Chinese leap months: the rule, how often they happen and the 2033 case

Twelve lunar months add up to about 354 days, eleven days short of the solar year. If nothing were done, Chinese New Year would drift backwards through the seasons. The Chinese calendar keeps it in place by inserting a 13th month, the leap month (闰月), about 7 times every 19 years. From 1901 to 2100 that happens 73 times.

The rule

The calendar in use today follows the rules set in 1645 (the Shixian calendar) and written down in China's national standard GB/T 33661-2017. In short:

• Each month begins on the day of a new moon, in Beijing time.
• The winter solstice always falls in the 11th month.
• Twelve of the 24 solar terms are principal terms (zhongqi), one per 30 degrees of the Sun's path. When 13 new moons fall between one 11th month and the next, the first month that contains no principal term becomes the leap month. It takes the number of the month before it.

Principal terms are about 30.4 days apart, a little longer than a lunar month of 29.5 days, so now and then a month slips between two of them. That month is the one repeated.

Which months repeat

The Earth moves slowest in early July, so the principal terms in summer are spaced further apart and a month without one is more likely there. That is why leap 4th, 5th and 6th months are the most common, and winter leap months are rare.

The rare ones in this period are the leap 10th month of 1984, the leap 9th month of 2014 and the leap 11th month of 2033.

The 2033 case

2033 is known among calendar specialists as a difficult year: the months around the winter solstice are close to the edges of the rule, and older calendar software placed its leap month differently. Under the current rules, which the Hong Kong Observatory's tables follow, 2033 has a leap 11th month starting December 22, 2033. Because that extra month comes after the winter solstice, the following Chinese New Year, February 19, 2034, is the third new moon after the solstice instead of the usual second, the only such case from 1902 to 2100.

Leap months from 2000 to 2050

How long a lunar year is

Lunar months have 29 or 30 days, so a 12-month year has 353 to 355 days and a 13-month year 383 to 385. Counts for the lunar years 1901 to 2099: