What is the difference between rhumb line and great circle?

A great circle is the shortest path across the curved earth but requires a constantly changing heading. A rhumb line holds a single constant compass course, which is simpler to steer but longer. The gap grows on long, high-latitude, east-west passages.

Why is distance measured in nautical miles?

One nautical mile equals one minute of arc of latitude, about 1.852 kilometres. This ties distance directly to angular position on the globe, which is why marine and air navigation use it. A speed of one nautical mile per hour is one knot.

How is great-circle distance calculated?

The tool uses the haversine formula on the two latitude/longitude points to get the central angle between them, multiplies by the earth's radius, then converts to nautical miles. Haversine is numerically stable even for very short distances.

When is the rhumb-line saving worth taking?

On short or near north-south passages the two routes are almost identical, so the constant-heading rhumb line is fine. On long east-west ocean crossings at high latitude the great circle can save many miles and hours, justifying the course changes.

Does this account for land, currents, or weather?

No. It returns the straight geodesic and constant-course distances over open water only. Real passage plans must route around land and traffic separation schemes and adjust for currents, weather routing, and draft restrictions.

Nautical Distance Calculator (Rhumb & Great-Circle)

For passage planning you need two numbers: the great-circle distance, which is the shortest path across the curved earth, and the rhumb-line distance, which holds a single constant compass heading. This calculator returns both in nautical miles from two lat/long positions, plus the initial course and the miles you save by sailing the great circle.

How it works

The great-circle distance uses the haversine formula to find the central angle between the two points, then scales by the earth’s radius:

a = sin²(Δφ/2) + cos φ1 · cos φ2 · sin²(Δλ/2)
central angle = 2 · atan2(√a, √(1−a))
distance (nm) = central angle · 3440.065

The rhumb line uses the Mercator inverse, where the constant course holds against a straightened-out longitude scale:

Δψ = ln( tan(π/4 + φ2/2) / tan(π/4 + φ1/2) )
q   = Δφ / Δψ   (or cos φ1 near east-west tracks)
rhumb distance (nm) = √(Δφ² + q²·Δλ²) · 3440.065

Here φ is latitude in radians, λ is longitude, and 3440.065 is the earth’s radius expressed in nautical miles.

Example and tips

From the English Channel to New York the great circle bows north toward Newfoundland and can save dozens of miles over the flat rhumb line, but it demands continual course changes. On a short hop down a coastline the two distances differ by a fraction of a mile, so steering a single rhumb-line heading is simpler with no real penalty. Remember both figures are open-water geodesics — real routing must clear land, traffic separation schemes, and weather.