How are prayer times calculated? Sun angles, methods and the Qibla direction

What sets the times: the position of the sun

The five daily prayers are defined not by the clock but by where the sun is in the sky. That is why the times depend on your latitude, longitude and the day of the year, and why Istanbul and Ankara are a few minutes apart: the sun rises and sets earlier further east.

To calculate the times, an app first works out the sun’s position for that day (its declination and the equation of time), then solves one question for each prayer: “how many degrees below or above the horizon is the sun?”

The five times, one by one

• Fajr (dawn): when the true dawn appears. The sun has not risen yet and sits a certain angle below the horizon; depending on the method this is between 15° and 19.5°.
• Sunrise: when the upper edge of the sun appears on the horizon. Because of atmospheric refraction, the sun becomes visible while it is still about 0.83° below the horizon.
• Dhuhr (noon): just after the sun reaches its highest point.
• Asr (afternoon): calculated from shadow length. In the standard (Shafi‘i, Maliki, Hanbali) rule it starts when an object’s shadow equals its height plus its noon shadow; in the Hanafi rule, twice its height plus its noon shadow. Calendars published in Turkey generally use the standard rule.
• Maghrib (sunset): when the sun sets.
• Isha (night): when the twilight glow disappears after sunset. Most methods use the sun reaching 15°–18° below the horizon; some use a fixed interval after Maghrib.

Why do calculation methods give different results?

The Fajr and Isha angles come from the observations and rulings of different institutions. The most common methods are:

In the same city, the gap between 15° and 19.5° can move Fajr by more than 20 minutes. Diyanet also adds a few minutes of precaution (temkin) to the calculated times, a safety margin for different parts of a city and differences in elevation. Most 1–3 minute differences between two apps come from this margin.

What happens at high latitudes?

In summer at high latitudes, such as northern Europe, the sun may never drop 18° below the horizon during the night. Fajr and Isha then cannot be found by angle, so apps use one of several rules: middle of the night, one-seventh of the night or an angle-based ratio. That is why you see bigger differences between apps in summer if you live in Germany or the Netherlands.

How is the Qibla direction found?

The Qibla is the direction of the shortest path to the Kaaba (21.4225° N, 39.8262° E). Because the Earth is a sphere, that path is not a straight line on a map but an arc of a great circle. The direction is given as an angle measured clockwise from north:

qibla = atan2( sin Δλ , cos φ · tan φₖ − sin φ · cos Δλ )

Here φ is your latitude, φₖ the latitude of the Kaaba and Δλ the difference in longitude. A few examples:

How reliable is a phone compass?

Phones measure magnetic north; a good app converts it to true north for your location. Nearby metal, speakers and magnetic cases can still throw it off. Calibrating by drawing a figure “8” in the air and lifting the phone off the table makes a noticeable difference.