Rhumb Line Distance Calculator
A rhumb line (loxodrome) is a course that crosses every meridian at the same angle, maintaining a constant compass bearing. This calculator computes the rhumb line distance and true course between two points using Mercator sailing formulas from Bowditch's American Practical Navigator. Enter coordinates in decimal degrees (use negative values for South latitude and West longitude). The rhumb line course is ideal for coastal passages where a steady compass heading simplifies steering, even if it is slightly longer than the great circle route.
Rhumb line formula (Mercator sailing)
dLat = lat2 - lat1 (degrees)
dLon = lon2 - lon1 (adjusted for antimeridian)
DMP = ln(tan(pi/4 + lat2/2)) - ln(tan(pi/4 + lat1/2)) (Mercator meridional parts)
Course = atan2(dLon, DMP) converted to 0-360 deg
Distance (nm) = |dLat * 60| / cos(course) (if dLat != 0)
Distance (nm) = |dLon * 60 * cos(lat1)| (if dLat == 0, due E/W)
1 degree of latitude = 60 nautical miles. Meridional parts use the natural log (Mercator) formula.
Rhumb line vs great circle navigation
- Rhumb lines appear as straight lines on Mercator charts; great circles appear as curved lines.
- For coastal passages under 600 nm, rhumb line distance is usually within 1% of great circle distance.
- The constant bearing makes rhumb line steering straightforward with a compass.
- Due East or due West courses follow a parallel of latitude and are pure rhumb lines.
Rhumb line calculator: frequently asked questions
What is a rhumb line?
A rhumb line, also called a loxodrome, is a path on the Earth's surface that crosses all meridians at the same angle. This means the compass bearing remains constant throughout the voyage, making it easy to steer but not the shortest route except along meridians or the equator.
How is rhumb line distance calculated?
Rhumb line distance uses the Mercator sailing formula. The departure and arrival latitudes are converted using Mercator meridional parts. The distance is calculated from the difference in latitude and the delta longitude divided by the course tangent. The result is in nautical miles.
When should I use a rhumb line instead of a great circle route?
Rhumb lines are simpler to steer and are preferred for shorter coastal passages, when the course difference from a great circle is negligible. Great circle routes are preferred for transoceanic passages above 20-30 degrees latitude where distance savings are significant.
Does a rhumb line follow a straight line on a chart?
Yes, on a standard Mercator chart a rhumb line appears as a straight line, which is why Mercator projections are so useful for navigation. On a globe or gnomonic chart, rhumb lines appear as curved spirals.
What is the difference in distance between rhumb and great circle routes?
At low latitudes (equatorial routes), the difference is minimal. At 50 degrees North across the North Atlantic, a great circle can be 100-300 nm shorter than the rhumb line course over a 3,000 nm passage.
Official sources
- National Geospatial-Intelligence Agency: Bowditch American Practical Navigator (Pub. 9).
- NOAA Office of Coast Survey: NOAA Ocean Service.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.