How to Calculate Fajir Prayer Time

07 Jan

Fajir is the first daily prayer time for practicing Muslims. In general, it begins at dawn’s first light and ends at sunrise. The times of prayer vary around the globe, just as the times of sunrise and sunset vary in different hemispheres. A simplistic method of determining Fajir time is to divide the hours between sunset and sunrise into seven equal parts, with the first daily prayer starting at the beginning of the seventh part. Although slightly time consuming, it is possible to calculate a more accurate time accounting for astronomical factors, such as the earth’s orbit and tilted axis.


  1. Calculate the following values to insert into the equations necessary to know the beginning and ending times of Fajir prayer. Record these values individually for the use of calculations throughout these instructions.
    Find d, using d= Julian date – 2451545.0. The value of Julian date can be found using the online page “Julian Date Converter” (see Resources).
    Find e, using e=23.439 – 0.00000036* d.
    Find g, using g = 357.529 + 0.98560028* d.
    Find q, using q=280.459 + 0.98564736* d.
    Find u, using u= q + 1.915* sin(g) + 0.020* sin(2*g).
    Find RA, using RA= arctan2(cos(e)* sin(u), cos(u))/ 15.

2  Calculate and record the Declination of the Sun, using D= arcsin(sin(e)* sin(u)); and, calculate the Equation of Time using Eq(T)= q/15 – RA.

3  Using the atlas, record the latitude (in the following equations, B) and the longitude (L in the following equations) of the location you will be praying.

4 Record the local time zone of your prayer area, or the number of hours your location is from Greenwich Mean Time (for example, London is 0 and Moscow is 3). Use the time zone to calculate the reference longitude of your location, or Ref.Long.=time zone*15.

5  To calculate the beginning of Fajir prayer use the equation Z-V, where Z=12+((Ref.Long.-L)/15)+(Eq(T)/60), and V=(1/15)*arcos((-sin18-sinD*sinB)/(cosD*cosB)). You have already calculated the values in these equations in the first four steps.

6  If you do not have a prediction of sunrise time, you must calculate the time to know the end of Fajir prayer. You can do this, as well, with the values you have already calculated. Sunrise=Dhuhr-T(0.83); where Dhuhr=12+time zone+(L/15)-(Eq(T)/60), and T(0.83)= (1/15)*arcos((-sin0.83-sinD*sinB)/(cosD*cosB)).

Read more: How to Calculate Fajir Prayer Time |



1 Comment

Posted by on January 7, 2011 in ISLAM (ARTICLES)


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One response to “How to Calculate Fajir Prayer Time

  1. sakthi

    January 7, 2011 at 9:48 am

    asalamu alikku va rahmathullahi thala va barakkathu..!


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