In order to calculate the specific prayer time of a location we should be able to determine the Longitude (Lng), Latitude (L) as well as the Local time zone of that location. The equation of time (EqT) is also obtained along with declination of the sun (D) using a specific algorithm.
DHUHR
Dhuhr = 12 + TimeZone – Lng/15 – EqT. This is the formula for Dhuhr, it calculates midday which is the point at which the sun rises to its highest in the sky.
SUNRISE/SUNSET
The time difference between the mid-day and the time at which sun reaches an angle α below the horizon can be computed using the following formula:
Both astronomical sunrise and sunset and sunset occur at α=0. But due to refraction of light by terristial atmosphere, actual sunrise appears slightly before astronomical sunrise and actual sunset occurs slightly after astronomical sunset.
The formula for actual sunrise and sunset is as follows:
Sunrise = Dhuhr – T(0.833), Sunset = Dhuhr + T(0.833).
FAJR/ESHA
There is not a universal rule on the angle to be used in calculating Fajr and Isha. There are different views depending on your country or region. The table below illustrates the different conventions used in some countries.
Convention Fajr Angle Isha Angle
Muslim World League 18 17
Islamic Society of North America (ISNA) 15 15
Egyptian General Authority of Survey 19.5 17.5
Umm al-Qura University, Makkah 18.5 90 min after Maghrib 120 min during Ramadan
University of Islamic Sciences, Karachi 18 18
Institute of Geophysics, University of Tehran 17.7 14*
Shia Ithna Ashari, Leva Research Institute, Qum 16 14
* Isha angle is not explicitly defined in Tehran method.
For example, according to Muslim World League convention, Fajr = Dhuhr – T(18) and Isha = Dhuhr + T(17).
ASR
There are two different views when it comes to calculating the Asr prayer time. The majority of schools (including Shafi’i, Maliki, Ja’fari, and Hanbali) say it is at the time when the length of any object’s shadow equals the length of the object itself plus the length of that object’s shadow at noon. The dominant opinion in the Hanafi school says that Asr begins when the length of any object’s shadow is twice the length of the object plus the length of that object’s shadow at noon.
The following formula computes the time difference between the mid-day and the time at which the object’s shadow equals t times the length of the object itself plus the length of that object’s shadow at noon:
Thus, in the first four schools of thought, Asr = Dhuhr + A(1), and in Hanafi school, Asr = Dhuhr + A(2).
MAGRHIB
The Sunni’s believe that the time for Maghrib prayer begins once the Sun has completely set beneath the horizon, that is, Maghrib = Sunset (some calculators suggest 1 to 3 minutes after Sunset for precaution). In the Shia’s view however, the dominant opinion is that as long as the redness in the eastern sky appearing after sunset has not passed overhead, Maghrib prayer should not be performed. It is usually taken into consideration by assuming a twilight angle like Maghrib = Dhuhr + T(4).
MIDNIGHT
Midnight is generally calculated as the mean time from Sunset to Sunrise, i.e., Midnight = 1/2(Sunrise – Sunset). In Shia point of view, the juridical midnight (the ending time for performing Isha prayer) is the mean time from Sunset to Fajr, i.e., Midnight = 1/2(Fajr – Sunset).