Prayer Times

Methods and Algorithms for Calculating Prayer Times

The five daily prayers are performed at strictly defined times, which are determined by the position of the Sun relative to the horizon. Our service uses mathematical algorithms from the open-source PrayTime library, adapted to ensure maximum schedule accuracy across 2,000+ cities. For a detailed explanation of the underlying astronomical formulas, you can refer to the official PrayTimes documentation.

Key Definitions

To accurately determine the time intervals for prayers (as well as the start and end times for fasting), it is necessary to establish key points of the solar day.

Time Definition
Fajr The moment when the sky first begins to lighten at dawn.
Sunrise The instant when the first edge of the Sun appears above the horizon.
Dhuhr The time when the Sun begins to decline after reaching its zenith (highest point in the sky).
Asr The moment when the length of an object’s shadow equals its height (or twice its height) plus the length of its noon shadow.
Sunset The instant when the Sun fully disappears below the horizon.
Maghrib The time shortly after sunset.
Isha The time when complete darkness sets in and no scattered twilight remains.
Midnight The midpoint between sunset and sunrise (or, in some traditions, between sunset and Fajr).

Astronomical Measures

Two astronomical measures are critical for calculating prayer times: the Equation of Time and the Declination of the Sun.

  • Equation of Time ($EqT$): The discrepancy between time measured by a sundial and standard clock time, caused by the Earth’s axial tilt and its elliptical orbit.
  • Declination of the Sun ($D$): The angle between the Sun’s rays and the plane of the Earth’s equator, which continuously changes throughout the year.

Basic Formulas

The calculation is based on geographic coordinates: latitude ($L$), longitude ($Lng$), and the local time zone ($TimeZone$).

Dhuhr

Dhuhr is calculated as the moment the Sun crosses the meridian:

$$Dhuhr = 12 + TimeZone — Lng/15 — EqT$$

Sunrise and Sunset

The time difference between solar noon and the moment the Sun reaches an angle $\alpha$ below the horizon is calculated using the following formula:

$$T(\alpha) = \frac{1}{15} \arccos\left( \frac{-\sin(\alpha) — \sin(L) \cdot \sin(D)}{\cos(L) \cdot \cos(D)} \right)$$

Taking atmospheric refraction into account ($\alpha = 0.833^\circ$):

  • $Sunrise = Dhuhr — T(0.833)$
  • $Sunset = Dhuhr + T(0.833)$

Asr

There are two main scholarly opinions regarding the start time of Asr. The formula calculates the time difference for a shadow factor $t$:

$$A(t) = \frac{1}{15} \arccos\left( \frac{\sin(\arctan(\frac{1}{t + \tan(L-D)})) — \sin(L) \cdot \sin(D)}{\cos(L) \cdot \cos(D)} \right)$$

  • Majority of schools (Shafi’i, Maliki, Hanbali): $Asr = Dhuhr + A(1)$
  • Hanafi school: $Asr = Dhuhr + A(2)$

Calculation Methods (Conventions)

Because Fajr and Isha angles vary based on regional conventions, our site supports the settings of leading global organizations:

Organization Fajr Angle Isha Angle
Muslim World League (MWL) 18° 17°
Islamic Society of North America (ISNA) 15° 15°
University of Islamic Sciences, Karachi 18° 18°
Umm al-Qura University, Makkah 18.5° 90 min after Maghrib (120 min during Ramadan)
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