The Vizier Nizam al-Mulk granted Omar a pension, which enabled him to devote himself to learning and research, especially in mathematics and astronomy. In 1074 he was invited to undertake astronomical research. Omar was also commissioned to build an observatory in the city of Isfahan in collaboration with other astronomers. Malik Shah appointed him a member of a group of eight scholars assigned to reform the Moslem calendar, a task comparable to Pope Gregorius XIII's revision of the Julian calendar. Their work inaugurated the Jalalaean or Seljuq era, beginning March 15, 1079. Omar's revision of the old Persian solar calendar was discontinued when Islamic orthodoxy gained power, but in 1925 it was again introduced in Iran.

The Iranian calendars or Persian calendars (Persian: گاهشماری ایرانی‌ Gahshomari-ye Irani) are a succession of calendars invented or used for over two millennia in Greater Iran. One of the longest chronological records in human history, the Iranian calendar has been modified time and again during its history to suit administrative, climatic, and religious purposes

The modern Iranian calendar (Solar Hejri) is now the official calendar in Iran and Afghanistan. It begins on the vernal equinox as determined by astronomical calculations for the Iran Standard Time meridian (52.5°E or GMT+3.5h). This determination of starting moment is more accurate than the Gregorian calendar because it is synchronized with the vernal equinox year,[1] but requires consulting an astronomical almanac. Its years are designated AP, short for Anno Persico. The Iranian year usually begins within a day of 21 March of the Gregorian calendar. To find the corresponding year of the Gregorian calendar, add 621 or 622 (depending on the time of the year) to a Solar Hejri year. A short table of year correspondences between the Persian and Gregorian calendars is provided below.

On 21 February 1911, the second Persian parliament adopted as the official calendar of Iran the Jalālī solar calendar with months bearing the names of the twelve constellations of the zodiac and the years named for the animals of the duodecennial cycle; it remained in use until 1925.[6] The present Iranian calendar was legally adopted on 31 March 1925, under the early Pahlavi dynasty. The law said that the first day of the year should be the first day of spring in "the true solar year", "as it has been" (کماکان). It also fixed the number of days in each month, which previously varied by year with the tropical zodiac. It revived the ancient Persian names, which are still used. It specified the origin of the calendar (Hegira of Muhammad from Mecca to Medina in 622 CE). It also deprecated the 12-year cycles of the Chinese-Uighur calendar which were not officially sanctioned but were commonly used.

The first six months (Farvardin–Shahrivar) have 31 days, the next five (Mehr–Bahman) have 30 days, and the last month (Esfand) has 29 days or 30 days in leap years. The reason the first six months have 31 days and the rest 30 may have to do with the fact that the sun moves slightly more slowly along the ecliptic in the northern spring and summer than in the northern autumn and winter (the time between the vernal equinox and the autumnal equinox is about 186 days and 10 hours, the opposite duration about 178 days, 20 hours).

The Solar Hejri calendar (Persian: گاهشماری هجری خورشیدی یا هجری شمسی) produces a five-year leap year interval after about every seven four-year leap year intervals. It usually follows a 33-year cycle with occasional interruptions by single 29-year or 37-year subcycles. By contrast, some less accurate predictive algorithms are suggestion based on confusion between average tropical year (365.2422 days, approximated with near 128-year cycles or 2820-year great cycles) and the mean interval between spring equinoxes (365.2424 days, approximated with a near 33-year cycle).

In 1976, Shah Mohammad Reza Pahlavi changed the origin of the calendar, using the birth of Cyrus as the first day, rather than the Hejra of Muhammad. Overnight, the year changed from 1355 to 2535. The change did not last however as it was "largely ignored".

In the Iranian calendar, every week begins on Saturday and ends on Friday. The names of the days of the week are as follows: shambe (natively spelled "shanbeh", Persian: شنبه), yekshambe, doshambe, seshambe, chæharshambe, panjshambe and jom'e (yek, do, se, chæhar, and panj are the Persian words for the numbers one through five). The name for Friday, jom'e, is Arabic (Persian: جمعه). Jom'e is sometimes referred to by the native Persian name, adineh ɒːdiːne (Persian: آدینه). In most Islamic countries, Friday is the weekly holiday.

Calculating the day of the week is easy, using an anchor date. One good such date is Sunday, 1 Farvardin 1372, which equals 21 March 1993. Assuming the 33-year cycle approximation, move back by one weekday to jump ahead by one 33-year cycle. Similarly, to jump back by one 33-year cycle, move ahead by one weekday.

As in the Gregorian calendar, dates move forward exactly one day of the week with each passing year, except if there is an intervening leap day when they move two days. The anchor date 1 Farvardin 1372 is chosen so that its 4th, 8th, ..., 32nd anniversaries come immediately after leap days, yet the anchor date itself does not immediately follow a leap day.