jalLeap: Determine Leap Year and First Day of Jalaali Year

In jalcal: Convert Between Jalaali (Persian or Solar Hijri) and Gregorian Calendar Dates

Determine Leap Year and First Day of Jalaali Year

Description

Based on the work by Kazimierz M. Borkowski (1996), this function determines whether a given Jalaali (Persian) year is a leap year and calculates the corresponding Gregorian year and the day in March when the Jalaali New Year (Nowruz) begins.

Usage

jalLeap(yearJ)

Arguments

yearJ

An integer representing the Jalaali (Persian) year.

Details

The Jalaali calendar is a solar calendar with an irregular leap year cycle, designed to align closely with the vernal equinox. Unlike the Gregorian calendar, which follows a fixed leap year rule, the Jalaali leap years are determined by a more complex astronomical system:

- A typical cycle lasts 33 years, with leap years occurring in years that leave a remainder of 1, 5, 9, 13, 17, 22, 26, or 30 when divided by 33. - The cycle is occasionally disrupted by "break years," which adjust for small differences between the astronomical year and the calculated calendar. - This function follows the leap year calculations and algorithm established by Kazimierz M. Borkowski (1996), who analysed equinox timings from AD 550 to 3800.

Value

A named list with the following elements:

leap	An integer: 0 if the Jalaali year is a leap year and 1, 2 or 3 if the Jallai year is a common year.
GregorianYear	The corresponding Gregorian year.
MarchDay	The Gregorian calendar day in March when the Jalaali year starts.

Author(s)

Abdollah Jalilian

References

- Borkowski, K. M. (1996). The Persian calendar for 3000 years. *Earth, Moon, and Planets*, 74, 223–230. [doi:10.1007/BF00055188](https://doi.org/10.1007/BF00055188)

Examples

# Check if 1403 is a leap year and get the start date of Nowruz
result <- jalLeap(1403)
print(result)

jalcal documentation built on April 3, 2025, 10:47 p.m.