The Solar Hijri calendar

Fact sheet

Scientific classification

• Solar: it follows the tropical year (the cycle of the seasons) alone, so each month always falls in the same season; its months have nothing to do with the moon, despite its era being tied to the Hijra.
• Astronomical: the New Year can only be known by computing the true moment of the equinox, making it one of the very few civil calendars based on the true position of the sun rather than an arithmetical mean. Reingold and Dershowitz place it among the “astronomical calendars” alongside the modern Chinese and the French Republican.
• Its accuracy: because the year is measured by the March equinox itself, no error accumulates: Nowruz stays with the equinox as long as the astronomical computation is correct. The year it follows is the “vernal equinox year” (about 365.2424 days), not the mean tropical year (about 365.2422 days) — which is right for a calendar whose New Year is the March equinox.
• The price of accuracy: there is no closed leap rule; determining a leap year requires astronomical computation, and the verdict can waver when the equinox falls very close to noon. That is why the Iranian authorities publish the calendar in advance.

Rules

1. The New Year: if the moment of the March equinox falls before true noon (the sun’s meridian transit) on the 52.5° E meridian, that day is 1 Farvardin; if after it, the next day. This is the wording of the Iranian law of 1925 as applied by the official authorities.
2. The months: Farvardin to Shahrivar have 31 days, Mehr to Bahman 30, and Esfand 29. These lengths approximate the time the sun spends in each zodiac sign: the sun is slower in the spring–summer half of the year, so its months are longer.
3. The leap year: if the next Nowruz is 366 days later, Esfand has 30 days. This is not decided by a numerical rule but by computing the two Nowruz days.
4. The week: for Iranians it begins on Saturday with Friday as the weekly holiday, as in the Muslim world; the calendar itself does not define the week.

Example (computed by the site’s engine): the 2025 equinox fell at 12:31 Tehran time, minutes after true noon at 52.5° E, so 20 March was not New Year’s Day, and the year 1404 began on 21 March 2025; so 1403 was a leap year.

Nowruz and leap years in recent years

The moment of the equinox in Tehran time, and the resulting Nowruz, computed by the site’s engine from NASA ephemeris data:

The equinox falls about 5 hours 49 minutes later each year, so it crosses noon roughly once every four years, producing a leap year. But between the leap years 1403 and 1408 there are five years, not four; this five-year interval recurs about once in every 33 years, keeping the mean year matched to the equinox. Between 1900 and 2150 Nowruz falls on 20 or 21 March, and until 1959 it sometimes fell on 22 March.

Months and their names

The Iranian month names are those of the ancient Zoroastrian months, most of them names of the “Amesha Spentas” and “Yazatas,” sacred beings and concepts of the Zoroastrian religion recorded by al-Biruni in “The Remaining Signs.” Afghanistan names the months after the Arabic zodiac signs, and this site shows them in their standard Arabic form (al-Hamal, al-Thawr, al-Jawza’, …, al-‘Adhra’ instead of Sunbula):

In Pashto the same signs have other local names. Before 1925 the months in official Iranian calendars were also named after the Arabic zodiac signs, and the new law revived the old Persian names.

Counting the years

• Solar Hijri: year 1 begins at the Nowruz of the year of the Hijra (622 CE), the Hijra itself falling about six months later. So the solar year = Gregorian − 621 from Nowruz to the end of December, and − 622 from January to Nowruz. Because the solar year is about 11 days longer than the lunar, the two counts now differ by 42–43 years (1405 solar corresponds to 1447–1448 lunar).
• Yazdegerdi: from the accession of Yazdegerd III, the last Sasanian king, on 16 June 632 CE. Zoroastrians still date by it.
• Jalali (Maliki): from the year of Malik-Shah’s reform (1079 CE). Astrologers used it for centuries, then the count from the Hijra prevailed.
• Shahanshahi (Imperial): from the accession of Cyrus the Great (559 BCE). Shah Mohammad Reza Pahlavi imposed it in 1976, so the count jumped from 1355 to 2535; it was abolished in 1978.
• Kurdish: used by many Kurds with the same solar months, counting the years from 612 BCE (the fall of Nineveh to the Medes and their allies): Kurdish year 2726 began with Nowruz 2026.

History

1. 6th c. BCE

   The months of the Behistun inscription

   The Behistun inscription of Darius I mentions Old Persian months with names different from today’s, in a lunisolar calendar on the Babylonian model.
2. 5th–4th c. BCE

   The Zoroastrian calendar

   Probably in the late Achaemenid period the Zoroastrian calendar appears: 12 months of 30 days named after the Amesha Spentas and Yazatas, followed by 5 days that Arab historians called “the five stolen days,” making a year of 365 days with no intercalation. Each of the thirty days of the month has its own name.
3. 224 CE

   The Sasanian calendar

   The Sasanian state was founded by Ardashir I, with the Zoroastrian calendar as its official calendar. With no intercalation, Nowruz moved earlier through the seasons by about a day every four years. Al-Biruni reports that the Sasanians intercalated a month every 120 years; modern historians doubt that this was applied regularly.
4. 632 CE

   The Yazdegerdi era

   The accession of Yazdegerd III, from which the Yazdegerdi era begins.
5. Abbasid era

   The Nowruz of al-Mu‘tadid

   Land tax was collected by the Persian year because of its link to the harvest, so as “Nowruz” moved earlier, farmers were asked to pay before their crops ripened. Al-Mutawakkil tried to delay it, and al-Mu‘tadid completed this in 282 AH / 895 CE with the “Mu‘tadidi Nowruz”: the opening of the tax year was moved to 11 June (Julian) and fixed by a four-year intercalation.
6. c. 1006 CE

   Nowruz returns to the equinox

   After centuries of drift the Zoroastrian Nowruz again coincided with the March equinox, which encouraged the call for a calendar that would keep it there.
7. 1079 CE

   The Jalali era

   Under the Seljuk sultan Jalal al-Dawla Malik-Shah and his vizier Nizam al-Mulk, a team of astronomers at the Isfahan observatory, among them Omar Khayyam, Abu Hatim al-Muzaffar al-Isfizari and Maymun ibn Najib al-Wasiti, set up the “Jalali era”: it begins with a Nowruz coinciding with the sun’s entry into Aries (15 March 1079, Julian), and the year is regulated by observation so that it does not drift. The sources attribute its months to the sun’s stay in the signs, and the 33-year cycle is attributed to Khayyam, though its precise attribution to him is debated.
8. 12th–19th c.

   The Jalali in the astronomical tables

   The lunar Hijri remained the calendar of state and religion, while the Jalali and its derivatives were used in astronomical tables, annual almanacs and agricultural taxes, often naming the months after the Arabic zodiac signs.
9. 1911

   The fiscal zodiac calendar

   The second Iranian Majlis (21 February 1911) adopted a solar calendar with zodiac names for financial affairs, in use until 1925.
10. 1922

    Afghanistan

    Afghanistan under Amanullah Khan adopted the Solar Hijri calendar with the Arabic zodiac names.
11. 31 March 1925

    The Iranian calendar law

    The law of the Iranian Majlis (11 Farvardin 1304) under Reza Khan’s government: a true solar year beginning on the first day of spring; month lengths of 6×31, then 5×30, then 29/30; revival of the old Persian month names; counting from the Hijra; and abolition of the Turco-Mongol twelve-animal cycle in official dating.
12. 1976–1978

    The Shahanshahi count

    Shah Mohammad Reza Pahlavi replaced the Hijri count with the Shahanshahi count; the Hijri count was restored in 1978 under pressure from the opposition shortly before the revolution.
13. 1979

    The constitution of the Islamic Republic

    Constitution of the Islamic Republic (Article 17): the official calendar starts from the Hijra of the Prophet ﷺ; both the solar and lunar Hijri calendars are recognized, and government offices work by the solar.
14. 1996–2001

    The first Taliban rule

    The first Taliban government made the lunar Hijri the state calendar in Afghanistan; the solar returned after its fall.
15. 2004

    The constitution of Afghanistan

    Constitution of Afghanistan (Article 18): the calendar is from the Hijra, and the basis of work of state offices is the Solar Hijri calendar.
16. 2022

    Official correspondence in Afghanistan

    According to Afghan press reports, the Taliban administration directed that official administrative correspondence use the lunar Hijri, while the solar remained in use in daily life and farming.

Arithmetical cycles

Because the official rule is astronomical, many have tried to approximate it with numerical cycles that avoid computing the equinox:

• The 33-year cycle: 8 leap years in every 33, a mean year of 365.24242 days, very close to the vernal equinox year. Compared with the astronomical computation in the site’s engine, its leap years match the official ones from 1900 CE to 2123 CE (year 1502), and then begin to diverge.
• The 2820-year cycle: proposed by Ahmad Birashk in the 20th century (683 leap years in 2820, divided into cycles of 128 and 132 years), and widely used in software. But it is less accurate than its proponents thought: it disagreed with the official calendar in 1403 and 1404 (making 1404 the leap year instead of 1403), and will disagree again in 1436 and 1469.

The conclusion of the scholarly literature (Borkowski 1996; Reingold and Dershowitz): the Iranian calendar is astronomical by nature, and the cycles are approximations valid over a limited range, not a substitute for calculation.

Current use

• Iran: the official calendar of the state and civil life; the annual calendar is issued by the Calendar Center of the Institute of Geophysics at the University of Tehran.
• Afghanistan: the predominant civil calendar in daily life, farming and education, with Arabic zodiac names in Dari and local names in Pashto.
• The Kurds: in Iran, Iraq and elsewhere, with the solar months and their own year count; Nowruz is a national festival.
• Nowruz: an official holiday in Iran, Afghanistan, Central Asia, Azerbaijan and the Kurdistan Region; UNESCO inscribed it on the intangible heritage list, and the United Nations recognized the “International Day of Nowruz” on 21 March.
• Zoroastrians: still use the 365-day Zoroastrian calendar in three forms: the “Shahanshahi” and “Qadimi” without intercalation, and the “Fasli” tied to the equinox.

On this site

• The site computes Nowruz by the same official rule: the moment of the equinox from NASA ephemeris data, compared with true noon at 52.5° E, with no table or approximate cycle; so it matches the official calendar even in the years where the arithmetical cycles fail.
• The months are shown with the Arabic zodiac names (al-Hamal, al-Thawr, …) in the Arabic interface, and with their Persian names in the English interface.
• The computation is extended before 1925 (proleptically) by the same rule, so its old dates are computed, not historical: before 1925 official dating was by the lunar Hijri, and local solar calendars differed in their month names and lengths.

Solar Hijri to Gregorian Gregorian to Solar Hijri