the chosen direction.

Extra percentage = (rhumb − great circle) / great circle × 100. A rhumb line is never shorter on the same sphere; the two are equal along the equator and along meridians.

At a pole the longitude is undefined, so the only rhumb line is the meridian — the tool says so instead of returning an infinite value.

Worked example

New York (40.6°, −73.8°) → London (51.6°, −0.5°). Great circle 5,536.892 km starting at 51.17° and arriving on 107.78°; rhumb line 5,755.565 km on a constant 77.73° — 218.7 km (3.95%) longer. The WGS84 geodesic, shown separately, is 5,551.759 km.

Common mistakes

  • Comparing a spherical great circle with an ellipsoidal distance and calling the gap a route difference. Compare routes on the same sphere first.
  • Steering the great circle's initial bearing all the way — it changes continuously.
  • Going the long way round across the date line. The default takes the shorter crossing; choose a direction to force the other.

Frequently asked questions

Which should I use for navigation?

Great circle is shortest; rhumb line is simpler to follow with a constant heading. Long ocean/air routes use great circles split into rhumb-line legs.

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Cite this tool

Zerdly. (2026). Great-Circle vs Rhumb Line Distance Comparison. Retrieved from https://www.zerdly.com/tools/great-circle-vs-rhumb-line-distance-comparison/

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.