Coordinates · constant bearing
Rhumb line distance and bearing.
Enter two points. Get the distance and single compass bearing along the rhumb line that crosses every meridian at the same angle, and compare it with the great circle.
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Rhumb lines versus great circles
A rhumb line (loxodrome) is a path of constant true bearing: it crosses every meridian at the same angle, so it is a straight line on a Mercator chart and easy to steer. A great circle is shorter but its bearing keeps changing. With Δψ = ln(tan(π/4 + φ2/2) / tan(π/4 + φ1/2)) and q = Δφ / Δψ (or cos φ1 on an east-west line), the Aviation Formulary gives distance = R × √(Δφ² + q² × Δλ²) and bearing = atan2(Δλ, Δψ), with Δλ taken the short way round.
Worked example. Toronto (43.6532, -79.3832) to London (51.5074, -0.1278): rhumb line 5,993 km on a constant bearing of 81.62°, against 5,712 km on the great circle, so the constant heading costs about 280 km extra. Along a single parallel or a single meridian the two distances are the same.
A rhumb line to or from a pole is undefined, because every meridian meets there, and the tool says so. It treats the earth as a sphere with the WGS 84 mean radius.
Frequently asked questions
Which earth radius does this use?
The mean radius of the WGS 84 ellipsoid, 6371.0088 km. Treating the earth as a sphere can differ from an ellipsoidal calculation by up to about 0.3%, so it is right for planning and general use but not for surveying.
Can I type degrees, minutes and seconds?
Yes. Each box accepts decimal degrees (43.6532), degrees and decimal minutes (43 39.19 N) or degrees, minutes and seconds (43°39′11″ N). Use a minus sign or the letters S and W for south and west.
When would I use a rhumb line instead of a great circle?
When holding one compass heading matters more than saving distance, as in traditional chart sailing over short or east-west legs. Over long ocean or air routes the great circle is shorter.
Why can't a rhumb line go to the pole?
A path of constant bearing spirals towards a pole without reaching it, so the distance to the pole itself is not finite by this method.
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Scope
Spherical-earth estimate. Not a navigation aid; check charts, weather and local rules for real passages.