How we compute a prayer time, and where the computation stops

A prayer time is not an observed fact: it is the result of an astronomical computation applied to a convention. The computation is the same everywhere; the convention is declared by an authority, and they do not agree with one another. This page says which of the two you are looking at, and what our computation is worth.

The computation, and its author

The method is the one PrayTimes.org documents: solar declination, equation of time, hour angle, asr by school, and a horizon constant of 0.833 degrees that holds atmospheric refraction and the sun's half-diameter. No value here is a religious rule. These are conventions declared by authorities, and the site republishes them as they stand.

The convention used is named on every page, with the authority that publishes it. The site never says which one is right: that is not a question a computation settles.

What the computation is worth, measured

The computation was compared time by time against another implementation, across 7 cities, 3 conventions and two seasons — 42 comparisons to the minute. Mean gap: 0.81 minute. Maximum gap: 2 minutes, never exceeded.

A positive gap means our computation gives a later time.

Why the tolerance is two minutes and not one

The 6 two-minute gaps all fall on maghrib or isha. Fajr, sunrise, dhuhr and asr never exceed one minute. The evening gap comes from the horizon constant and from rounding, not from the algorithm: two correct implementations diverge there, and neither is wrong.

The build tolerance is therefore two minutes. This is not a loosening: a one-minute tolerance would have failed correct code, and it is this check that established it.

Where the computation refuses to answer

Above 48.57 degrees north, the sun never descends to 17 degrees below the horizon at the summer solstice. Isha has no time that day — not a time that is hard to compute: no time at all. Fajr meets the same fate a little further north.

This is not a northern edge case. Of the 2,851 cities recorded, 1,130 are affected on at least one day of the year, and 3,551 places of worship out of 6,916. France north of Lyon, Belgium, the Netherlands, the United Kingdom and almost all of Germany lie above the threshold: this is the majority case for this site's readers.

When the angle is never reached, the computation returns an absence, never an invented time. In Stockholm, on 21 June 2026, fajr and isha have no time: the page says so and does not fill the hole.

The rule applied when the angle is missing, and who took it

The site does not choose a rule. For each country it applies the one adopted by the very authority whose convention it already republishes. Where that authority has not pronounced, nothing is applied: the absence remains an absence.

For countries whose declared convention is that of the Muslim World League, the decision exists. Its fiqh council took it with the Islamic Crescents' Observation Project after four meetings — including a conference held in Brussels on 25 and 26 May 2009, devoted to the European countries. The method is called Local Relative Estimation — estimation relative locale and applies between 48.6 and 66.6 degrees of latitude.

That band is not a round number chosen by a committee: 48.6 is the fajr threshold at 18 degrees, that is 90 − 23.44 − 18, and the upper bound is the polar circle. The authority reasoned on the same physics as this computation, and that can be checked.

The procedure, in seven steps

1. calculer l'ecart entre le coucher et l'isha — « Isha Length »
2. calculer l'ecart entre le coucher et le lever — « Night Length »
3. en deduire le rapport « Isha Percentage »
4. en faire la moyenne sur les jours ou l'angle EST atteint — « Average Isha Percentage »
5. appliquer ce pourcentage pour l'isha les jours ou l'angle n'est pas atteint
6. appliquer le meme pourcentage pour le fajr
7. pendant la periode de disparition, retirer 5 minutes par jour a l'isha de la veille (et en ajouter 5 au fajr) jusqu'a raccord

Procedure republished as its publisher publishes it, without rewriting.

Where it applies, and where nothing applies

No recorded city lies above the threshold: the question does not arise, and the page does not raise it.

For the other countries, the authority we follow publishes no rule for the days when the angle is not reached. We therefore apply none, and we do not fill the gap with another authority's: that would be deciding in place of the one we cite. The page shows the absence and gives the reason for it.

An estimated time is never presented as a computed one

When the rule applies, the page says so and names the rule. The reader sees which of the two they are looking at — that is the distinction the decision itself seeks to preserve, and it would vanish if both were shown the same way.

A divergence we do not hide

A British source describing the same Brussels committee names the method adopted “aqrab al-ayyam” — “the nearest day” — and not local relative estimation. These are two different rules, and we do not claim they coincide. We republish the procedure as written, citing its publisher and its date, and we record the discrepancy here rather than choosing in silence.

An ambiguity in the procedure, and what it costs

The sixth step says to apply “the same percentage” to fajr. That reads two ways: the same value as isha's, or the same computation transposed to fajr. Both are defensible, and they do not give the same time, since fajr is measured at 18 degrees and isha at 17.

The gap is not negligible: up to 6 minutes on fajr in Amsterdam at the solstice, which is more than the tolerance we accept from another implementation. We keep the second computation, the only one consistent with the physics of the two angles, and we write here that the question remains open.

What this computation rests on, and what it does not do

The cities and places of worship come from OpenStreetMap, recorded on 15 September 2026. The derived database is published under the same licence, ODbL, with attribution.

The comparison implementation was used for development only. Its licence is not established to this day, and the site sends it no request in production — neither for a time nor for a check.

No prayer time on this site is requested from an outside service. Everything is computed at build time, from the city's coordinates and the declared convention.

© OpenStreetMap contributors