How Prayer Times Are Calculated: The Sun, Twilight Angles, and the Global Methods

The astronomical basis of prayer times

The whole matter reduces to one thing: the sun’s position relative to your horizon on that day. Prayer times are computed from astronomical equations taking your city’s coordinates and the date, yielding three daily quantities: the solar declination (the sun’s position north or south of the equator, ranging ‎+23.44° to ‎−23.44°), the equation of time (a difference of up to about ‎±16 minutes between solar and mechanical clocks), and the sun’s altitude at each prayer:

• Dhuhr: the sun crossing the meridian (solar noon), plus a minute of caution.
• Sunrise and Maghrib: the sun’s edge touching the horizon at ‎−0.83° (the sun’s apparent radius plus atmospheric refraction).
• Fajr and Isha: the sun reaching a defined twilight angle below the horizon, set by the adopting authority.
• Asr: when an object’s shadow equals its own length according to the majority (Shafiʿi, Maliki, Hanbali) or twice its length according to the Hanafi school.

Twilight angles: why the methods differ

All methods agree on Dhuhr and Maghrib — they are sharp astronomical boundaries — and disagree precisely on Fajr and Isha: when does the first true light of dawn appear, and when does twilight fully vanish? Each authority adopted an angle from its own local twilight observations, producing differences that can exceed twenty minutes between two methods in your city. The table below summarizes the major methods with their angles and ranges of use:

The major global methods in detail

Muslim World League (MWL) — Fajr 18°, Isha 17°: headquartered in Makkah and founded in 1962; the most widely used international standard across Europe, Asia and Africa.

Umm al-Qura — Fajr 18.5°, Isha 90 minutes after Maghrib (120 in Ramadan): Saudi Arabia’s official method, detailed in The Umm al-Qura Calendar.

ISNA — Fajr and Isha 15°/15°: adopted by the Fiqh Council of North America in 2007 to suit North American latitudes, where large twilight angles produce extremely late times in summer.

Egyptian General Authority of Survey — Fajr 19.5°, Isha 17.5°: one of the oldest methods, widespread in Egypt, Africa, parts of the Levant and Iraq, known for the earliest Fajr among the methods.

University of Islamic Sciences, Karachi — Fajr and Isha 18°/18°: the standard of Pakistan and the Indian subcontinent, commonly paired with the Hanafi Asr (double shadow).

The high-latitude problem

Above roughly 48° N (London, northern Europe, Canada, the northern US states) the summer sun never descends to 18° below the horizon at all, so Fajr and Isha by large angles are mathematically undefined. Scholars and authorities apply three well-known solutions:

• Nearest valid day: using the angles of the last day before summer on which the computation was valid, or the nearest sound latitude.
• One-seventh of the night: dividing the night into seven parts, with Isha after one part elapses and Fajr one part before sunrise.
• Middle of the night: setting Isha at the midpoint between Maghrib and the next day’s Fajr, and Fajr shortly before sunrise.

A practical fourth option is adopting a smaller angle such as ISNA’s 15°, which remains computable at most inhabited latitudes.

Which method should I choose?

The settled rule: follow your local mosque and authority — the differences between methods are not right against wrong, but the adopted angles of different bodies. Absent a local reference, pick your country or region’s method from the table above. This site sets each city page’s default method by country (Umm al-Qura for Saudi Arabia, Egyptian for Egypt, MWL for Europe, ISNA for North America, and so on), with switching and comparison available. Our equations and methodology are detailed on the methodology page.

Sources and references

• Muslim World League (Makkah): the adopting authority of the MWL method (18°/17°).
• Islamic Society of North America (ISNA): the adopting authority of the North American method (15°/15°).
• King Abdulaziz City for Science and Technology (KACST): reference for the Umm al-Qura parameters (18.5°, Isha 90 minutes after Maghrib).
• Diyanet İşleri Başkanlığı (Turkey): Turkey’s official method (18°/17°).