Qibla Direction Calculator

The Qibla is the direction of the Kaaba in Makkah. Because the Earth is round, the direction you face is the start of the great circle from your place to the Kaaba: the shortest path over the Earth's surface, the way a plane flies. Its angle, measured clockwise from true north, is the Qibla bearing. This is the method used by almost every mosque, Islamic authority and Qibla app today.

The formula

Δλ = Kaaba longitude − your longitude
y = sin Δλ × cos(Kaaba latitude)
x = cos(your latitude) × sin(Kaaba latitude) − sin(your latitude) × cos(Kaaba latitude) × cos Δλ
Qibla = atan2(y, x), turned into 0° to 360° clockwise from true north
distance: cos c = sin(your lat) × sin(Kaaba lat) + cos(your lat) × cos(Kaaba lat) × cos Δλ, then c (in radians) × 6,371 km

The Kaaba is at 21.4225° N, 39.8262° E. North and east are positive, south and west negative. atan2(y, x) is the angle whose tangent is y ÷ x, placed in the right quarter of the circle by the signs of y and x. The distance shown in the result uses the Earth's true oval shape (the WGS-84 ellipsoid, Vincenty's method), which is a few km more accurate than the round-Earth figure.

Worked example

Take Dubai: 25.2048° N, 55.2708° E.

Δλ = 39.8262 − 55.2708 = −15.4446°. So sin Δλ = −0.26631 and cos Δλ = 0.96389. For the latitudes, sin 25.2048° = 0.42586, cos 25.2048° = 0.90479, sin 21.4225° = 0.36524 and cos 21.4225° = 0.93091.

y = −0.26631 × 0.93091 = −0.24791.

x = 0.90479 × 0.36524 − 0.42586 × 0.93091 × 0.96389 = 0.33047 − 0.38212 = −0.05165.

y ÷ x = −0.24791 ÷ −0.05165 = 4.7998, and the angle with that tangent is 78.23°. Both y and x are negative, so the direction is in the south-west quarter: 180° + 78.23° = 258.23°. The Qibla from Dubai is 258.2° from true north, west-south-west, or 11.8° south of due west (270° − 258.2°).

Distance: cos c = 0.42586 × 0.36524 + 0.90479 × 0.93091 × 0.96389 = 0.15554 + 0.81186 = 0.96740, so c = 14.669° = 0.25602 radians, and 0.25602 × 6,371 km = 1,631 km on a round Earth. On the true oval Earth it is 1,633 km (1,015 miles, 882 nautical miles), which is what the result shows.

Qibla from major cities

Great circle or rhumb line?

A rhumb line keeps one compass heading the whole way, so it is a straight line on a normal (Mercator) map. It looks natural on a flat map, but it is longer. From New York the rhumb line to Makkah heads 101.3° (east-south-east), while the great circle starts at 58.5° (east-north-east). Measured on the same round Earth, the rhumb line is about 10,965 km and the great circle about 10,306 km, so the flat-map route is about 660 km longer. Islamic scholars and bodies such as national religious authorities use the great-circle direction, because the Qibla means facing the Kaaba by the shortest way across the Earth. A few older North American mosques were built facing south-east using the flat-map direction. Switch to Advanced to compare the two for your place. Close to Makkah the two are almost the same.

True north and magnetic north

The bearing above is from true north (towards the North Pole). A magnetic compass points to magnetic north, which differs by the magnetic declination: a few degrees in the Gulf and India, but 10° to 15° or more in parts of North America. To use a compass, subtract an east declination from the true bearing (or add a west one). Example: with 2° E, a true 258.2° reads 256.2° on a compass. Your phone's compass app or NOAA's magnetic field calculator shows the declination for your place; this calculator does not guess it for you.

Using the sun

When the sun is directly over the Kaaba (around 27–28 May and 15–16 July, at about 12:18 and 12:27 Makkah time), it sits exactly in the Qibla direction for everyone who can see it, so shadows point straight away from the Qibla. When it is over the opposite side of the Earth (about 12–13 January and 28–29 November, around 00:29 and 00:09 Makkah time, which is daytime in the Americas and the Pacific), shadows point towards the Qibla. The exact date and minute shift slightly from year to year; the calculator works them out from the sun's position (NOAA solar equations) for the coming year and shows them in your time zone. A few minutes either side still gives a direction good to a degree or two in most places.

Method: great-circle initial bearing on a sphere and distance on the WGS-84 ellipsoid (Vincenty). Bearings and distances were checked on 13 October 2026 against an independent calculation in Python (3-D vectors for the bearing, geographiclib for the distance) for Doha, Dubai, London, New York, Jakarta, Sydney and Cape Town, all within 0.01° and 1 km. Sun times were checked against the astral library to within a minute. City coordinates are for the city centre; for the exact spot, type your coordinates or use your location.