How Prayer Times Are Calculated (And Why Dhuhr Is Never at Noon)

Key takeaways

• A prayer time is not a clock time. It is a position of the sun, converted into a clock time for one exact location on one exact date.
• Dhuhr tracks solar noon rather than 12:00. Boston and Detroit share a time zone, and their Dhuhr is 48 minutes apart.
• The equation of time moves solar noon across the year, so one fixed city's Dhuhr drifts by 31 minutes between February and November.
• The sun's declination stretches the day around noon: in Chicago, Fajr moves by 2 hours 19 minutes between the solstices while solar noon barely moves at all.
• The twilight angle even decides whether your city has an answer: on the solstice London is computable under a 15-degree convention and needs an estimate under an 18-degree one.
• Fajr and Isha depend on a twilight angle an authority settled on, and Asr on a shadow factor. Those two numbers are the only genuinely human choices in the calculation.

A prayer timetable looks like a list of clock times. It is really a list of sun positions, and it only becomes a clock at the very last step.

Every prayer time is a position of the sun

Prayer times are calculated from where the sun is, seen from your exact coordinates on a specific date. Nothing in the definition is a clock. The open reference model published by PrayTimes defines each time by a solar event, and the arithmetic converts that event into local time only at the end.

Time	Defined by the sun
Fajr	"The moment when the sky first begins to lighten at dawn": the sun a set angle below the horizon
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"
Asr	When an object's shadow reaches a set multiple of its own height, plus its noon shadow
Maghrib	"Soon after sunset"
Isha	"The time when complete darkness sets in, and no scattered twilight remains in the sky"

Four of these reduce to a single function. PrayTimes writes it as T(α), "the time difference between the mid-day and the time at which sun reaches an angle α below the horizon". Change α and the same machinery produces Fajr, Isha, sunrise or sunset. Only Dhuhr and Asr work differently, and both are covered below.

This is why an app asks for coordinates rather than a city name, and why it needs the date rather than just the time zone. Two things drive the whole calculation: where the sun crosses your meridian, and how high it climbs when it does.

Why Dhuhr is never at noon

Dhuhr follows solar noon, the moment the sun actually crosses your meridian, and solar noon is almost never 12:00. Two separate things push it around: where you sit inside your time zone, and where the earth sits in its orbit. Both appear in the formula PrayTimes publishes as Dhuhr = 12 + TimeZone - Lng/15 - EqT.

Your longitude moves it by up to an hour

A time zone is a political stripe roughly 15 degrees wide, and everyone inside it agrees to read the same clock. The sun does not agree. It crosses each meridian in turn, taking four minutes per degree of longitude.

The effect is not subtle. Boston and Detroit are both on Eastern time and sit at almost the same latitude, but they are 12 degrees of longitude apart. On 11 February 2026 the AlAdhan engine puts Boston's Dhuhr at 11:58 and Detroit's at 12:46. That is a 48-minute gap from longitude alone, on the same day, in the same time zone.

Twelve degrees times four minutes is 48. The clock is shared; the sun is not.

The equation of time moves it again

The second term is stranger. The earth's orbit is elliptical and its axis is tilted, so the sun runs ahead of and behind the clock across the year. Astronomers call that gap the equation of time. PrayTimes gives its range: a sundial can be "ahead (fast) by up to 16 minutes 33 seconds (around November 3)" or "behind (slow) by up to 14 minutes 6 seconds (around February 12)".

Those two extremes are about 31 minutes apart, and that is what a timetable shows. In Chicago, Dhuhr falls at 12:05 on 11 February 2026 and 11:34 on 3 November 2026, both on standard time with no daylight saving involved: a 31-minute drift in one fixed location, with nothing moving but the earth.

The method behind that number is not proprietary to prayer apps. NOAA's solar equations give solar noon as snoon = 720 - 4*longitude - eqtime, the same relationship in minutes that PrayTimes writes in hours, and PrayTimes takes its solar position from the US Naval Observatory's published approximation, citing it by name. A prayer timetable is running the same astronomy a weather service runs.

Declination stretches the day around noon

The second astronomical input decides how far the other prayers sit from Dhuhr. PrayTimes names both: "Two key astronomical measures are essential for accurately computing prayer times: the Equation of Time and the Declination of the Sun". Declination is "the angle between the Sun's rays and the plane of the Earth's equator", and it "varies continuously throughout the year due to the axial tilt of the Earth".

The Naval Observatory reduces it to two lines: the earth's tilt is e = 23.439 - 0.00000036 D, and the sun's declination is sin d = sin e sin L, where L is the sun's position along the ecliptic. That tilt is the entire reason seasons exist, and the entire reason a prayer timetable is a different shape in June than in December.

The size of the effect is easy to miss until you put two dates side by side. In Chicago on the summer solstice, Fajr is at 03:32 and Isha at 22:13, a span of 18 hours 41 minutes. On the winter solstice, Fajr is at 05:51 and Isha at 17:47, a span of 11 hours 56 minutes. Fajr alone moves by 2 hours 19 minutes between them.

Solar noon, meanwhile, hardly moves at all. Chicago's Dhuhr reads 12:52 in June and 11:49 in December, but 60 of those 63 minutes are daylight saving, a clock convention layered on top of the astronomy. Correct for it and real solar noon shifts by about three minutes. Declination stretches the day; it does not slide the middle of it.

Fajr and Isha are angles, and angles are chosen

Fajr and Isha are the only prayers whose definition contains a number that people had to agree on. Both are twilight events: Fajr when the sky first lightens, Isha when the last scattered light goes. Turning "first light" into a time means deciding how far below the horizon the sun must be, and that depth is a figure an authority settled on rather than one every timetable measures afresh.

So a timetable using one convention and a timetable using another disagree about Fajr and Isha while agreeing exactly about Dhuhr and Maghrib, which in these conventions contain no angle to choose. Which authorities use which angles, and how to choose between them, is a separate subject covered on its own.

Which prayers a disagreement lands on therefore has a mechanical explanation, and following that trail to decide which timetable to trust is a separate subject, covered on its own.

Asr is a ratio, not an angle

Asr is defined by shadow length rather than by the sun's depth below the horizon. PrayTimes states both established readings: the convention followed in the Shafi'i, Maliki, Ja'fari and Hanbali schools starts Asr when an object's shadow equals its own height plus its noon shadow, while "the Hanafi school follows a different interpretation, asserting that Asr begins when the shadow is twice the length of the object plus its shadow length at noon".

In the formula this is one factor, t, set to 1 or 2. The gap it produces is large, and it varies with latitude and season. In Chicago on 11 February 2026, holding the calculation method constant, Asr falls at 14:53 under the first reading and 15:36 under the Hanafi one: a difference of 43 minutes.

Setting this in an app does not make the times more or less correct. It selects which established convention the app computes, and the one to match is your mosque's.

Sunrise and sunset are not when the sun crosses the horizon

The horizon lies to the eye, and the calculation corrects for it. The atmosphere bends sunlight, so the sun appears above the horizon while it is still geometrically below it, and the disc has a width of its own. Both are handled with a single constant.

PrayTimes notes that "due to the refraction of light by terrestrial atmosphere, actual sunrise appears slightly before astronomical sunrise and actual sunset occurs after astronomical sunset", and so uses T(0.833) rather than T(0). NOAA states the same correction from the other direction: for sunrise and sunset "the zenith is set to 90.833 (the approximate correction for atmospheric refraction at sunrise and sunset, and the size of the solar disk)". The two numbers are one constant, measured from opposite ends.

Maghrib then sits on top of sunset, and it is the one definition in the table that is not a number at all: "soon after sunset". How soon is a convention, which is why some timetables add a few minutes to sunset and others do not.

Altitude is the honest gap. Standing higher lets you see a lower horizon, which should push sunset later, and PrayTimes says elevation could be handled "by slightly increasing the above constant 0.833". It then records what happens in practice, which is nothing: "the constant is considered the same regardless of the elevation". Most timetables, including the ones apps generate, do not adjust for how high you are.

Where the angle never arrives, and who decides where that is

Far enough north, the calculation stops having an answer. If the sun never drops as far below the horizon as the convention requires, no moment satisfies the definition, and PrayTimes says so plainly: in these periods "the determination of Fajr and Isha is not possible using the usual formulas".

The part that gets missed is that "far enough north" is not a fixed place. It moves with the angle, so the convention decides whether your own city has an answer at all.

London makes the point precisely. On the summer solstice the sun reaches just over 15 degrees below the London horizon at its lowest.

Under a 15-degree convention that is enough, barely, and Fajr is genuinely computed: AlAdhan returns 01:16, and that time is the sun rather than an estimate. Under an 18-degree convention the sun never arrives, the formula has nothing to return, and the same engine falls back to an estimate of 01:02. Same city, same night, same sun. One choice of angle decides whether the answer is astronomy or approximation.

Move 250 kilometres north and the choice disappears. At Manchester the sun gets only about 13 degrees down, so even the 15-degree convention has no answer and every timetable there is estimating.

The fallback rules disagree with each other

That is when the fallback rules take over, and they do not agree with each other. Holding the method constant at Manchester on the same night, AlAdhan puts Fajr at 01:11 under Middle of the Night, 02:55 under Angle-Based and 03:40 under One-Seventh: a spread of two and a half hours, from the rule alone.

The three rules divide the night rather than measure the sky. The Middle of the Night rule splits sunset-to-sunrise in half. The One-Seventh rule splits it into seven parts, putting Isha after the first and Fajr at the start of the last. The Angle-Based rule divides the night in proportion to the twilight angle the convention would otherwise have used.

All three lean on a definition the table above leaves out, midnight, which PrayTimes gives as "the midpoint between sunset and sunrise (or, in some traditions, between sunset and Fajr)". Even the fallback has a convention inside it.

These are not obscure options. AlAdhan exposes the choice as a parameter, describing it as the method to use "if you are checking timings in the UK or Sweden", and PrayTimes' own library states that "the default method used in PrayTime is MidNight". Push far enough north and even the rules run out: where the sun never sets at all, there is no night left to divide.

Scholars differ on which rule to follow. That makes it a question for your local mosque or scholar rather than a setting to guess at.

What this means for your app

An app is doing five things, and each is a place two timetables can legitimately differ. It reads your coordinates, applies your time zone, computes the sun's position for the date, applies a twilight convention for Fajr and Isha, and applies a shadow factor for Asr.

Worth noticing which of those is actually uncertain. The astronomy is not the weak link: the Naval Observatory puts its own solar approximation at "about 1 arcminute within two centuries of 2000", a precision no timetable printed to the minute can even express. Everything that makes two honest timetables disagree comes from the human choices layered on top, and from how precisely the app knows where you are.

Muslim App exposes the parts that are conventions rather than physics. It offers "madhhab and latitude adjustments when needed", lets you "choose different calculation methods from various Islamic authorities", and lets you "add or subtract minutes from each prayer time to match your local mosque". Location comes from GPS, and you can "manually search and select your city from the location settings within the app" when you would rather pin it.

Compare the times for your own city against the timetable your mosque prints. If they differ, the arithmetic is rarely the reason: what an app can be set to is the convention, and matching your mosque is a settings question rather than a mathematical one.

The sun does the work

None of this is guesswork. The astronomy has been settled for centuries and is published openly by NOAA and the Naval Observatory. The only genuinely human choices are the twilight angle, the shadow factor, and what to do when the sun refuses to cooperate at high latitude. Everything else your app shows is arithmetic performed on your coordinates.

Muslim App computes prayer times for your exact location with madhhab and latitude adjustments, per-prayer minute corrections to match your mosque, and times that keep working offline once your location is saved. Download it for iOS or Android and set it to the convention your mosque follows.