This page shows how every prayer time on this site is calculated: the inputs, the parameters of each method, the formulas, a worked example for today, the sources, the measured accuracy and the known limits.
Worked example: New York City, NY, today. Every city page shows the same block for its own coordinates and date.
How these times are calculated (method, formulas, worked example, sources)
1. Inputs
| Place | New York City, NY |
|---|---|
| Latitude, longitude | 40.7143, -74.0060 |
| Date | 2026-10-10 |
| Time zone | America/New_York (EDT, UTC-04:00, daylight saving time) |
| Elevation | not used (sea-level horizon) |
2. Method parameters
| Method | Islamic Society of North America (ISNA) |
|---|---|
| Fajr angle | 15.0° |
| Isha | 15.0° |
| Asr | Standard (shadow factor 1) |
| High-latitude rule | not needed on this date |
| Adjustments | none |
| Rounding | to the nearest minute |
3. Formulas
D = JD − 2451545.0g = 357.529 + 0.98560028 D ; q = 280.459 + 0.98564736 DL = q + 1.915 sin g + 0.020 sin 2g ; e = 23.439 − 0.00000036 DRA = atan2(cos e · sin L, cos L) / 15 ; δ = asin(sin e · sin L)EqT = q/15 − RADhuhr (local mean solar time) = 12 − EqT ; clock time = Dhuhr − λ/15 + UTC offsetT(a) = (1/15) · acos[(sin a − sin φ · sin δ) / (cos φ · cos δ)]Sunrise = Dhuhr − T(−0.833°) ; Maghrib = Dhuhr + T(−0.833°)Fajr = Dhuhr − T(−Fajr angle) ; Isha = Dhuhr + T(−Isha angle)Asr = Dhuhr + T(a) with a = arccot(s + tan|φ − δ(noon)|), s = 1 or 20.833° = 0.567° refraction + 0.2667° solar semi-diameter
φ is latitude, λ longitude (east positive), δ the Sun's declination. The Sun's position is evaluated at each event's own time and the calculation is iterated twice. Clock times come from the IANA time-zone rules, so daylight saving time is always applied correctly.
4. Worked example for 2026-10-10
Sun at solar noon:
| JD (0h UT) | 2461323.5 |
|---|---|
| D | 9779.1965 |
| g | 275.9078° |
| q | 199.2982° |
| L | 197.3893° |
| e | 23.43548° |
| RA | 13.06877 h |
| δ | -6.82645° |
| EqT | 13.067 min |
| Prayer | δ | a | T(a) | Solar time | UTC | Clock time |
|---|---|---|---|---|---|---|
| Fajr | -6.7172° | -15.000° | 6.9355 h | 04:50:53 | 09:46:54 | 05:47 |
| Sunrise | -6.7369° | -0.833° | 5.6851 h | 06:05:53 | 11:01:55 | 07:02 |
| Dhuhr | -6.8265° | — | — | 11:46:56 | 16:42:57 | 12:43 |
| Asr | -6.8762° | 25.539° | 3.1610 h | 14:56:33 | 19:52:35 | 15:53 |
| Maghrib | -6.9157° | -0.833° | 5.6747 h | 17:27:21 | 22:23:23 | 18:23 |
| Isha | -6.9354° | -15.000° | 6.9230 h | 18:42:14 | 23:38:16 | 19:38 |
5. Measured accuracy
The engine is tested against an independent implementation (adhan-js 4.4.6) on 377 cases across 15 US cities and 13 dates, including daylight-saving transition days and Fairbanks, Alaska. The largest difference measured is 59.9 seconds.
Exception: in 5 Alaskan winter cases the Sun barely climbs above the Asr altitude, so Asr becomes very sensitive and differed by up to 4.2 minutes. Pages flag such dates.
6. Limits
- These are astronomical calculations, not a religious ruling. Mosques publish their own iqama times and may use another method or add a few minutes of caution; follow your local mosque.
- Elevation and local horizon (mountains, buildings) are not taken into account.
7. Method reference
| Method | Fajr | Isha |
|---|---|---|
| Islamic Society of North America (ISNA) | 15.0° | 15.0° |
| Muslim World League (MWL) | 18.0° | 17.0° |
| Egyptian General Authority of Survey | 19.5° | 17.5° |
| University of Islamic Sciences, Karachi | 18.0° | 18.0° |
| Umm al-Qura University, Makkah | 18.5° | 90 min after Maghrib (120 in Ramadan) |
8. Sources
- Jean Meeus, Astronomical Algorithms, 2nd ed., Willmann-Bell, 1998 (Julian Day, chapter 7)
- U.S. Naval Observatory, Approximate Solar Coordinates (low-precision formulas for the Sun)
- The Astronomical Almanac, Section C: low-precision formulas for the Sun's coordinates
- NOAA Global Monitoring Laboratory, Solar Calculator
- PrayTimes.org, Prayer Times Calculation (Dhuhr, sunrise/sunset with 0.833°, Asr shadow rule, method table, high-latitude methods)
- Islamic Society of North America (ISNA); angles 15°/15° as listed in the PrayTimes.org method table
- Muslim World League: Fajr 18°, Isha 17°
- Egyptian General Authority of Survey: Fajr 19.5°, Isha 17.5°
- University of Islamic Sciences, Karachi: Fajr 18°, Isha 18°
- Umm al-Qura University, Makkah: Fajr 18.5°, Isha 90 minutes after Maghrib (120 in Ramadan)
- IANA Time Zone Database
- GeoNames (geonames.org), cities15000, CC BY 4.0 — city coordinates and population
- timezone-boundary-builder (ODbL) — offline timezone polygon lookup
- adhan-js 4.4.6 (MIT) — independent reference implementation used for the accuracy tests
Methodology v1.0, reviewed 2026-10 · engine 1.0. Methodology and changelog
Changelog
- Methodology v1.0 (2026-10): first published version. Sun position evaluated at each prayer's own time; Asr threshold from the noon declination; measured accuracy published.