Persian Calendar Converter

The Persian or Solar Hijri calendar is a solar calendar whose year begins at the instant of the March equinox as observed on the 52.5 degrees east meridian (Iran Standard Time), so Nowruz falls on 20, 21 or occasionally 22 March. Its epoch is the Hijra of 622 CE, the same starting point as the Islamic lunar calendar, which is why Persian year numbers run roughly 621 or 622 behind Gregorian ones. Month lengths are fixed by statute: Farvardin through Shahrivar have 31 days, Mehr through Bahman have 30, and Esfand has 29 days in a common year and 30 in a leap year, giving 365 or 366 days. Conversion routines do not translate calendars directly; they route both dates through the Julian Day Number, a continuous integer count of days that is calendar-agnostic. The Persian epoch sits at JDN 1948320 or 1948321 depending on whether the noon or midnight convention is used. Two caveats matter for any converter. First, the arithmetic leap rule used here is the Birashk 2820-year cycle approximation, not the observational equinox rule that Iran actually applies, so predicted leap years can disagree in a handful of cases such as 1403 and 1436 AP. Second, the Hijri output uses a tabular 30-year cycle with 11 leap years of 355 days, giving a mean month of 29.530556 days against the true synodic month of 29.530589 days. Because most Muslim countries begin months on a physical crescent sighting, tabular Hijri dates can differ from locally declared dates by one or two days.

The Iranian solar calendar in its classical form dates to 1079 CE, when the Seljuk sultan Malik-Shah I commissioned a group of astronomers at Isfahan, among them the mathematician and poet Omar Khayyam, to reform the drifting Yazdegerdi calendar of 365 days that had no leap correction at all. The resulting Jalali calendar tied the year start to the vernal equinox and achieved a mean year length closer to the tropical year than the Julian calendar then in use in Europe. Its leap years were determined by observation of the equinox rather than by a fixed rule, which is why medieval sources give no single leap algorithm. The modern statutory form was adopted by the Iranian parliament on 31 March 1925, which fixed the 31 or 30 or 29 day month pattern, standardized the Persian month names drawn from Zoroastrian tradition, and retained the equinox as the year boundary. Afghanistan adopted the same structure in 1957 while using Arabic month names. In 1976 Mohammad Reza Shah Pahlavi replaced the Hijra epoch with an imperial era counted from Cyrus the Great, so 1355 AP became 2535; public opposition forced a reversal in 1978. The Julian Day Number that underpins the conversion algorithm was proposed separately by Joseph Justus Scaliger in his 1583 work De emendatione temporum, and the systematic JDN bridge method used by modern software was set out by Edward Reingold and Nachum Dershowitz in Calendrical Calculations, first published in 1997.