Work out prayer time estimate instantly with clear inputs, formula shown and shareable results.
Solar declination is computed from the day of the year, the sunrise hour angle from the standard cos H = -tan(latitude) tan(declination), and Fajr and Isha from the same relation at the chosen twilight depression angle. These are solar times, not clock times, so a longitude and timezone correction plus the equation of time is needed before they match a published prayer timetable.
Hour angle
cos H = -tan(latitude) x tan(declination); day length = 2H / 15 hours
Twilight
cos H = (sin(-angle) - sin(lat) sin(decl)) / (cos(lat) cos(decl))
cos H = -tan(latitude) x tan(declination); day length = 2H / 15 hours. Solar declination is computed from the day of the year, the sunrise hour angle from the standard cos H = -tan(latitude) tan(declination), and Fajr and Isha from the same relation at the chosen twilight depression angle.
These are solar times, not clock times, so a longitude and timezone correction plus the equation of time is needed before they match a published prayer timetable.
Enter latitude, date, twilight angle for fajr and isha. The defaults shown are a realistic worked example — swap in your own figures to get a result you can use.