Great Circle Calculator

• a = sin²(Δφ/2) + cosφ₁·cosφ₂·sin²(Δλ/2)
• distance = 2·atan2(√a, √(1−a)) × 3440.065 nm
• initial course = atan2(sinΔλ·cosφ₂, cosφ₁·sinφ₂ − sinφ₁·cosφ₂·cosΔλ)

New York JFK (40.64° N, 73.78° W) to London LHR (51.47° N, 0.45° W).

1. 1.Convert coordinates to signed decimal degrees (W and S are negative).
2. 2.Haversine central angle × 3440.065 nm ≈ 3009 nm.
3. 3.Initial course = atan2(...) ≈ 051° true.
4. 4.The final course differs (great circles curve) ≈ 108° true.

≈ 3009 nm, initial course ≈ 051°, final course ≈ 108°.

A great circle is the shortest path between two points on the globe — the track airliners actually fly. Because the meridians converge, the true course changes continuously along it, so the initial and final courses differ. Enter each coordinate in decimal degrees and pick its hemisphere; the tool returns the distance, both courses, and the midpoint.

The great-circle track is shortest but its heading changes constantly; a rhumb line holds a constant heading but is longer. On a Lambert chart a great circle plots as a near-straight line — that's why high-latitude navigation uses them.