FindMyQibla

Guide · 4 minutes

How the Qibla Direction Is Calculated

The Qibla is the shortest path over a curved Earth. This is the maths behind the bearing — in plain language, with the actual numbers we use.

The idea in one paragraph

Take your position and the Kaaba’s position, both as latitude and longitude. Draw the shortest path between them over the Earth’s surface — a great circle, like the equator but tilted. The angle where that path leaves your position, measured clockwise from true north, is the Qibla bearing. That single formula is the entire calculation.

The actual numbers we use

  • Kaaba: 21.422487° N, 39.826206° E
  • Earth: treated as a sphere with radius 6,371.0088 km
  • Bearing formula: θ = atan2( sin(Δλ)·cos(φ₂), cos(φ₁)·sin(φ₂) − sin(φ₁)·cos(φ₂)·cos(Δλ) ), where φ₁, λ₁ are your latitude and longitude, φ₂, λ₂ the Kaaba’s, and Δλ their difference in longitude. The result is normalised to 0–360°.
  • Distance: haversine formula with the same inputs, clamped to handle floating-point edge cases.

Feed it London (51.5074° N, −0.1278° E) and you get 119.0° and 4,794 km. Feed it New York (40.7128° N, −74.0060° W) and you get 58.5° and 10,306 km. Same inputs, same outputs, every time — the calculation is deterministic. Try any pair of coordinates in the angle calculator and compare against an independent reference; differences should be fractions of a degree, traceable to how precisely each tool pins the Kaaba’s coordinates.

Why flat maps mislead

The maps most people know — Mercator and its cousins — stretch the poles to make a sphere fit a rectangle. On that stretched picture, a straight ruler line from London to Mecca is not the shortest path; the true shortest path arcs noticeably north, passing over eastern Europe rather than down the Mediterranean. This is the same reason flight paths look “wrong” on a flat map: the curve is the geometry telling the truth, and the straight line is the projection lying.

Practical consequence: never measure a bearing off a flat map with a protractor and expect it to match a great-circle calculation. The two answer different questions. The map page draws the great-circle line for you, so what you see and what the compass says agree.

What the calculation doesn’t cover

  • The Earth isn’t a perfect sphere. It’s very slightly flattened at the poles. Using a spherical model introduces errors measured in hundredths of a degree — far below what any phone compass can resolve.
  • Your position is the weak link. A phone GPS indoors can be 20–50 metres off. That moves the bearing by a fraction of a degree at UK distances — negligible — but the position you feed in matters more than the formula ever will.
  • Bearing ≠ heading. The calculation gives a bearing from true north. Your phone’s idea of north is magnetic, offset by local declination, and polluted by nearby metal. The gap between a perfect bearing and a wobbly phone reading is hardware, not maths — see compass troubleshooting.
  • Near the Kaaba and near the antipode the bearing stops being meaningful: stand inside Mecca and every direction is arguably the Qibla; stand at the exact antipode and all directions are. The tool flags both cases instead of printing a number.

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