Great Circle Bearing Calculator
The great circle bearing calculator finds the initial compass course and shortest-path distance between two points on Earth using the haversine formula, as described in Bowditch's American Practical Navigator. A great circle is the shortest route between two points on a sphere. Unlike a rhumb line, the bearing changes continuously as you travel; this calculator gives the initial bearing at the departure point. Enter latitudes and longitudes in decimal degrees (negative values for South and West). The result is the true initial bearing (0 to 360 degrees) and the great circle distance in nautical miles.
Great circle bearing formula
dLon = lon2 - lon1 (radians)
bearing = atan2(sin(dLon)*cos(lat2), cos(lat1)*sin(lat2) - sin(lat1)*cos(lat2)*cos(dLon))
Initial bearing = (bearing * 180/pi + 360) mod 360
a = sin(dLat/2)^2 + cos(lat1)*cos(lat2)*sin(dLon/2)^2
Distance (nm) = 2 * atan2(sqrt(a), sqrt(1-a)) * 3,440.065
All angles are converted to radians before calculation. Earth radius used: 6,371 km = 3,440.065 nm.
Understanding great circle navigation
- Great circle routes appear as curved lines on Mercator charts but are straight on gnomonic projections.
- Transoceanic voyages gain significant distance savings over rhumb lines at higher latitudes.
- The initial bearing returned is true bearing. Add magnetic variation to convert to magnetic course.
- For short distances (under 600 nm), the difference between great circle and rhumb line is negligible.
Great circle bearing: frequently asked questions
What is a great circle bearing?
A great circle bearing is the initial direction you must travel along the shortest path (great circle) between two points on a sphere. Because the Earth is curved, this bearing changes as you travel, so it differs from a rhumb line course which maintains a constant compass heading.
How is the initial bearing calculated?
The initial bearing uses the formula: bearing = atan2(sin(dLon)*cos(lat2), cos(lat1)*sin(lat2) - sin(lat1)*cos(lat2)*cos(dLon)), converted to degrees and adjusted to a 0-360 range. This gives the direction at the starting point.
What is the difference between great circle and rhumb line navigation?
A great circle route is the shortest distance on a sphere but requires a constantly changing compass course. A rhumb line maintains a constant compass bearing but is slightly longer than the great circle route, except along meridians or the equator.
Why does my GPS show a different bearing than this calculator?
Small differences arise because GPS devices may use WGS-84 ellipsoid calculations rather than a perfect sphere. For most practical marine navigation purposes, the spherical haversine formula is sufficiently accurate.
What units does the distance output use?
Distance is given in nautical miles (nm), which are defined as 1,852 meters or one minute of arc along a meridian. Nautical miles are the standard unit for marine and aviation navigation.
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.