How to Calculate Great Circle Distance Between Two Points

Why great-circle distance is the one that counts

A flat chart makes two distant points look joined by a straight line. The Earth isn't flat, so the shortest real path curves toward whichever pole sits on the far side of that line. Over a long enough distance the gap between the great circle and a straight rhumb line stretches into hundreds of miles — which is the actual reason airliners fly an initial heading and then keep adjusting, rather than holding one compass course the whole way.

The great-circle distance formula

The haversine formula works the distance out on a sphere of Earth's radius, from the two latitudes and the difference in longitude. A second formula, same four coordinates, gives the initial course. Both want decimal degrees: South and West are negative, which trips people up more than the actual trigonometry does.

How to calculate it in E6B Calc

On E6B, open Great Circle under Navigation.
Type From latitude and From longitude for the departure point, in decimal degrees.
Type To latitude and To longitude for the destination.
Optionally type a Ground speed to also get the time for the leg.
Read Distance and Initial course. The other two distance units appear below, and a Time line appears once you enter a ground speed.

Worked examples

E6B Calc results; distance 1 decimal, course whole degrees true
From	To	Distance	Other units	Initial course	Time at 420 kt
Chicago 41.9786, −87.9048	London 51.4700, −0.4543	3,425.6 nm	3,942.1 sm, 6,344.3 km	048°T	8 h 9 min
Los Angeles 33.9416, −118.4085	Tokyo 35.5494, 139.7798	4,758.4 nm	5,475.9 sm, 8,812.6 km	306°T	11 h 20 min

Both routes run well north of the line a flat map would make you draw, since 048° and 306° both point noticeably poleward of due east or due west. That's the great circle doing exactly its job: shortest path, not the most intuitive-looking one on a Mercator projection.

Reading the coordinates right

South and West are negative: Sydney is about −33.87 latitude, Los Angeles about −118.41 longitude. A positive Sydney latitude, for example, returns a route straight through the wrong hemisphere.
Decimal degrees only: convert minutes and seconds first (for example 41°58.7'N is 41.978).
A value outside ±90° latitude or ±180° longitude gets flagged Out of range rather than silently returning a wrong answer.
The initial course is true, and it drifts along the route — past the first few hundred miles you're no longer heading exactly 048° or 306°. Normal for a great circle, not a bug.

Questions and answers

What is the great-circle distance formula?

The haversine formula: it takes the two latitudes, the difference in longitude, and Earth's radius, and returns the shortest distance over the curved surface. E6B Calc runs it on the coordinates you type.

Why is the great-circle route not a straight line on a map?

A flat map distorts the sphere. The shortest real path curves toward whichever pole is nearer the straight line, which is why long east-west routes look bowed on a typical map projection.

Does it give the course for the whole flight or just the start?

Just the start. The initial course is correct for the beginning of the great circle; the true course changes gradually as you follow it, which this single calculation does not track leg by leg.

Can I get the time for the leg too?

Yes. Add a ground speed and the screen shows the time, using the same time-speed-distance formula as the Time · Speed · Distance screen.

Is the great-circle calculator free?

Yes, with no limits, like every navigation calculator in the app.

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How do you calculate the great-circle distance between two coordinates?