Initial Great Circle Bearing
Also known as initial bearing · great circle course · forward azimuth · initial course to steer · bearing between two coordinates
Worked example: JFK → LHR initial bearing → 051.3° true — press Try an example to run it live, then adjust anything.
Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Try different units for next level excitement!
The great circle →
UniversityApplied Field Engineering
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Initial Great Circle Bearing explained
This is the course to steer at the instant of departure, and only at that instant. On any great circle other than a meridian or the equator, the track crosses each successive meridian at a different angle, so the bearing changes continuously the whole way along. That is not a defect of the calculation. It is precisely what makes the great circle shorter than the constant-course alternative, and the two facts cannot be separated.
Treating an initial bearing as a course to hold is the classic error of the subject and it is worth being specific about the damage. Departing New York for London on 051° and holding 051° does not put you in London; it puts you well to the south of it, because the great circle bends north of the constant-bearing track and then comes back down. On a high-latitude crossing the divergence runs to tens of miles within a few hours. The working practice, from Bowditch onward, is to break the great circle into legs — commonly every 5° of longitude, or every few hours of running — and recompute this bearing at each waypoint. What you are actually sailing is a chain of short rhumb lines that approximates the great circle, which is exactly what a chart plotter's route function does for you now.
The two-argument arctangent matters more than it looks. Using a plain collapses the four quadrants into two and returns a bearing 180° wrong for half of all possible destinations — the answer looks perfectly reasonable, which is what makes it dangerous. The function used here keeps the signs of both arguments and then the result is wrapped into 0° to 360°, because that is the range a compass card, a chart and a controller all speak in. A bearing of −130° is a programmer's answer, not a navigator's.
Finally, this is a TRUE bearing: measured from true north, which is where the meridians on the chart point. It is not a compass course and it is not a magnetic course. Before anyone steers it, variation for the place and deviation for the vessel have to be applied, and in the air a wind correction angle goes on before either of those. Each of those has its own page here, and the order they are applied in is not arbitrary.
Initial Great Circle Bearing formula
- = Initial true bearing (°)
- = Latitude of the departure (°)
- = Longitude of the departure (°)
- = Latitude of the destination (°)
- = Longitude of the destination (°)
Missing one of these? Work it out first, then come back
- Initial true bearing — Destination Latitude from Course and Distance, Cross Track Error
- Latitude of the departure — Destination Latitude from Course and Distance, Angle of Incidence on a Tilted Surface
- Longitude of the departure — Longitude to Solar Time Difference, Destination Latitude from Course and Distance
- Latitude of the destination — Destination Latitude from Course and Distance, Angle of Incidence on a Tilted Surface
- Longitude of the destination — Longitude to Solar Time Difference, Destination Latitude from Course and Distance