One takvim, 118 places

How the takvim is built

One day, six vakats

Sarajevo’s 21 June, in summer time. Every other place in the takvim is this row plus its own minutes: one for Zora and sunrise, another for Podne, a third for the afternoon and evening.

Zora

2:40

Izlazak sunca

4:57

Podne

12:49

Ikindija

16:55

Akšam

20:38

Jacija

22:34

The sun over Sarajevo that day: sunrise 5:04, noon 12:48, sunset 20:32. So the takvim’s sunrise is early and its Akšam late, margins it keeps all year: sunrise 8 to 4 minutes early, Akšam 4 to 8 late. Zora is the moment the sun is 18.0° below the horizon, every day of the year to within 0.1°; Jacija is 16.0°; Ikindija is when a shadow is its object’s length plus its noon shadow (a factor of 1.0).

Podne moves with longitude only, so its offset never changes. Zora and Akšam swap over the year: the north-west is later on summer evenings and winter mornings.

The whole year

A year in Sarajevo

The six vakats for every day of the year, over the sky they are timed by: full night, the twilight between night and day, and daylight. Zora sits right on the edge of night, at 18°; Jacija a little inside the twilight, at 16°. The dashed lines are the real sunrise and sunset; the takvim’s sunrise and Akšam sit just outside them, too close to part at this scale, so the readout gives the margin in minutes. Point at the chart, or tap it, for a day’s times.

Against other methods

Why Bosnian times differ

Every method agrees on noon, sunrise and sunset; they disagree on three things. How deep below the horizon the sun must be for Zora and Jacija. Whether to add a margin of minutes to the moments the sun gives. And which shadow marks Ikindija. Here are the methods in wide use, set against Sarajevo’s takvim: each dot is how many minutes later (right) or earlier (left) a method puts that vakat.

Three things set the takvim apart. Its margins: sunrise 6 minutes before the Muslim World League’s, Akšam 6 minutes after it, the same kind of margin Diyanet adds (7 minutes off sunrise, 7 minutes onto Akšam), which is why Diyanet’s dots sit on the line for both. Its Jacija angle: 16°, shallower than anyone’s here but ISNA’s, so its Jacija comes 7 minutes before the League’s and Diyanet’s. And its Ikindija, at the first shadow length, with no margin: Diyanet adds 4 minutes. The Hanafi rule of two shadow lengths, which some apps offer, would put Ikindija in Sarajevo at 18:09 on 21 June instead of 16:55.

The step

A month, one offset

How to read it. The line along zero is Sarajevo. The curve is the sun: how many minutes later (above zero) or earlier (below) it sets in Bihać than in Sarajevo, day by day. It sits above zero because Bihać lies west of Sarajevo, and it bends with the seasons because Bihać lies north of it: further north the summer days are longer and the winter days shorter. The staircase is the takvim, which cannot follow a curve: it holds one whole number of minutes for a month, then steps. The shading between them is how far the takvim’s Akšam is off the sun that day, before Sarajevo’s own margin of about 6 minutes is added on top.

In Bihać the gap averages 0.5 minutes and is widest on 1 November, at 1.2. Point at the chart, or tap it, for any day.

The finding

The south, mirrored

In Trebinje the staircase does not follow the curve at all; it runs the other way. Trebinje lies 1.1° south of Sarajevo, so its summer days are shorter and its winter days longer: the sun sets there earlier than in Sarajevo in June and later in December. The takvim moves Trebinje’s Akšam later in June and earlier in December. The dashed line is the sun Trebinje would have if it lay 1.1° north of Sarajevo instead: that is the line the staircase follows.

It is not only Trebinje. Of the 33 places in the takvim more than 0.15° south of Sarajevo, 28 fit a latitude as far north better than their own. At their real latitude the takvim misses them by 2.3 minutes on average; at the mirrored one by 0.7, close to what it misses the 68 places north of Sarajevo by (0.3, most of it rounding to whole minutes). In summer the mirroring makes Akšam later than it needs to be, an extra margin; in winter it takes the margin away, which is how Akšam in eastern Herzegovina comes before sunset.

The Takvim explains how it makes these offsets, and the explanation suggests a likely cause. A place’s correction is one part for longitude and one for latitude, and the latitude part is written as

t = Δ × g × (φ − φ₀)

where φ is the place’s latitude and φ₀ Sarajevo’s, so for a place south of Sarajevo the bracket is already negative. The same text then gives a rule for the sign: “Korekcija je pozitivna (+) za mjesta sjeverno od Sarajeva a negativna (−) za mjesta južno”, the correction is positive north of Sarajevo and negative south of it. Applied on top of the bracket, that sign turns the correction around for every place to the south, which is exactly the mirroring above. That is a reading of the published method, not a confirmed account of how the tables were worked out. The same text puts their accuracy “u granicama jedne minute”, within a minute; south of Sarajevo they miss by 2.3 minutes on average.

Takvim against the sun

Where it drifts

Akšam in the takvim, minus sunset computed for the town’s own coordinates, across a year. Near Sarajevo it stays inside the margin all year. South of it the offsets miss by more each season (the mirroring above), and in winter the misses use the margin up. Trebinje’s December offset puts Akšam 3 minutes before Sarajevo’s, though in winter the sun there sets later than in Sarajevo, not earlier. It comes early there on 64 days, in January, November and December.

1. Trebinje−2.4 to +14.9 min
2. Bileća−1.5 to +13.7 min
3. Neum−1.5 to +13.5 min
4. Ljubinje−1.6 to +13.3 min
5. Novi Pazar+0.8 to +14.1 min
6. Sarajevo, for scale+4.4 to +7.9 min

Caveats

How sure this is

The times are the Islamic Community’s. Sarajevo’s match its 2026 calendar to the minute, and every place’s monthly offset matches the per-city tables in its 2023 Takvim; vaktija.ba serves the same numbers today. The tables in the newest printed edition were not checked line by line.

“Before sunset” here means before sunset computed the standard way: the sun’s centre 0.833° below a flat, sea-level horizon, accurate to well under a minute. That is the yardstick that shows Sarajevo’s own Akšam 4 to 8 minutes after sunset all year, the margin the takvim adds on purpose. By the same yardstick the margin is gone in Trebinje, Bileća, Ljubinje and Neum in winter, by 1.5 to 2.4 minutes.

What someone sees on the ground can differ. Hills to the south-west, where the winter sun sets, can hide it earlier than the computed sunset; the air bends its light by a little more or less with the weather, worth up to about a minute; and one time serves a whole municipality, whose ends are about half a minute apart. That is why Stolac, Čapljina and Gacko, early by under a minute on a few days, are shown as marginal and not counted.

None of this is a ruling on when to pray or break the fast. That belongs to the Islamic Community, whose muvekit draws up the takvim.

Method

How it was measured

The takvim is the one Vaktija ships, the same one vaktija.ba serves: Sarajevo’s day for every date, and each place’s offset per month in whole minutes. Both halves are the Islamic Community’s own. Sarajevo’s times match its 2026 calendar, and the offsets match the per-city tables (“Mjesne vremenske razlike”) in its 2023 Takvim; for the seven places where Akšam ever comes before the computed sunset, all 84 monthly rows agree. The method of the offsets is the one its 2025 Takvim describes. The takvim itself names Akšam “zalazak Sunca”, sunset.

The sun is computed for each place’s coordinates, from OpenStreetMap, with NOAA’s solar calculator (after Meeus), checked against standard values for the equation of time and the sun’s declination, for every day of 2026. Sunrise and sunset are the sun’s centre 0.833° below a flat, sea-level horizon; hills and valleys, which move the sun people actually see, are not in it. Times are in Europe/Sarajevo, summer time included.

The other methods use the parameters of the open-source adhan library: their twilight angles, Asr at one shadow length, and their fixed minute adjustments. Diyanet’s is adhan’s approximation of the Turkish Presidency of Religious Affairs’ published margins; its own published times can differ by a minute or so.

Sources: Vaktija’s takvim · coordinates © OpenStreetMap contributors · map: geoBoundaries (CC BY 4.0) · NOAA solar calculator · adhan