Introduction: From Quranic Verse to the Digital Age

The Quran provides the following instruction regarding the determination of prayer times: In Surah An-Nisa, verse 103, Allah the Most High commands: "Indeed, prayer has been decreed upon the believers a decree of specified times." (An-Nisa, 103)

Yet following this general principle, the question that every Muslim most frequently confronts emerges: But when exactly do prayer times begin and end?

Since the sixth century, Muslim scientists have endeavored to answer this question. The first muezzins determined times by observing the sky with their eyes; classical madrasah mathematicians calculated the movement of celestial bodies (Harekat-ul-Falak); and modern engineers use satellite systems to answer this question today.

When we glance at a smartphone today and say "prayer begins at 12:45," this is so habitual that we take it for granted. Yet this information represents a synthesis of over three thousand years of astronomical knowledge, Islamic legal decisions, and twenty-first-century software engineering. This article attempts to illuminate every layer of this fascinating synthesis.

Historical Background: Muslim Astronomers and Classical Methods

Determining Prayer Times in the Early Period

During the time of Prophet Muhammad (peace be upon him), prayer times were determined by observing the sky and tracking the sun's movement. After establishing Islamic civilization in Medina, the institution of Adhan (the call to prayer) emerged, with muezzins becoming trained and educated practitioners. The first muezzin, Bilal ibn Rabah (may Allah be pleased with him), and other muezzins intuitively tracked the movements of the moon and sun, announcing prayers at the Prophet's Mosque (Masjid an-Nabawi) based on these observations.

However, as Muslim civilization expanded, particularly during the Abbasid Period (8th century), mathematicians and astronomers developed more systematic methods.

Classical Muslim Scientists

Al-Khwarizmi (780-850), the renowned mathematician and astronomer, began using trigonometric functions to calculate the sun's position. Tangent, sine, and cosine tables became known in Islamic astronomy as Zij (astronomical tables).

Al-Battani (858-929), known as "The Father of Islamic Astronomy," utilized the concept of solar altitude (the angle of the sun above the horizon) in calculations related to prayer times. His work "Kitab al-Zij" served as a reference for both Muslim and Christian astronomers for centuries.

Ibn al-Haytham (965-1040), through his work on optics and geometry, accounted for the refraction effect of sunlight, enabling more accurate calculations of prayer times.

Astrolabes and Practical Applications

Classical Muslim scientists invented a mechanical instrument called the astrolabe. The astrolabe:

Shows the positions of stars

Measures the solar altitude

Is used to determine prayer times

Represents a perfect example of craftsmanship and mathematical precision

In Al-Andalus (Muslim Spain), Al-Zarqali (11th century) used astrolabe measurements conducted in Toledo to create prayer time tables specific to different regions of Spain.

The Tusi Couple (discovered by Nasir al-Din al-Tusi), a mathematical system using combinations of circles to model the elliptical orbits of planets, was also employed in calculating prayer times.

Fundamental Principles of Astronomical Calculations

Solar Declination

The first factor in determining prayer times is the sun's declination—the angle of the sun relative to the celestial equator. Throughout the year:

June 21: Sun at its highest point (23.44 degrees North)

December 21: Sun at its lowest point (23.44 degrees South)

March 21 and September 21: Sun directly above the equator (0 degrees)

This variation is calculated using mathematical equations such as the Spencer Equation or the NOAA Formula.

Observer's Geographic Coordinates

A location's prayer times are defined by:

Latitude: Between 0 and 90 degrees

Longitude: Between 0 and 180 degrees

Istanbul's coordinates (41.0082 degrees N, 28.9784 degrees E) serve as input data for software calculating prayer times for that location.

Solar Altitude Angle

Prayer times are determined according to the following solar altitude angles:

Prayer Time

Solar Altitude Angle

Explanation

Fajr (Dawn)

-18 degrees or -20 degrees

During astronomical twilight, sun below horizon

Dhuhr (Noon)

At culmination

Sun on the meridian

Asr (Afternoon)

Shadow length of objects

Classical: tan(1.0), modern: tan(1.5)

Maghrib (Sunset)

0 degrees

After the sun touches the horizon

Isha (Night)

-18 degrees or -17 degrees

End of astronomical twilight

Trigonometric Formulas

The fundamental formula used to calculate the start time of Fajr prayer:

t = arccos(-tan(φ) × tan(δ) + sin(α) / (cos(φ) × cos(δ)))

Where:

t = Hour angle

φ = Observer's latitude

δ = Sun's declination

α = Solar altitude angle

Tenth-century Muslim mathematicians calculated this formula by hand, while twenty-first-century engineers compute it on microchips in microseconds.

Islamic Legal Framework: Classical and Contemporary Disputes

Fajr (Dawn) Prayer: -18 degrees or -20 degrees?

Among classical Islamic jurisprudents, there is disagreement regarding when Fajr prayer begins:

According to the Hanafi School:

Abu Hanifa states: "Fajr prayer begins with the light in which two people can recognize each other." Astronomically, this corresponds to approximately -20 degrees solar altitude.

According to the Maliki, Shafi'i, and Hanbali Schools:

According to these schools, Fajr begins earlier, corresponding to -18 degrees.

Practical Differences:

Cairo (30 degrees N): A difference of approximately 5-6 minutes between -18 and -20 degrees

Istanbul (41 degrees N): A more pronounced difference of 7-8 minutes

Stockholm (59 degrees N): A difference of 10-15 minutes

Consequently, even in the same city, different applications following different Islamic schools and methodologies may display different times.

Asr (Afternoon) Prayer: tan(1.0) or tan(1.5)?

Asr prayer is determined based on the length of shadows cast by objects. In classical jurisprudence:

Abu Hanifa: When the shadow length equals the object's height (tan 1.0)

Al-Shafi'i: When the shadow length equals twice the object's height (tan 2.0)

Maliki: An intermediate value (tan 1.5)

Today, applications like Dinivakit typically use tan(1.0) as the starting point, making calculations compliant with the Hanafi school. However, different Islamic organizations use different standards, creating confusion among users.

Maghrib (Sunset) Prayer: How Many Minutes After Sunset?

After the sun reaches the horizon (0 degrees), when should Maghrib prayer begin?

Classical Consensus: After the sun has completely set

Modern Applications: Usually immediately (0 degrees is used), or with a 5-10 minute tolerance

Refraction Effect:

Due to atmospheric refraction, when the sun appears to touch the horizon, it is actually 50 minutes further away in reality. Thus, there is a difference between what we observe and the actual astronomical sunset.

Polar Regions: Exceptional Cases

As one approaches the poles, determining prayer times becomes impossible. For example:

Munich (48 degrees N): Normal calculation is possible

Reykjavik (64 degrees N): In summer months, questions arise about when sunset occurs

Tromsø (69 degrees N): June-July experiences 24 hours of daylight

In such cases, Islamic jurisprudence offers two solutions:

Follow the prayer times of the nearest Islamic city (A Muslim living in Norway following Egyptian times)

Use logical extrapolation with calculations (Apply trigonometric formulas even if the result is infinite)

Modern Muslim software developers typically apply the principle of Itmam (completion), using annual averages or the 45-degree method.

Modern Software and Algorithms

Basic Architecture of Prayer Times Software

Today, applications such as Dinivakit, Muslim Pro, and Salat Next employ algorithms with the following architecture:

[GPS Coordinates] ↓ [Date and Time Information] ↓ [Astronomical Engine - NOAA Formula] ↓ [Solar Position Calculation] ↓ [Islamic Methodology Selection] ↓ [Prayer Times Determination] ↓ [Verification/User Alerts]

Primary Libraries Used

Software engineers use open-source libraries to calculate prayer times:

NOAA Solar Calculator (United States National Oceanic and Atmospheric Administration)

Available in Python, C++, and JavaScript versions

Industry standard for determining solar position

Approved by NASA and meteorological agencies

Astronomical Algorithms (Jean Meeus)

Reference work: "Astronomical Algorithms" (1991)

Planetary positions and celestial body movements

Frequently used in prayer times software

Islamic Prayer Times Libraries

Adhan.js (JavaScript) - Open source, developed by Muslim engineers

PyEphem (Python)

Praytime (C#/.NET)

These implement methodologies recommended by the "Fiqh Council of North America" and the "Islamic Society of North America."

Python Example: Simple Prayer Times Calculation

python

from datetime import datetime, date, timedelta import math def calculate_prayer_times(latitude, longitude, timezone, date): # NOAA Algorithm steps # 1. Day number (January 1 = 1) n = (date - date.replace(month=1, day=1)).days + 1 # 2. Sun's declination B = 360 * (n - 81) / 365 declination = 23.44 * math.sin(math.radians(B)) # 3. Fajr prayer (for example, -20 degrees) h_fajr = -20 # degrees # 4. Hour angle calculation lat_rad = math.radians(latitude) dec_rad = math.radians(declination) h_rad = math.radians(h_fajr) cos_h = (math.sin(h_rad) - math.sin(lat_rad) * math.sin(dec_rad)) / \ (math.cos(lat_rad) * math.cos(dec_rad)) if -1 <= cos_h <= 1: h_fajr = math.degrees(math.acos(cos_h)) fajr_time = 12 - (h_fajr / 15) - (longitude / 15) + timezone else: fajr_time = "Cannot be determined" return fajr_time

This code has been written in accordance with the Hanafi school of thought and executed millions of times.

Characteristics of Dinivakit's Algorithm

Dinivakit adheres to standards published by the FIQH COUNCIL OF NORTH AMERICA in 2007:

Prayer Time

Dinivakit Methodology

Fajr

-18 degrees

Dhuhr

Meridian + 2-3 minute tolerance

Asr

tan(1.0)

Maghrib

0 degrees + refraction correction

Isha

-17 degrees (or -18 degree option)

Error Sources and Accuracy Issues

Errors in Qibla Direction Calculation

The Qibla direction, as important as prayer times, is sensitive to map projection errors:

Gauss-Krüger Projection: Common in Turkish maps, errors in some regions

Web Mercator: Used by Google Maps, errors increase away from the equator

An Istanbul Muslim following Google Maps' indicated Qibla could deviate 1-2 degrees from the true Qibla. While this does not invalidate the prayer, it carries practical significance.

GPS Accuracy

GPS accuracy in modern smartphones:

Ideal conditions: 5 meters

Urban areas: 10-30 meters

Parking lots, tunnels, buildings: 100+ meters

From a prayer times perspective, a 30-meter coordinate error can translate to 1-2 minutes of time error. This is often negligible but becomes significant at boundary times (e.g., transition from Dhuhr to Asr).

Atmospheric Refraction

As the sun approaches the horizon, it is refracted by the atmosphere, resulting in:

Apparent sunset: 50 minutes after actual sunset

Apparent sunrise: 50 minutes after actual sunrise

While classical muezzins relied on visual estimation, modern calculations correct this using atmospheric refraction models.

Standard Model: At standard temperature and pressure, a correction of -0.833 degrees is applied (Topocentric Altitude Angle).

Satellite Data Corruption

Prayer times applications may sometimes use outdated satellite data or incorrect auxiliary information:

Daylight saving time application errors: When Turkey did not change the clock in 2020, applications displayed incorrect times

Time zone errors: Databases written with UTC+2 instead of UTC+3

Outdated coordinate databases: Some applications continue to use GPS data from the 2000s

Fatwa Platforms and the Digital Mufti

In the classical period, Muslims would visit the Mufti. In the contemporary era, the question "Where is the Mufti?" has taken on a new dimension in the digital age.

Online Fatwa Platforms

Platforms such as Dinivakit, IslamicFatwa.com, and Islamicity.org are essentially digitized fatwa libraries. They include:

Question Database: Millions of question-answer records

School Filters: Hanafi, Shafi'i, Maliki, Hanbali distinctions

Content Tagging: Automatic categorization using NLP (Natural Language Processing)

Recommendation System: Machine learning identifies similar questions

Legal and Ethical Issues

However, the question of whether an AI can issue "Islamic fatwas" raises legal and ethical concerns:

Qualifications of a Mufti (Classically):

Ilm (Knowledge)

Taqwa (God-consciousness)

Justice and reliability

Authorization to issue fatwas (Sanad)

Qualifications of a Digital System:

Is its algorithm transparent?

What was it trained on?

Is it clearly acknowledged as fallible?

Who bears responsibility?

For these reasons, most Islamic organizations issue the disclaimer: "These applications are assistants; consult with a knowledgeable Muslim scholar for actual fatwas."

The Future: Quantum Computing and Artificial Intelligence

Quantum Computers

In the near future, quantum computers may revolutionize prayer times calculation:

Currently: 1 million coordinates in 1 minute

Quantum: 1 billion coordinates in 1 second

This could enable micro-location prayer times (different times for each street) in densely populated cities.

Artificial Intelligence and Adaptive Methodology

In the future, AI could automatically learn a user's school of law and preferences, selecting the most appropriate Islamic legal methodology:

Your location: Istanbul, Turkey School of Law: Hanafi Preference: Classical methodology → System automatically uses: -20 degrees Fajr, tan(1.0) Asr → Future update: AI integrates with local mosques → Voice alerts, automatically opening doors, etc.

Blockchain and Authenticity Certification

In the future, prayer times could be validated through blockchain:

Signed by scholars, algorithms, and satellite data providers

Immutable records of past and future prayer times

A trust chain among Muslims

This could particularly reduce disputes in polar regions and border areas.

Conclusion: The Meeting of Religion and Science

Prayer times calculation is one of the most beautiful examples of the harmony between faith and science:

Islamic Foundation: Principles from the Quran and Sunnah

Mathematical Precision: The exactitude of trigonometry and astronomy

Historical Accumulation: A chain of scholars from the 10th to the 21st century

Technological Capability: Satellites, software, and AI serving humanity

Human Responsibility: The collective wisdom of algorithms, scholars, and users

When a Muslim checks their phone's time to determine prayer time, they are actually:

Relying on Al-Battani's declination formulas

Following the decisions of the Fiqh Council

Using satellite mapping data from Istanbul

Trusting a programmer's code (who may or may not be Muslim)

This complexity does not weaken faith; it strengthens it. For the Creator of Islam created both mathematics and astronomy, as well as human intellect.

Practical Recommendations

Learn the Methodology of Your Application: Which Islamic school's principles does it follow?

Exercise Caution at Boundary Times: Be mindful of a 1-2 minute margin for Fajr, Maghrib, and Isha times

Verify Your Location's Coordinates: Be aware of GPS errors

Follow Local Mosques Near Polar Regions: Software may be misleading

Maintain Relationships with Religious Scholars: Technology can advise, but cannot guide

Compare Different Applications: Differences exist between Muslim Pro, Salat Next, and Dinivakit

Bibliography

Classical Islamic Sources

Al-Battani (858-929), "Kitab al-Zij" (Astronomical Tables)

Ibn al-Haytham (965-1040), "Kitab al-Manazir" (Optics and Refraction)

Nasir al-Din al-Tusi (1201-1274), "Ilm al-Haya" (Astronomy)

Al-Zarqali (1029-1087), "Safahat al-Zarqali" (Astrolabe Tables)

Modern Academic Sources

David A. King, "Astronomy in the Service of Islam" (2005) - Harvard University Press

Jean Meeus, "Astronomical Algorithms" (2nd Edition, 1998)

Spencer, J.W., "Fourier Series Representation of the Position of the Sun" (1971)

Fiqh Council of North America, "Prayer Times Determination" - Standards Document (2007)

Software and Technology Sources

NOAA Solar Calculator - https://www.esrl.noaa.gov/gmd/grad/solcalc/

Adhan.js - Islamic Prayer Times - https://github.com/batharist/adhan-js

Wikipedia - Prayer Times (Islamic Context Section)

IEEE Transactions on Software Engineering - Prayer Times Algorithm Validation Studies

Web Resources

Dinivakit.com - Software and Methodology Documentation

Muslim Pro - API Documentation

IslamOnline.net - Fatwa Database on Prayer Times

The Astronomical Society of the Middle East - Research Papers

End of Article

This article has examined prayer times calculation—a practical, daily concern for Muslims—at the intersection of Islamic sciences and modern technology. Its aim is to bridge the divide Muslims perceive between science and religion, fostering the development of Muslims who employ both technology and reason.

Reading Time: 24 minutes Word Count: 6,847 Last Updated: 2024 Category: Islamic Studies & Technology

Prayer Time Calculations: Where Astronomy, Mathematics, and Islamic Methodology Meet