Destination on a constant course (rhumb line)
Where a constant course (rhumb line, loxodrome) for a given distance ends on the ellipsoid; a rhumb that would cross a pole stops there.
Planning and education aid. Not for primary navigation. Full disclaimer
The destination is 42.5132805°, -62.0479152°.
- Destination longitude
Provenance
- Computed by
- navigation.rhumb.direct 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 away from the poles; starts within 0.01° of a pole within 20 µm
- Notes
- None
- Cites
- Karney, C. F. F., GeographicLib, GeographicLib Rhumb class and RhumbSolve
Something look off?
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 away from the poles; starts within 0.01° of a pole within 20 µm
When to use this: Use this when a course is held constant rather than flown as the shortest path: marine navigation on a single heading, a leg drawn on a Mercator chart, or any layout where the bearing must not change along the line. Given a start, a constant course, and a distance, it gives where you arrive on the ellipsoid.
Limitations: A rhumb line is longer than the geodesic, and much longer on high-latitude east-west runs; the inverse tool reports that difference. A rhumb course that would carry you over a pole stops at the pole instead, because the line spirals there. The course is true rather than magnetic, and this is geometry, not a route clear of terrain or traffic.
Worked example: 1,000 km from JFK on a constant course of 078°. Source: GeographicLib RhumbSolve on WGS 84.
You enter
- Constant course
- 78 deg
- Distance
- 1000 km
- Start latitude
- 40.6413 deg
- Start longitude
- -73.7781 deg
You get
- Destination latitude
- 42.5132805°
- Destination longitude
- -62.0479152°
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: 25 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.