Prayer Time Calculation Methods and Angles

Open two prayer apps in the same city and Fajr can differ by fifteen minutes. That usually isn't a bug. It usually means each app is answering a slightly different question: when do we say Fajr has begun? This page explains how that question is turned into arithmetic, and exactly what this site does.

What is actually being computed

Prayer times aren't a stored timetable. They're derived from the sun's position relative to your horizon. The calculation needs three inputs: latitude, longitude, and the date. From those it derives the sun's declination for that day and the equation of time, then solves for the moment the sun reaches a given altitude.

Some times have a direct geometric definition: Dhuhr is when the sun crosses the meridian; sunrise and Maghrib are when the sun's disc meets the horizon. Fajr and Isha are different. Both are tied to twilight, and twilight is a gradual fade, not a sharp instant. That is precisely where methods diverge.

What a "Fajr angle" means

Because twilight is gradual, a measurable threshold was needed. The one adopted is how far the sun has sunk below the horizon.

When a method uses a Fajr angle of 18°, it means: find the moment the sun's centre sits 18 degrees below the horizon before sunrise. A larger angle puts the sun deeper down, so the time comes earlier. A 19.5° Fajr is earlier than a 15° Fajr.

The size of that gap isn't constant. At mid-latitudes one degree is worth roughly five minutes in winter and can reach seven minutes near the summer solstice, because the sun descends at a shallower angle and takes longer to cross the same degree. This seasonal variation is a major reason the difference between two apps isn't stable across the year.

The methods this site implements

Seventeen methods are implemented. Every figure below is what the calculation actually uses:

Fajr ranges from 12° to 20° across that table. That spread isn't a difference in computational accuracy — it's a difference in the threshold each authority adopted, which is a scholarly and institutional judgement, not a programming one.

Angle versus fixed interval

Three methods above don't use an angle for Isha at all: Umm al-Qura, Gulf Region, and Qatar. They add a fixed interval after Maghrib.

Here is Makkah on the Umm al-Qura method, computed by this site's engine:

The interval never moves, while an angle-based Isha produces an interval that shifts with the seasons. In Makkah on 21 June 2026, MWL's 17° Isha falls at 20:26 while Umm al-Qura gives 20:36 — ten minutes apart. On 21 December the gap widens to fifteen minutes. That is the practical difference between an angle and an interval.

TimesPrayers currently applies a fixed 90-minute interval after Maghrib throughout the year.

When an authority applies minute adjustments

Some authorities don't publish only a raw angle. They publish a table that already contains precautionary minutes — temkin in Turkey, ihtiyat in Malaysia and Indonesia. Compute the angle alone and you'll miss the official table by several minutes.

Turkey

Turkey is the clearest officially documented case. Diyanet İşleri Başkanlığı, the Turkish authority for religious affairs, publishes an explicit temkin table: sunrise is shifted seven minutes earlier, while five minutes are added to Dhuhr, four to Asr and seven to Maghrib; no adjustment is applied to imsak or Isha. This site applies those same published adjustments on top of the 18°/17° angles.

Malaysia

In Malaysia, JAKIM uses 20° for Fajr and 18° for Isha. TimesPrayers applies its own minute adjustments to align with published schedules; these adjustments are not official figures attributed to JAKIM.

Indonesia

In Indonesia, this site uses the 20° and 18° angles matching the Ministry of Religious Affairs criteria, and applies no separate ihtiyath minute adjustment. Kemenag materials describe precautionary minute additions in the preparation of prayer schedules; that is not applied here.

Morocco

In Morocco, this site uses an 18° Fajr with a fixed six-minute shift earlier. We compared the result against the published Rabat schedule of the Ministry of Habous and Islamic Affairs on four dates in August–September 2026, and our Fajr landed within one to two minutes of the published time in the sample examined. We do not attribute a specific calculation angle to the ministry.

How Asr is computed

Asr has two widely used definitions, both based on shadow length:

• Shadow factor 1 — Asr begins when an object's shadow equals its own length, plus the shadow at noon. This is the default here.
• Shadow factor 2 — Asr begins when the shadow reaches twice the object's length, plus the noon shadow.

The difference is substantial, not marginal. In Cairo on 21 March 2026 under MWL, factor 1 gives Asr at 15:30 and factor 2 gives 16:24 — fifty-four minutes apart.

The site supports both definitions and uses shadow factor 1 by default. Which definition a user follows depends on the school or authority they follow.

How the method is chosen automatically

When you open a city page, the site picks the method by that city's country: Egypt and Libya use the Egyptian method, France the French union's, Turkey Diyanet, Iran Tehran, Pakistan/India/Bangladesh/Afghanistan Karachi, Malaysia JAKIM, Indonesia its Ministry of Religious Affairs, Singapore and Brunei the regional method. Any country not mapped uses MWL as the fallback method in the current implementation.

What this looks like in the final times

One example ties it together. Cairo (30.0444°N, 31.2357°E), 21 March 2026, UTC+2, computed by this site:

Sunrise, Dhuhr and Maghrib are identical across all five — their definitions are geometric and don't depend on a chosen twilight threshold. The entire spread sits in Fajr and Isha: twenty-one minutes between the narrowest Fajr angle (ISNA 15°) and the widest (Egyptian 19.5°). Asr matches here because all five share the same default shadow factor.

High latitudes

The further you go north or south, the sooner you reach a day when the sun never sinks to the required angle at all — so there is no astronomical Fajr or Isha that day. A night-splitting estimation rule is used instead. This site implements three common rules, plus a fourth of its own used for German locations that chooses between the real calculation and the estimate depending on whether the angle is genuinely reached with enough margin. A separate guide covers this in detail.

Choosing what suits you

The practical rule is simple: follow what your mosque or your country's authority uses. The point is to pray with the congregation, not to match a number. That is why the site defaults to the method associated with the city's country.

If you compare against another source, compare fairly: same date, same coordinates, same method, same Asr definition. Most apparent errors turn out to be two different settings.