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Leap Years in the Persian Calendar

As an observational calendar based on the timing of the astronomical seasons, the Solar Hijri calendar does not have mathematical rules to determine leap years. However, there is a rule-based version that achieves a similarly high degree of accuracy.

Iran flag waving in the wind above the skyline of Tehran lit by the orange glow of sunset.

Iranian flag over Tehran, Iran.


Seasons Determine Leap Years

The Solar Hijri calendar year begins and ends with the vernal equinox. Like in the Gregorian calendar, there are common years with 365 days and leap years with 366 days.

The distribution of leap years, however, is not determined by mathematical rules, but by the actual timing of the equinoxes. This makes the Solar Hijri calendar, which is the official calendar in Iran and Afghanistan, one of the world's most accurate calendar systems.

Rule-Based Alternative

Several proposals for mathematical leap year rules have been made to approximate the inherent accuracy of the Solar Hijri calendar without relying solely on astronomical observations. With a deviation from the solar year of only 1 day in about 110,000 years, the most widely accepted set of rules are about as accurate as the observational calendar:

  • Group years into periods of 2820 years each. The current 2820-year cycle began in 1096 CE.
  • Divide the periods into 88 cycles of varying lengths, following this pattern for the first 84 cycles:
    29 years, 33 years, 33 years, 33 years,
    29 years, 33 years, 33 years, 33 years...
  • The final cycle in each 2820-year period is 37 years long; the pattern for the final 4 cycles is:
    29 years, 33 years, 33 years, 37 years.
  • Number the years in each cycle starting with 0. For instance, the year 1096 CE is year 0, 1097 CE is year 1, 1098 CE is year 2, and so on.
  • All years whose ordinal numbers are evenly divisible by 4 are leap years. The first year of each cycle (ordinal number 0) is a common year.

Topics: Leap Year