Two phones on one sofa, two different dawn times. Which one is wrong? Often neither. The gap comes from prayer times calculation, a craft where hard astronomy meets human judgment, and most of us never see the workings. Here’s the surprising part: very few of the differences are about maths. Most are about choices. Let’s go through them in order.
Eight Markers That Divide the Day
- Fajr: the east turns pale before the day begins.
- Sunrise: the top rim of the sun clears the horizon.
- Dhuhr: the sun slips past its Zenith, the highest point of its path.
- Asr: the afternoon time, set by how long shadows have grown.
- Sunset: the sun has dropped fully out of sight.
- Maghrib: the evening prayer, which follows soon after.
- Isha: the western glow has faded and the sky is properly dark.
- Midnight: the centre of the night, which comes in two versions.
Tell the Calculator Where You Stand
A calculator knows nothing about you until you give it a place. It needs your Latitude (how far north or south you are), your Longitude (how far east or west), and your Time Zone, so the sun’s local schedule lands on your own clock. It needs the date too, because the Season keeps nudging the sun’s path. Height above the sea, or Elevation, could shift the horizon times slightly, but nearly every tool leaves it out so results stay consistent.
After that comes the human part: choosing how deep the sun must sink before the dawn and night prayers begin, and which school’s rule governs the afternoon one.
Two Slow Wobbles in the Sky
Two measures do most of the heavy lifting. Both drift slowly through the year, and together they explain why the timetable shifts a little every single day.
| Measure | What it describes | Why it moves | Extreme values | Effect on your timetable |
| Equation of Time | The gap between sundial time and clock time | Earth’s oval orbit, plus its axial tilt | About +16 min 33 s (around 3 November) and about −14 min 6 s (around 12 February) | Moves midday by up to a quarter of an hour |
| Declination of the Sun | The angle between the sun’s rays and the plane of the equator | The same lean of the Earth as it circles the sun | Roughly +23.4° at the June solstice to −23.4° in December | Decides day length, so every prayer boundary slides earlier or later |
.Midday, Horizon Edges and Every Other Formula in One Place
Noon is the easy one. Take twelve, add your zone offset, subtract your east-west position divided by fifteen, then subtract the sundial gap. The answer is Solar noon. Many timetables push it a minute or two later, so the prayer never starts before the sun has clearly begun to descend.
The morning and evening edges are handled differently. Calculators place the sun 0.833° under the geometric horizon, because of Refraction: air bends light, so the sun appears a touch early and lingers a touch late.
Everything else is built on top of midday. In the table below, T(α) means the time the sun needs to travel from noon down to an angle α below the horizon, and A(t) means the time until a shadow reaches t times the object’s height, plus its noon shadow.
| Time | Calculation method | Notes |
| Midday | 12 + time zone − longitude ÷ 15 − equation of time | Add a 1 to 2 minute safety margin |
| Sunrise | Midday − T(0.833) | The extra 0.833° covers atmospheric bending |
| Dawn prayer | Midday − T(dawn angle) | Angle depends on the convention you choose |
| Afternoon prayer (majority schools) | Midday + A(1) | Shadow equals the object’s height plus its noon shadow |
| Afternoon prayer (double-shadow school) | Midday + A(2) | Shadow equals twice the height plus its noon shadow |
| Sunset | Midday + T(0.833) | Same constant as sunrise |
| Evening prayer (Sunni) | Sunset, plus 1 to 3 minutes | Precaution only |
| Evening prayer (Shia) | Midday + T(4) | Waits for the red glow to pass |
| Night prayer | Midday + T(night angle) | Or a fixed gap after sunset in some conventions |
| Astronomical midnight | Sunset + ½ × (sunrise − sunset) | Exact middle of sunset to sunrise |
| Legal midnight | Sunset + ½ × (dawn − sunset) | Closes the night prayer’s preferred window |
For the two helper functions, with latitude L and sun declination D, the standard forms are:
- T(α) = (1 ÷ 15) × arccos[(−sin α − sin L × sin D) ÷ (cos L × cos D)]
- A(t) = (1 ÷ 15) × arccos[(sin(arccot(t + tan |L − D|)) − sin L × sin D) ÷ (cos L × cos D)]
Once you have L, D, the equation of time and your zone, a phone can run all eleven rows in a fraction of a second.
.Finding Noon and the Rim of the Sun
Noon is the neat one. Take twelve, add your zone offset, subtract your east-west position divided by fifteen, then subtract the sundial gap from the table. The answer is Solar noon. Many timetables push it a minute or two later, so the prayer never starts before the sun has clearly begun to descend.
The morning and evening edges are handled differently. Calculators place the sun 0.833° under the geometric horizon. The odd little figure exists because of Refraction: air bends light, so the sun appears a touch early and lingers a touch late.
Dawn and Night: Where Scholars Part Ways
For these two prayers, the key question is how far below the horizon the sun has sunk. That depth is called the Twilight angle. You will also see it written as the Angle of depression, or Solar depression; it is the same idea. Most apps apply Fixed degrees that never change through the year. It is tidy, even if it can never be perfect.
Dusk has three scientific stages that people often blur together. Astronomical twilight ends at 18°, Nautical twilight at 12°, and Civil twilight at 6°. The legal meaning of true dawn matches none of them cleanly. Some medieval texts may even have recorded Stellar elevation, the height of a chosen star, rather than the sun’s own depth. Lining up an old figure beside a modern one is therefore risky.
Different bodies publish different settings. Here they are side by side:
| Convention | Dawn angle | Night angle |
| Muslim World League | 18 | 17 |
| Islamic Society of North America (ISNA) | 15 | 15 |
| Egyptian General Authority of Survey | 19.5 | 17.5 |
| Umm al-Qura University, Makkah | 18.5 | 90 minutes after the evening prayer (120 in Ramadan) |
| University of Islamic Sciences, Karachi | 18 | 18 |
| Institute of Geophysics, University of Tehran | 17.7 | Not explicitly defined |
| Leva Research Institute, Qum | 16 | 14 |
| Muslims of France (UOIF) | 12 | 12 |
| Spiritual Administration of Muslims of Russia | 16 | 15 |
| Islamic Religious Council of Singapore (Majlis Ugama Islam Singapura) | 20 | 18 |
Using the first row as an example: dawn = midday − T(18), and night = midday + T(17). Here T(α) is the time the sun needs to travel from noon down to an angle α below the horizon.
Notice the spread. Dawn alone runs from 12 to 20. That gap is the single biggest reason prayer times calculation gives different answers from one app to the next.
Afternoon: One Shadow, Two Rules
On the afternoon prayer, jurists divide into two camps. The Shafi’i, Maliki, Hanbali and Ja’fari schools begin it when an object’s Shadow length equals its own height, plus the shadow it cast at noon. The Hanafi school waits until that figure doubles. The result is a later time, often by close to an hour depending on place and date. If a friend’s afternoon time is far from yours, check this switch before suspecting the maths.
Evening Prayer and the Dark Hours
Most calculations start the evening prayer once the sun is completely gone, with a Precautionary delay of one to three minutes. These gaps are Fiqhi, meaning they come from legal reasoning, not astronomy. No equation can settle them for you.The night has two definitions as well. Astronomical midnight is the exact halfway point between the sun going down and coming back up. Legal midnight is the halfway point between the sun going down and the start of the dawn prayer, and it closes the preferred window for the night prayer.
When Night Refuses to Fall
Travel far enough north in summer and a glow hangs around until morning. These Abnormal periods break the standard formulas, so scholars proposed three workarounds.
The Middle of the Night idea splits the dark hours in half and places both prayers at the dividing line. The One-Seventh of the Night idea cuts the night into seven slices: the night prayer follows the first, and the dawn prayer opens the last. The Angle-Based Method sits between them. It divides the night in proportion to the angle over sixty, so a bigger angle gives a longer first portion. Most apps tuck these under a “far north” option.
Choosing a Setting You Can Live With
Honestly, none is flawless. Years of field studies by moonsighting.com and independent researchers show that the timings are Not scientifically deterministic. They move with place, height and time of year.
The Fiqh Council of North America (FCNA) weighed the data and settled on a practical Approximation, so worshippers would not have to scan the sky daily. Its advice is 15° for both prayers in the USA and 13° for both in Canada, all year. In most apps this appears as the North American option.
Anyone able to make a careful Observation of their own sky may add some Caution: pray the dawn and night prayers a few minutes after the listed time, and Hasten the end of the pre-fast meal by the same margin. The Council calls this a suggestion, not a rule.
My advice is to follow your local mosque. Staying in step with your community beats arguing over one degree. Treat prayer times calculation as a very good guide, not a final ruling.
Slip-Ups to Avoid
- Mixing methods, such as taking dawn from one chart and night from another.
- Forgetting daylight saving, which gives a perfect chart for the wrong clock.
- Leaving an app on your old city after a trip.
- Treating a rounded minute as a hard legal border.
Wrapping Up
At its core, prayer times calculation is astronomy shaking hands with scholarly choice. Know your place, your convention and your school, and what remains is plain arithmetic, with a small cushion for whatever doubt is left.
FAQs
Why do two apps disagree?
They use different conventions, or a different afternoon school. Compare the table above with your app’s settings.
Does altitude matter?
In theory, yes. In practice the horizon value stays fixed.
Is the maths good enough for fasting?
Mostly. The result of prayer times calculation is best used with a small buffer.
How are prayer times calculated?
Prayer times are calculated based on the position of the sun at a specific location and date. The main factors include sunrise, sunset, dawn, and the sun’s angle below the horizon.
- Fajr: Begins at dawn, when the first light appears before sunrise.
- Dhuhr: Begins after the sun passes its highest point (solar noon).
- Asr: Calculated based on the length of an object’s shadow, according to the selected Islamic calculation method.
- Maghrib: Begins immediately after sunset.
- Isha: Begins when twilight disappears after sunset
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