Rhumb line distance and course

The constant course and distance of the rhumb line (loxodrome) between two points on the ellipsoid, and how much longer it is than the shortest route.

Go the other way: Destination on a constant course (rhumb line) →

Planning and education aid. Not for primary navigation. Full disclaimer

Computing your own values needs JavaScript and WebAssembly. The worked example below was computed when this page was built, and the documentation under "How we got this" applies.

5,774.19km

The rhumb line runs 5,774.19 km on a constant course of 77.9684139°, 219.281 km longer than the shortest route.

Constant course
Geodesic distance
Extra distance
Extra over the geodesic (%)

Provenance

Computed by: navigation.rhumb.inverse 1.0.1, core 0.1.0
Model: Rhumb line on WGS 84 (conformal latitude and Krüger series)
Accuracy: Within 1 µm of GeographicLib's RhumbSolve (47 nm typical); the course within 1e-10°
Notes: None
Cites: Karney, C. F. F., GeographicLib, GeographicLib Rhumb class and RhumbSolve; Karney, C. F. F., Journal of Geodesy, Algorithms for geodesics

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Start latitude Decimal degrees, north positive, like 40.6413 · plain numbers mean degrees Start longitude Decimal degrees, east positive, like -73.7781 · plain numbers mean degrees End latitude Decimal degrees, north positive, like 40.6413 · plain numbers mean degrees End longitude Decimal degrees, east positive, like -73.7781 · plain numbers mean degrees Ellipsoidoptional wgs84 (default), grs80, clarke1866, intl1924, airy1830, bessel1841, or krassovsky1940

More options 2

Custom semi-major axisoptional With inverse flattening, like 3396190 m (Mars) · plain numbers mean m Custom inverse flatteningoptional Like 169.894; 0 for a sphere

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How we got thisFormula, worked example, sources, and proof

Model: Rhumb line on WGS 84 (conformal latitude and Krüger series, as GeographicLib's Rhumb)

Accuracy: Within 1 µm of GeographicLib's RhumbSolve (47 nm typical); the course within 1e-10°

When to use this: Use this when you want the single course that connects two points and the distance along it: the heading to steer without changing it, a line as drawn on a Mercator chart, or a comparison against the shortest route. The extra distance over the geodesic is reported, which is what tells you whether holding one course is worth it.

Limitations: The rhumb line is not the shortest path, and near the poles the difference grows quickly. The course is true. As with any two-point geometry here, it takes no account of terrain, airspace, traffic, or current, and a course held on a compass also needs the magnetic variation applied.

Worked example: New York JFK to London Heathrow by rhumb line. Source: add-navigation-and-geometry rhumb scenario: course 77.968°, 5,774,190 m, 219.3 km (3.9%) longer than the geodesic. It is golden test vector v001, and every build checks the tool still gives its answer within its tolerance.

You enter

Start latitude: 40.6413 deg
End latitude: 51.47 deg
Start longitude: -73.7781 deg
End longitude: -0.4543 deg

You get

Rhumb distance: 5,774.19 km
Constant course: 77.9684139°
Geodesic distance: 5,554.909 km
Extra distance: 219.281 km
Extra over the geodesic (%): 3.95

Review: Not yet independently reviewed by a geodesist.

Last verified: 2026-09-18, when a maintainer last confirmed this tool's sources at the issuer. See the sources ledger.

Status: version 1.0.1, core 0.1.0. See this tool in the verification report.

Changes

2026-09-23, fixed: Short distances lost their meaning: a 0.859 m geodesic showed as 0.001 km. Distances in the navigation tools (version 1.0.1) still show to the meter in kilometers, but a short one now keeps three significant digits, down to the millimeter, so it shows as 0.000859 km. Differences such as the rhumb line's extra distance keep fixed decimals. Values are unchanged. Changelog
2026-09-19, changed: The rhumb-line tools are stable. They reproduce Bowditch's Mercator sailing examples (NGA Pub. 9, 2024 edition) to within its 1 minute = 1 nautical mile convention, and match GeographicLib's RhumbSolve within 0.4 µm on 2,000 pairs run through the tools, including nearly east-west, nearly meridional, and near-pole lines. The Bowditch citation is now the 2024 edition, verified at NGA. Results are unchanged. Changelog
2026-09-19, added: New navigation tools: rhumb lines, cross-track and along-track distance, fly-by turn anticipation, time-speed-distance with arrival times, closest point of approach, and route legs with true and magnetic courses; and the first geometry tool, polygon area on the ellipsoid. Changelog

Checked against: 24 golden test vectors (download the test vectors, each with its source and tolerance). See how results are checked and every source.

Sources

GeographicLib Rhumb class and RhumbSolve, Karney, C. F. F., GeographicLib, GeographicLib 2.x. Rhumb lines on the ellipsoid (Rhumb, RhumbSolve). Read free.
Algorithms for geodesics, Karney, C. F. F., Journal of Geodesy, Vol. 87, No. 1. pp. 43-55.

Learn the concept: Haversine vs. geodesic distance explained

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