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How to Calculate Islamic Prayer Times

The following equations may be used to calculate the prayer times; copied from a WEB site which I do not remember from where. I still could not figure out how it generates the times.

One should know a little about the Islamic Prayer times to understand the concept behind these calculations. Basicly, Islamic Prayer times are location and date specific. A calculator for general use must have a location input and a date input. Location should be in terms of meridian and parallel of a city (for instance). The calculator then calculates the sun's movement based on the location and the date entered by the user; and then generates the prayer time. The time pattern is quite complex but of course there is a logic behind it.

Here is the calculation:

(R-L) T

Z = 12+ ----- + --- ........1

15 60

1 {sin(-0.8333-0.0347(H)^0.5)}-sinD.sinB

U= -- arccos -------------------------------------- ........2

15 cosD.cosB

1 -sinG-sinD.sinB

V= -- arccos --------------- ........3

15 cosD.cosB

1 sin{arccot(1+tan(B-D)}-sinD.sinB

W= -- arccos -------------------------------- ........4

15 cosD.cosB

1 sin{arccot(2+tan(B-D)}-sinD.sinB

X= -- arccos -------------------------------- ........5

15 cosD.cosB

where

B= latitude of place

L= longitude of place

R= reference longitude (i.e. TIME BAND x 15)

H= height above sea level in metres

D= declination angle of sun from celestial equator (-ve in southern hemisphere)

T= equation of time

G= twilight angle

'Names of prayer times:

Fajr = Z-V

Sunrise = Z-U

Zuhr = Z

Asr1 (Shafi) = Z+W

Asr2 (Hanafi) = Z+X

Maghrib/Sunset = Z+U

Isha = Z+V

The algorithms to calculate T and D are not shown here. These algorithms may be found in, for example, Jean Meeus' Astronomical Algorithms. Zuhr time is calculated using equation 1. The time for sunrise and sunset/ maghrib may be calculated by subtracting or adding 'U'(obtained from equation 2) to the Zuhr time respectively.

Fajr and Isha times may be calculated by subtracting or adding 'V' (obtained from equation 3) to the Zuhr time respectively. The term G (twilight angle) in equation 3 is usually set to 18 degrees. For a location with an extreme latitude, days in summer may be so long that twilight persists between sunset and the next sunrise. Under these circumstances, 'V' is undefined and Fajr and Isha have to be determined using agreed principles of fiqh.

The start of Asr time (Shafi) may be obtained by adding 'W' (obtained from equation 4) to Zuhr; Asr time (Hanafi) is calculated by adding 'X' (obtained from equation 5) to Zuhr.

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"If the Earth were a single state, Istanbul would be its capital." Napoleon Bonaparte

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