Qibla Direction Calculator

How it works

Initial great-circle bearing θ = atan2( sin Δλ · cos φ₂ , cos φ₁ · sin φ₂ − sin φ₁ · cos φ₂ · cos Δλ ) with the Kaaba at 21.4225° N, 39.8262° E; magnetic bearing = true bearing − declination (east +); distance = R · arccos(sin φ₁ sin φ₂ + cos φ₁ cos φ₂ cos Δλ)

The Qibla is the direction of the Kaaba, and on a round Earth “direction” means the initial bearing of the shortest path, the great circle. That produces results that surprise map readers: from New York the Qibla is north-east, not east-south-east, because the shortest route arcs over the North Atlantic — the same reason airliners fly polar routes. A compass needle points to magnetic north, which differs from true north by the local declination (a dozen degrees or more in places), so the true bearing must be corrected for a physical compass, though phone apps handle this. Twice a year the sun passes directly over Mecca, and at that moment every shadow on the sunlit half of the planet points away from the Qibla — a centuries-old check that needs no instruments.

Worked example

From New York (40.71° N, 74.01° W) the great-circle bearing to the Kaaba is 58.5° — north-east — at a distance of about 10,300 km; with −12.5° of magnetic declination a compass should read about 71°. The constant-bearing rhumb line would point 101°, about 43° away, which is why using a flat map misleads.

Frequently asked questions