Why the Chinese Calendar Has Leap Months

Leap months

A Chinese leap month is an additional lunar month. It gives a year thirteen months while keeping the familiar month numbers one through twelve. The added month repeats the preceding number with the label leap. Like any other month, it has its own days, beginning at lunar day one. This is part of the calendar's lunisolar structure: months follow the Moon, while the arrangement of months also follows the solar seasons.

Why twelve lunar months are too short

The average interval between new moons, called a synodic month, is about 29.5306 days. Twelve such intervals total approximately 354.37 days. The mean tropical year, which tracks the seasonal cycle, is about 365.2422 days. The yearly shortfall is almost eleven days. Without intercalation, the beginning of a twelve-month lunar year would move progressively earlier through the seasons.

The difference becomes clearer over a longer interval:

Nineteen twelve-month years contain 228 months. Adding seven gives 235, which is very close in length to nineteen solar years. This explains the familiar description “seven leap months in nineteen years.” It is an approximation to the two astronomical cycles, not a repeating lookup schedule for the modern calendar. Actual month placement depends on new moons and solar terms.

A leap month still lasts 29 or 30 calendar days. Those lengths come from the dates of successive new moons, so an extra month need not have the same length as the ordinary month whose number it repeats. Chinese intercalation is independent of February 29 in the Gregorian calendar.

The intercalation rule

The 24 solar terms divide the Sun's annual apparent path into steps of 15 degrees. Alternate terms form the twelve principal terms, spaced 30 degrees apart. Winter Solstice is one of them. These markers connect lunar-month numbering to the seasons.

The modern procedure starts with the lunar month containing Winter Solstice, which is month eleven. Identify two successive solstice-containing months and count the lunar months from the beginning of the first up to, but excluding, the beginning of the second. If there are twelve, that interval needs no leap month. If there are thirteen, its first month without a principal term is the leap month. Number the other months in sequence and let the leap month repeat its predecessor's number.

This month-eleven-to-month-eleven interval is different from a lunar year running from one New Year to the next. A calculation therefore needs information on both sides of the year being numbered. It also assigns events to whole calendar days: a month starts at midnight on the date containing the new moon, rather than at the instant of conjunction. A principal term falling on that opening date belongs to the new month.

Leap month six in 2025

The month sequence in 2025 shows how a month can contain a solar term without containing a principal term. Dates at both ends of each range are included.

Beginning of Autumn falls on August 7, inside the leap month. It belongs to the other set of twelve solar terms, so it does not fill the missing principal-term position. End of Heat falls on the opening date of month seven and belongs to that new month.

Birthdays and historical records

Treat the leap label as part of a date's identity. A complete record gives the lunar year, month number, leap status and lunar day together. An ordinary month and its leap month contain separate sets of dates, even though their numbers repeat.

For a birthday record, keep the original birth date separate from the rule chosen for annual celebration. A year without the corresponding leap month has no exact recurrence of that leap-month date. The calendar identifies the available dates, while the choice of a substitute celebration date belongs to the family.

For an older document, also preserve its wording, place and historical year designation. Earlier astronomical methods and time conventions can produce dates different from a modern calculation extended backwards.