True Course Calculator

Work out true course instantly with clear inputs, formula shown and shareable results.

About True Course Calculator

The initial great-circle course between two positions comes from the spherical bearing formula, and the distance from the haversine formula using a mean Earth radius of 3440.065 nautical miles. On a long leg the course changes continuously, so the final course differs from the initial one.

Formula

Great-circle course

theta = atan2(sin(dLon) x cos(lat2), cos(lat1) x sin(lat2) - sin(lat1) x cos(lat2) x cos(dLon))

Worked example

With the default values below, True Course Calculator returns Initial true course of 144.8. Change any input above and every figure here is recalculated in your browser.

Inputs used

Departure latitude: 51.5 °
Departure longitude: -0.45 °
Destination latitude: 48.85 °
Destination longitude: 2.35 °

Results

Initial true course: 144.8 °
Great-circle distance: 192.08 nm
Final true course: 147.0 °
Distance in kilometres: 355.73 km

Step by step

1Values used
2Great-circle course
3Initial true course= 144.8 °
4Great-circle distance= 192.08 nm
5Final true course= 147.0 °
6Distance in kilometres= 355.73 km

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 2 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
Aviation results are planning estimates only. Always verify take-off, landing, fuel, weight and balance figures against the certified Aircraft Flight Manual, current performance charts and applicable aviation regulations before flight.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Aviation results are planning estimates only. Always verify take-off, landing, fuel, weight and balance figures against the certified Aircraft Flight Manual, current performance charts and applicable aviation regulations before flight.

Frequently Asked Questions

Why do initial and final course differ?

A great circle crosses each meridian at a different angle. Only tracks along the equator or a meridian keep a constant true course.

Is this the same as a rhumb line?

No. A rhumb line holds a constant course but is longer. The great circle is the shortest path and is what long-range navigation systems fly.