Which Way Is It? The Direction to Anywhere on Earth
Ask which way Mecca is from New York and a flat map says southeast. Every qibla compass in New York points northeast. The compass is right.
Two answers to "which way?"
For a place a few kilometres away, "which way is it?" has one obvious answer. For a place on the other side of the world it has two. There is the direction a flat map suggests, and there is the true direction: the way you would face to set off along the shortest route over the globe.
The true direction is the initial bearing of the great circle between the two places. It is what a globe, a flight planner and a qibla compass all use, and it can differ from the flat-map direction by 40 degrees or more.
The qibla: a real-world great circle
Muslims face the Kaaba in Mecca during prayer, and the direction to it is called the qibla. Mosques and qibla apps generally use the great-circle direction, the start of the shortest route over the globe.
From North America that gives an answer that surprises people. Mecca lies well south of New York, about 21 degrees north against 41, so a flat map suggests facing southeast. But the shortest route curves up over the North Atlantic, and the qibla in New York is about 58 degrees, east-northeast.
The qibla from major cities
Great-circle direction to the Kaaba, measured clockwise from true north, with the distance.
| City | Direction | Distance |
|---|---|---|
| London | 119 degrees (ESE) | 4,794 km |
| Paris | 119 degrees (ESE) | 4,496 km |
| New York | 58 degrees (ENE) | 10,306 km |
| Toronto | 55 degrees (NE) | 10,496 km |
| Los Angeles | 24 degrees (NNE) | 13,424 km |
| Istanbul | 152 degrees (SSE) | 2,405 km |
| Cairo | 136 degrees (SE) | 1,287 km |
| Lagos | 63 degrees (ENE) | 4,251 km |
| Cape Town | 23 degrees (NNE) | 6,558 km |
| Delhi | 267 degrees (W) | 3,835 km |
| Kuala Lumpur | 293 degrees (WNW) | 6,974 km |
| Jakarta | 295 degrees (WNW) | 7,920 km |
| Tokyo | 293 degrees (WNW) | 9,472 km |
| Sydney | 277 degrees (W) | 13,236 km |
Directions are from true north. A magnetic compass needs the local declination applied, which qibla apps do automatically.
The poles: the easy ones
From anywhere on Earth, the North Pole is due north, 000 degrees, and the South Pole is due south, 180 degrees. That is simply what north and south mean: true north is the direction towards the North Pole along your meridian.
Stand on the North Pole itself and every direction is south. Stand on the exact opposite side of the Earth from somewhere, its antipode, and every direction leads there: from Madrid, the antipode is near the town of Weber on New Zealand's North Island, and a great circle in any direction you choose would reach it.
How the direction is calculated
The initial great-circle bearing from point 1 to point 2, with latitudes φ1, φ2 and the difference in longitude Δλ, is: θ = atan2( sin Δλ · cos φ2 , cos φ1 · sin φ2 - sin φ1 · cos φ2 · cos Δλ ).
- New York (40.71 N, 74.01 W) to London (51.51 N, 0.13 W): Δλ = 73.88 degrees
- Top: sin 73.88 × cos 51.51 = 0.598; bottom: cos 40.71 × sin 51.51 - sin 40.71 × cos 51.51 × cos 73.88 = 0.481
- atan2(0.598, 0.481) = 51.2 degrees
The shortest route from New York to London sets off at about 051 degrees, northeast. Add 360 to a negative result so the bearing always lands between 0 and 360.
Directions in GeoAzimuth
GeoAzimuth runs this calculation in reverse. Each arrow shows the direction from a hidden city to a real city you know, worked out exactly like the example above. Knowing that long-distance directions bend towards the poles is often what cracks a hard level.
Check what you learned
Five questions on the direction to faraway places. Pass at 70% or better to complete the lesson.
Practice with Games
Ready to test what you learned? Jump into a game and put it into practice.
The direction to anywhere, in one paragraph
The true direction from one place to another is the initial bearing of the great circle between them: the compass direction you would face to set off along the shortest route over the globe. For nearby places it matches what a map shows, but for faraway places it can differ from the flat-map direction by 40 degrees or more. The classic example is the qibla, the direction Muslims face towards the Kaaba in Mecca: from New York it is about 58 degrees, east-northeast, even though Mecca lies much further south, because the shortest route curves over the North Atlantic. The bearing is calculated with θ = atan2(sin Δλ · cos φ2, cos φ1 · sin φ2 - sin φ1 · cos φ2 · cos Δλ), giving about 051 degrees from New York to London. From anywhere, the North Pole is due north and the South Pole due south, and following a great circle the compass heading changes continuously along the way.
Common questions about direction
Which way is Mecca from where I am?
Use the great-circle direction, which is what mosques and qibla apps use. The interactive compass on this page shows it from many cities or from your own location. From London it is about 119 degrees, from New York about 58 degrees and from Sydney about 277 degrees.
Why does the qibla point northeast from North America?
Because the shortest route from North America to Mecca curves north over the Atlantic before coming down to Arabia. A flat map makes the direction look like southeast, but on the globe the great circle leaves heading northeast.
How do I calculate the bearing between two points?
Use the initial great-circle bearing: θ = atan2(sin Δλ · cos φ2, cos φ1 · sin φ2 - sin φ1 · cos φ2 · cos Δλ), where φ are the latitudes and Δλ is the difference in longitude. Convert the result to degrees and add 360 if it is negative.
Which direction is the North Pole?
From anywhere on Earth it is due north, 000 degrees, because true north is defined as the direction towards the North Pole. A magnetic compass points towards magnetic north instead, which differs by the local magnetic declination.
Is the direction to a place the same as the direction back?
Only over short distances. Over long distances the directions are not exact opposites, because the great circle changes heading along the way. From New York, London is at about 51 degrees, but from London, New York is at about 288 degrees, not 231.