How Leap Year Rules Work Across Calendars

No calendar fits nature exactly. The tropical year is about 365.2422 days and the average lunar month about 29.53 days, and neither divides evenly into whole days or into each other. Every calendar therefore needs an intercalation rule, a way to add days or months so that it does not drift away from the seasons or the Moon.

Solar calendars add days. The Julian calendar adds one every four years, averaging 365.25 days and drifting by a day every 128 years or so. The Gregorian rule skips leap days in century years not divisible by 400, giving 365.2425 days. The Revised Julian calendar used by several Orthodox churches keeps century leap years only when the year leaves a remainder of 200 or 600 on division by 900, which matches the Gregorian calendar until 2800. The Ethiopian and Coptic calendars add a sixth day to their short thirteenth month every four years without exception.

Lunisolar calendars add whole months. The Hebrew calendar inserts Adar I in seven years of every 19, following the Metonic cycle in which 19 solar years almost equal 235 lunar months. The Chinese calendar inserts a leap month whenever a month contains no principal solar term, and Hindu calendars add an adhika masa roughly every 32 to 33 months.

Purely lunar calendars ignore the Sun entirely. The tabular Islamic calendar adds a day to the last month in 11 years out of every 30, keeping the months aligned with the Moon while the year as a whole moves through the seasons in about 33 years. At the other extreme, the Solar Hijri calendar of Iran needs no fixed rule at all: each year simply starts on the day of the March equinox as observed for Iran.