How Prayer Times Are Calculated: The Comprehensive Science Guide (2026)
Learn the solar science and mathematical formulas used to calculate Fajr, Dhuhr, Asr, Maghrib, and Isha. Read about twilight angles, latitudes, and adjustments.
Table of Contents
The Solar Science of Prayer Times
Daily prayer times are determined by the sun's position relative to the Earth. Spherical trigonometry and declination formulas calculate the exact timing of Fajr, Dhuhr, Asr, Maghrib, and Isha based on geographical coordinates.
Key Takeaways for Calculations
| Prayer | Astronomical Criterion |
|---|---|
| Fajr | Sun reaches a specific angle below the horizon (usually -18° or -15°) |
| Dhuhr | Sun passes the local meridian (solar noon) |
| Asr | Shadow of an object equals its height (standard) or twice its height (Hanafi) |
| Maghrib | Upper edge of the sun sinks below the horizon (-0.833° angle) |
| Isha | Sun reaches a specific angle below the horizon (usually -18° or -15°) |
The Hour Angle Formula
To compute the time when the sun reaches a specific altitude angle, astronomers calculate the Hour Angle ($H$) using the following formula:
cos(H) = (sin(a) - sin(d) * sin(f)) / (cos(d) * cos(f))
Where $a$ is the altitude angle of the sun, $d$ is the solar declination, and $f$ is the latitude of the observer. This calculation allows applications to estimate timings accurately anywhere in the world.
This guide has been verified by our editorial board. Astronomical data matches calculated equational metrics, and liturgical instructions conform with established traditional jurisprudential Fiqh sources.
Frequently Asked Questions
Academic & Shariah References
- Astronomical Algorithms by Jean Meeus
- AlAdhan API Core Calculation Guidelines
- HM Nautical Almanac Office Publications
About The Author
Dr. Sarah Jenkins holds a PhD in Astrophysics from Oxford University. She specializes in solar positioning algorithms and coordinates calculations for geographical mapping platforms.