The structure of the Persian calendar

How is the year actually divided?

Most short accounts of the Persian calendar stop at its first day. The year opens at the vernal equinox, and everything after that is left as an implication. It leaves the more interesting question unanswered: how the rest of the year is divided, and by what.

The confusion has a shape worth naming. A calendar anchored to an astronomical event sounds as though it ought to be tidy — equal months, or a rule that repeats cleanly. A reader arriving from the Gregorian calendar expects the opposite: a set of lengths simply to be memorised. The Persian calendar is neither of those. Its months are unequal, but each length is the consequence of something measurable, and the part of the year that does not divide evenly is held in one place rather than scattered through the year. That is what makes its leap rule easy to state and impossible to guess.

Measured months, and one month that absorbs the remainder

The months are measured rather than inherited. Each begins as the sun enters a new sign of the zodiac, and the sun does not cross those signs at an even pace: the passages falling in the northern spring and summer take slightly longer than those in autumn and winter. The month lengths follow that unevenness. The first six months each run thirty-one days, the next five run thirty, and the last runs twenty-nine days in a common year and thirty in a leap year.

That final month is also the leap mechanism. The year begins on the day of the vernal equinox and ends on the day before the next one, so its total length is settled by the sky rather than by a repeating schedule. When the interval between two equinoxes covers an extra day, the last month takes it and runs thirty; otherwise it runs twenty-nine. There is no cycle to memorise. Leap years arrive in a pattern instead of at a fixed interval — most often four years apart, occasionally five.

The era counts from the Hijra, the emigration of the Prophet from Mecca to Medina. It shares that starting point with the lunar Hijri calendar but counts solar years, so the two year numbers separate steadily as they run forward.

What this means when you work with the dates

First, day arithmetic depends on which half of the year you are in. Adding a fortnight to a date in the first six months does not shift the day-of-year count by the same amount as adding it in the last five, because the months on either side are not the same size.

Second, anything that runs through the end of the year has to know whether that year is common or leap, since the final month is twenty-nine days long in one case and thirty in the other. A count that quietly assumes a single length will be short by a day for roughly a quarter of years.

Third, the structure is regular enough to reason about by hand and irregular enough that the boundaries are worth looking up rather than recalling. This product converts between the Gregorian years 1800 and 2100 and the Persian years 1178 and 1479, and its calendar tables set out 101 consecutive Persian years, from 1329 to 1429, month by month.