NauticTools2Coastal navigation
Great circle navigation – the shortest way across the ocean
On the chart, the straight line between two harbours is not the shortest route. The great circle is shorter – on long east-west passages in higher latitudes often by dozens of miles. NauticTools2 calculates the distance, the initial and final course, the vertex and the waypoints to sail the route.
- Great circle distance
- Initial and final course
- Vertex
- Meridian crossings
- Rhumb line comparison
What is a great circle?
A great circle is any circle on the earth whose centre is the centre of the earth – the equator, for example, or any meridian. The arc of a great circle between two positions is their shortest connection. The catch: it crosses the meridians at ever-changing angles, so the course changes all the time.
A rhumb line, by contrast, keeps a constant course. On a Mercator chart it is a straight line, but on the globe it is a detour. The great circle appears on the chart as a curve bowed towards the pole.
When do you need it?
- Ocean passages: Over long distances the great circle saves time and provisions – across the North Atlantic easily 30 nm or more.
- Route planning: The great circle is split into several rhumb-line legs. Each is sailed on a constant course; together they follow the great circle.
- Knowing the limits: The vertex shows how far towards the pole the route goes – important with ice limits or storm areas.
Formulas and working
Great circle distance
Find the angle d from the formula above; distance = d (degrees) · 60 nm.
Initial course
tan C = sin d.long / (cos latA · tan latB − sin latA · cos d.long), then put it in the right quadrant.
Final course
Work out the initial course from B to A and add 180°.
Vertex
cos latV = sin C · cos latA – the highest latitude of the great circle. Its longitude follows from the difference of longitude to the start.
Meridian crossings
The great circle's latitude at every whole degree of longitude between start and destination, plus course and distance of each leg.
Worked example
From a position south of Cape Race (46°30.0′ N 053°00.0′ W) to a position south of the Isles of Scilly (49°40.0′ N 006°14.0′ W): how long is the great circle, what are its courses, and where is the vertex?
Great circle distance = 1853.6 nm
Initial course = 066.7°, final course = 102.4°
Vertex = 50°47.3′ N 022°17.7′ W
Rhumb line = course 084.2°, 1883.3 nm → saving 29.7 nm
Things to watch out for
- The course keeps changing: Steer the initial course only to the next waypoint, then take the new course.
- Not always worth it: In low latitudes and on north-south passages the saving is small. On a meridian or the equator, great circle and rhumb line are the same.
- Weather and currents matter more: For sailing yachts, wind systems and currents often decide the route more than pure distance.
- High latitudes: The vertex can lie far towards the pole. If necessary, plan a composite route with a limiting latitude.
How it works in NauticTools2
Start and destination
By hand or from saved waypoints. Any position you enter can be saved as a waypoint straight away.
Calculate
Distance, initial and final course, vertex and the rhumb line comparison appear with full working.
Meridian crossings
The table lists the latitude at each whole degree of longitude plus course and distance to the next point. The whole route can be saved as waypoints with one click.
Printable calculation record
Every calculation can be printed as a clear record or saved as a PDF – with inputs, result, full working and, here, all meridian crossings too. Handy for passage planning, in the classroom and for your files.
View the example record as PDF ›
Frequently asked questions
Why is the great circle shorter although it looks longer on the chart?
Because the Mercator chart distorts the earth: everything is stretched towards the poles. What looks like a detour on the chart is the direct route on the globe.
What is the vertex?
The point of the great circle nearest the pole. There the great circle runs exactly east-west; its course is 090° or 270°.
How do you sail a great circle in practice?
Put waypoints on the great circle, for example at the meridian crossings, and sail a rhumb line from waypoint to waypoint. The course then stays constant leg by leg.
Related tools
- Dead Reckoning – course and distance on the rhumb line
- Distance, Speed and Time – passage time from distance and speed
NauticTools2 is free and runs on Windows 10 and 11. An Android version is in preparation.
Get it from the Microsoft Store