About

Islamic prayer times are derived from the apparent position of the Sun relative to the observer's horizon. Each of the five daily prayers (Fajr, Dhuhr, Asr, Maghrib, Isha) corresponds to a specific solar angle or shadow-length ratio. Getting these times wrong by even a few minutes means praying outside the valid window, which invalidates the prayer in all four Sunni madhabs and Jafari fiqh. Manual estimation fails at high latitudes (> 48°N) where twilight persistence distorts Fajr and Isha boundaries.

This calculator implements the full astronomical algorithm: Julian Date conversion, solar declination via the ecliptic longitude of the Sun, the Equation of Time, and hour-angle inversion for each prayer's threshold angle. Calculation methods differ by authority. The Muslim World League sets Fajr at 18° and Isha at 17°. ISNA uses 15° for both. The Egyptian General Authority uses 19.5° and 17.5°. The Umm al-Qura method defines Isha as 90 minutes after Maghrib. Asr timing depends on juristic school: Shafi'i triggers when an object's shadow exceeds its length plus the noon shadow, Hanafi when it exceeds twice its length. This tool computes all variants with atmospheric refraction correction of 0.833° and outputs a full monthly timetable suitable for mosque notice boards.

Formulas

The solar declination δ determines how high the Sun climbs. It is computed from the ecliptic longitude λ:

δ = arcsin(sin(λ) ⋅ sin(23.44°))

The Equation of Time EqT corrects for Earth's orbital eccentricity and axial tilt. Solar noon T_noon at longitude φ with timezone offset TZ:

T_noon = 12 + TZ × 15 − φ15 − EqT60

For a prayer defined by sun angle α below the horizon, the hour angle HA is:

HA = 115 ⋅ arccos(−sin(α) − sin(L) ⋅ sin(δ)cos(L) ⋅ cos(δ))

Asr time uses shadow ratio t (Shafi'i: t = 1, Hanafi: t = 2):

A = arctan(1t + tan(|L − δ|))

Where L = observer latitude, δ = solar declination, φ = longitude, TZ = UTC offset in hours, α = sun depression angle for the given prayer.

Reference Data

Calculation Method	Authority	Fajr Angle	Isha Angle / Offset	Region of Use
Muslim World League (MWL)	Muslim World League	18°	17°	Europe, Far East, parts of USA
Islamic Society of North America (ISNA)	ISNA	15°	15°	North America
Egyptian General Authority	Egyptian General Authority of Survey	19.5°	17.5°	Africa, Syria, Lebanon, Malaysia
Umm al-Qura University	Umm al-Qura, Makkah	18.5°	90 min after Maghrib	Saudi Arabia
University of Islamic Sciences, Karachi	University of Islamic Sciences	18°	18°	Pakistan, Bangladesh, India, Afghanistan
Institute of Geophysics, Tehran	Institute of Geophysics, University of Tehran	17.7°	14°	Iran, Shia communities
Shia Ithna-Ashari (Jafari)	Jafari Fiqh Council	16°	14°	Shia communities worldwide
Gulf Region	Various Gulf authorities	19.5°	90 min after Maghrib (Ramadan: 120 min)	UAE, Kuwait, Qatar
Kuwait	State of Kuwait	18°	17.5°	Kuwait
Qatar	State of Qatar	18°	90 min after Maghrib	Qatar
Singapore (MUIS)	Majlis Ugama Islam Singapura	20°	18°	Singapore, Brunei
Turkey (Diyanet)	Presidency of Religious Affairs	18°	17°	Turkey, Balkans, Central Asia
France (UOIF)	Union des Organisations Islamiques de France	12°	12°	France, parts of Western Europe

Frequently Asked Questions

The difference stems from the Fajr and Isha depression angles. The Muslim World League uses 18° for Fajr while ISNA uses 15°. A 3° difference in sun angle translates to roughly 12 - 20 minutes depending on latitude and season. At higher latitudes (above 50°N), this gap widens dramatically because the sun traverses the horizon at a shallower angle. Choose the method endorsed by your local Islamic authority or mosque.

Above approximately 48.5°N in summer, the sun may never dip 18° below the horizon, making Fajr/Isha undefined astronomically. Common solutions include the "nearest day" method (using the last valid day's times), the "one-seventh of the night" method (dividing nighttime into seven equal parts), or following Makkah's proportional times. This calculator returns the computed value when possible and flags persistent twilight conditions.

Shafi'i jurisprudence defines Asr as when an object's shadow length equals the object's height plus its noon shadow (shadow factor t = 1). Hanafi school requires the shadow to reach twice the object's height plus the noon shadow (t = 2). This results in Hanafi Asr starting roughly 30 - 60 minutes later than Shafi'i, depending on latitude and solar declination.

The standard refraction correction is 0.833°, meaning the sun appears above the horizon when geometrically it is 0.833° below it. This correction assumes standard atmospheric pressure (1010 mbar) and temperature (10°C). At very high altitudes or extreme temperatures, actual refraction varies. Desert heat can increase refraction by 1 - 2 minutes. This tool uses the standard correction. For coastal or mountainous locations, consider adding a 1 - 2 minute safety margin to Maghrib.

Yes. A person at higher elevation sees the sun rise earlier and set later than someone at sea level. For every 1000m of elevation, sunrise shifts roughly 1 - 3 minutes earlier. Some authorities recommend adding an altitude correction of 0.0347 × √h degrees to the sunrise/sunset depression angle, where h is elevation in meters. This calculator allows you to input elevation for this correction.

The astronomical algorithm used here (based on Jean Meeus) achieves accuracy within ±1 minute for solar noon and ±2 minutes for sunrise/sunset across most latitudes between 60°S and 60°N. Differences from local mosque times typically arise from three factors: different calculation method selection, altitude correction, and institutional safety margins (some mosques add 2 - 5 minutes to Fajr/Isha for precaution).