The Persian calendar is one of the oldest solar calendars in the world, with roots dating back to the Achaemenid Empire (6th century BCE). The modern Persian calendar was formalized during the reign of Malik-Shah I in 1079 CE by a commission of astronomers including Omar Khayyam. This Jalali calendar was remarkably accurate, with an error of only one day every 3,770 years. The calendar was officially adopted in Iran in 1925 and remains the national calendar of Iran and Afghanistan.
The Persian calendar is a solar calendar based on the Earth's orbit around the Sun. The year begins at the exact moment of the vernal equinox (Nowruz, around March 20-21). It has 12 months: the first six (Farvardin to Shahrivar) have 31 days, the next five (Mehr to Bahman) have 30 days, and the last month (Esfand) has 29 days in common years and 30 days in leap years. Leap years follow a 33-year cycle, with years 1, 5, 9, 13, 17, 22, 26, and 30 in each cycle being leap.
Persian to Gregorian: To convert 22 Bahman 1404 to Gregorian: 1 Farvardin 1404 = March 20, 2025. Add 31ร6 + 30ร4 + 22 = 328 days โ February 11, 2026.
Gregorian to Persian: 21 February 2026 = 3 Esfand 1404.
Sources: Encyclopรฆdia Iranica, "The Persian Calendar" (Dr. Kazimierz M. Borkowski, 1996).
The Islamic calendar was established in 638 CE by Caliph Umar ibn al-Khattab, with its epoch set to 622 CEโthe year of the Hijra (Prophet Muhammad's migration to Medina). Before Islam, Arabs used a lunisolar calendar with intercalary months (Nasฤซ'), which was prohibited in the Qur'an (9:36-37). The modern Islamic calendar is purely lunar, consisting of 12 months based on moon sightings.
The Islamic calendar has 354 or 355 days, about 11 days shorter than the solar year. Months alternate between 30 and 29 days, with the last month (Dhu al-Hijjah) having 30 days in leap years. Leap years follow a 30-year cycle with 11 leap years (years 2, 5, 7, 10, 13, 16, 18, 21, 24, 26, 29). The day begins at sunset, and months start with the sighting of the new moon.
Hijri to Gregorian (approximate): Gregorian year = Hijri year + 622 - floor(Hijri year/33). For 1447 AH: 1447 + 622 - 43 = 2026.
Sources: "ฤthฤr al-bฤqฤซyah" (Al-Biruni, 1000 CE), "Calendrical Calculations" (Dershowitz & Reingold, 1997).
The Hebrew calendar's origins trace to the Babylonian exile (6th century BCE) when Jews adopted the Babylonian lunisolar calendar. The current mathematical rules were developed during the Talmudic period (200-500 CE) and codified by Maimonides in his Mishneh Torah (1178 CE). The calendar's epoch (Anno Mundi) is calculated as 3761 BCE based on biblical genealogies.
The Hebrew calendar is lunisolar: months follow the moon (29 or 30 days), while years are adjusted to the solar cycle using the 19-year Metonic cycle. Seven leap years per cycle (years 3, 6, 8, 11, 14, 17, 19) add a 13th month (Adar I). The day begins at sunset.
Hebrew to Gregorian: Add 3760 to Hebrew year for dates after Rosh Hashanah (September-December), or 3761 for dates before.
Sources: "Mishneh Torah" (Maimonides, 1178), "The Hebrew Calendar" (A. Spier, 1986).
The Gregorian calendar was introduced by Pope Gregory XIII in October 1582 via the papal bull Inter gravissimas, reforming the Julian calendar (45 BCE). The Julian calendar's 365.25-day average had accumulated a 10-day drift by the 16th century, moving the vernal equinox from March 21 to March 11.
The Gregorian calendar has 12 months (31, 28/29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31 days). Leap years occur every 4 years, except centuries not divisible by 400, giving an average year of 365.2425 days.
Julian Day formula: JDN = day + floor((153m+2)/5) + 365y + floor(y/4) - floor(y/100) + floor(y/400) - 32045. For 21 February 2026: JDN = 2461108.
Sources: "Inter Gravissimas" (Pope Gregory XIII, 1582), "Calendrical Calculations" (Dershowitz & Reingold, 1997).
Different civilizations developed calendars based on local astronomical observations and religious needs.
The Persian calendar's equinox-based system makes it one of the most accurate.
The 354-day Islamic year is 11 days shorter than the solar year.
Gregorian: divisible by 4, except centuries not divisible by 400. Persian: 33-year cycle. Islamic: 11 leap years per 30-year cycle. Hebrew: 7 leap years per 19-year cycle.
Gregorian/Persian: midnight. Islamic/Hebrew: sunset.
A continuous day count since 4713 BCE, used for astronomical calculations.
To correct the 10-day drift from the Julian calendar.
Calculate days from Persian epoch (March 20, 622).
The lunisolar Hebrew calendar keeps holidays in the same seasons but shifts relative to Gregorian.
Tabular uses fixed cycles; observational depends on actual moon sighting.
A 19-year cycle where 235 lunar months โ 19 solar years.
Use the Julian Day Number as an intermediate.
It begins at the vernal equinox (Nowruz).
Muharram, Safar, Rabi' I, Rabi' II, Jumada I, Jumada II, Rajab, Sha'ban, Ramadan, Shawwal, Dhu al-Qa'dah, Dhu al-Hijjah.
2026 Gregorian โ 1404-1405 Persian โ 1447-1448 AH โ 5786 Hebrew.
Cheshvan and Kislev lengths vary to prevent holidays from falling on unsuitable days.
Introduced by Julius Caesar (45 BCE), with leap years every 4 years.
Months 1-6: 31, months 7-11: 30, month 12: 29/30.
622 CE, the year of Prophet Muhammad's migration (Hijra).
Gregorian year = Hijri year + 622 - floor(Hijri/33).
Latin for "in the year of the world," the Hebrew calendar's epoch (3761 BCE).
Tradition and ecclesiastical independence.
Solar follows Earth's orbit (365 days); Lunar follows moon phases (354 days).
In the 33-year cycle, leap years are those where year % 33 โ {1,5,9,13,17,22,26,30}.
Qur'an 9:36: Rajab, Dhu al-Qa'dah, Dhu al-Hijjah, Muharram.
The mean lunar conjunction in Hebrew calendar.
The Jalali calendar (1079 CE) influenced Turkish and Mogul calendars.
Shanbeh (Sat), Yekshanbeh (Sun), Doshanbeh (Mon), Seshanbeh (Tue), Chahฤrshanbeh (Wed), Panjshanbeh (Thu), Jom'eh (Fri).
Add 3760 for dates after Rosh Hashanah, 3761 for dates before.
Pope Gregory XIII commissioned the reform.
References: Encyclopรฆdia Britannica, Encyclopรฆdia Iranica, "Calendrical Calculations" (Dershowitz & Reingold, Cambridge University Press, 1997), "Chronology of Ancient Nations" (Al-Biruni), "Mishneh Torah" (Maimonides).