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Great circle and rhumb line

Distance and course between two positions: the shortest way (great circle) and the constant-course way (rhumb line), and how much the great circle saves.

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To
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Positions as decimal degrees (−33.8568), degrees and minutes (33 51.408 S) or degrees, minutes and seconds (33°51'24"S). South and west are negative.

Fill in the fields to see the result.

How it works

Great circle: the shortest route on the sphere. Distance from the haversine formula, where one minute of arc is one nautical mile; initial course = atan2(sin Δλ · cos φ₂, cos φ₁ · sin φ₂ − sin φ₁ · cos φ₂ · cos Δλ). The course changes all the way along, so it is sailed as a series of rhumb lines between waypoints.

Rhumb line (Mercator sailing): one course all the way. Course = atan2(Δλ, ΔMP), where ΔMP is the difference of meridional parts; distance = d.lat / cos(course), or departure along a parallel.

Both are worked on a sphere. The spheroidal results of ECDIS and passage-planning software differ by up to about 0.5%. The route across the date line is taken the short way.

For training and cross-checking. Not a substitute for approved navigation equipment, nautical publications and the ship’s own procedures. Calculations run in your browser and nothing you type is stored; a PDF you download is made on our server and not kept.

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