BYTETOOLS

Rhumb Line Calculator

Work out the constant compass course and distance between two coordinates, the rhumb midpoint, and how much longer it is than the great circle.

A rhumb line (loxodrome) crosses every meridian at the same angle, so you can steer one compass course the whole way. It is always at least as long as the great circle. Coordinates are WGS-84; the maths is spherical, using a mean radius of 6 371 008.8 m.

From

To

5198.009
Rhumb distance (km)
260.13°
Constant course
5034.219
Great circle (km)
3.25%
Extra distance

Rhumb line

Steer 260.13° (W) for 5198.009 km

Rhumb distance
5198.009 km · 3229.893 mi · 2806.700 nmi
Great-circle distance
5034.219 km · 3128.119 mi · 2718.261 nmi
Great-circle initial bearing
286.90° WNW — and it keeps changing along the way
Extra distance vs the great circle
163.790 km (3.254%)
Rhumb midpoint
46.358750, -38.816798
Midpoint in DMS
46°21'31.50"N 38°49'0.47"W

What is the Rhumb Line Calculator?

A rhumb line, or loxodrome, crosses every meridian at the same angle, so you can hold one compass course from start to finish.

  • Constant course and rhumb distance between any two coordinates
  • Destination mode: a start point plus a course and distance gives the arrival position
  • Loxodromic midpoint, which is not the same as the great-circle midpoint
  • Side-by-side comparison with the great-circle distance and initial bearing
  • Kilometres, miles and nautical miles together, with compass points spelled out
  • Computed locally in your browser — no coordinates are uploaded

How to use the Rhumb Line Calculator

  1. 1

    Choose whether you want the course between two points or the destination from a course and distance.

  2. 2

    Enter the coordinates in decimal degrees or DMS.

  3. 3

    For the destination mode, type the distance to run and the constant course in degrees.

  4. 4

    Pick the distance unit — kilometres, miles or nautical miles.

  5. 5

    Read the course to steer, the distance, the rhumb midpoint and the comparison with the great circle.

About the Rhumb Line Calculator

A rhumb line, or loxodrome, crosses every meridian at the same angle, so you can hold one compass course from start to finish. That is why it has been the navigator's working line since the age of sail, and why it appears as a straight line on a Mercator chart. This calculator gives you the course to steer, the distance to run and the loxodromic midpoint between any two points.

It also shows what the convenience costs. The same panel reports the great-circle distance and initial bearing so you can see exactly how many extra kilometres the constant course adds — negligible on a short hop, substantial on a high-latitude ocean crossing. A second mode works the other way: give it a start point, a course and a distance, and it tells you where you end up.

All courses shown are true bearings, not magnetic, so apply your local variation before steering. Everything runs in your browser with no uploads, so passage plans and waypoints stay on your device.

Frequently asked questions

What is a rhumb line?

It is a path that crosses every meridian at a constant angle, so a vessel following it never changes course. On a Mercator chart it plots as a straight line, which is exactly what that projection was invented for. Mathematicians call it a loxodrome.

When should I use a rhumb line instead of a great circle?

Use a rhumb line for short and mid-length passages where the extra distance is trivial and holding one course is worth far more than saving a few miles. On long east-west runs at high latitude the great circle wins by enough to matter, and navigators split it into rhumb-line legs between waypoints.

How much longer is a rhumb line than the great circle?

It depends entirely on the route. North-south passages are identical, since a meridian is both. Short passages differ by a fraction of a percent. A transatlantic crossing at 50 degrees north can add a few percent, and a long run near the poles can add far more. This tool shows the exact figure for your pair of points.

Is the course magnetic or true?

True — measured clockwise from geographic north. To steer it on a magnetic compass you must apply your local variation, and then deviation for your particular vessel or aircraft. Nautical charts print the variation for the area in the compass rose.

Why can't I use a rhumb line through a pole?

The formula relies on stretched latitude, the same quantity Mercator's projection uses, and it goes to infinity at the poles. A rhumb line approaching a pole spirals in without ever arriving, so the calculator asks you to move the point a little away from exactly 90 degrees.

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