Lunisolar Calendars - Calculating A Leap Month

Calculating A Leap Month

A rough idea of the frequency of the intercalary or leap month in all lunisolar calendars can be obtained by the following calculation, using approximate lengths of months and years in days:

• Year: 365.25, Month: 29.53
• 365.25/(12 × 29.53) = 1.0307
• 1/0.0307 = 32.57 common months between leap months
• 32.57/12 = 2.7 common years between leap years

A representative sequence of common and leap years is ccLccLcLccLccLccLcL, which is the classic nineteen-year Metonic cycle. The Buddhist and Hebrew calendars restrict the leap month to a single month of the year; the number of common months between leap months is, therefore, usually 36, but occasionally only 24 months. Because the Chinese and Hindu lunisolar calendars allow the leap month to occur after or before (respectively) any month but use the true motion of the sun, their leap months do not usually occur within a couple of months of perihelion, when the apparent speed of the sun along the ecliptic is fastest (now about 3 January). This increases the usual number of common months between leap months to roughly 34 months when a doublet of common years occurs, while reducing the number to about 29 months when only a common singleton occurs.