Before you start protesting, we are not talking about the Western (Gregorian) calendar but about the Chinese one 😉 .

In the Western calendar, a year has 365 days, but one orbit of Earth around the Sun takes 365.25 days, 6 hours more! To compensate for this shortage, an extra day is added (29 February), when the year is divisible by 4. As 2025 is not divisible by 4, it is NOT a leap year. Have a look at Appendix* f for more details.

MoonThe Chinese calendar is a lunar calendar, based on the orbit of the Moon around the Earth. One orbit takes on average 29.53 days. Therefore, a lunar year is 12 x 29.53 = 354.36 days, 11-12 days shorter than the solar year.

As a result the lunar year moves forward 11-12 days yearly with respect to the solar year. The Islamic calendar is doing that.

Does that matter? It depends, for an agricultural society it does, because a lunar calendar has no relation with the seasons.

The solar year has seasons because the Earth’s axis is tilted. Here is a diagram. There are two times when the Sun is right above the equator. Day and night are of equal length all over the world. They are called the Spring equinox (~ 21 March) and the Autumnal equinox (~21 September). Around 21 June, the Sun reaches its northernmost position, the Summer Solstice, when daylight is at its maximum in the Northern hemisphere. Half a year later, the daylight is minimal. around 21 December, the Winter Solstice. (Of course in the Southern hemisphere it is just the other way around).

I wrote “around” and in the diagram a few dates are mentioned. In Appendix 2 I will explain why the dates vary, although the events are fixed.

Another way to describe the location of the Sun, is by using degrees (ecliptic longitude is the technical term).. We start at the Spring equinox (0°), and go counterclockwise. Then the Summer solstice is at 90°, the Autumnal equinox at 180°, and the Winter solstice at 270°.

Can we also divide the solar year in months? Sure, by dividing the Sun’s orbit in 12 sectors, each of 30 degrees. Each sector corresponds to a solar month. It is what the Chinese solar calendar does. It introduces 24 Solar Terms, two for each month, one for the start and one for the center. It is called the Center Point of that month. (similar to a Full Moon day in the lunar calendar). Here is a diagram of the 24 Solar Terms.

The diagram contains lots of information, the names of the solar terms (in English and Chinese) and the approximate dates. When you are Chinese, you may find a few familiar names: Qing Ming (15°), Dhong Zhi (270°) and Li Chun (315°). More about this in Appendix 3.

To explain the lunisolar calendar, we need the dates for the lunar and the solar months. Lunar data( for the years 2005-2045) can be found here and the Solar Terms (for the years 1900-2049) are here.

Here is the info for the first lunar month in 2025. The link above gives 29 January at 20:35 for the New Moon. So, the first month of CNY starts at 29 Januarty. The next New Moon is at 28 February, so the last day of the first month is 27 February.

The Solar calendar starts with Li Chun (the beginning of Spring). Using the Solar Terms link above, we find the date for that solar term: 3 February at 22:10, so the first solar month starts on 3 February. The next solar term (Rain Water) is at 18 February 18:-0, so tne Center Point is on 18 February. I have collected the results in the table below. The first lunar month contains the first solar center point.

I have done the same for the next two lunar months.More or less the same but the Solar Center Point shifts to more the end of the lunar month (8 resp. 7 days). That makes sense because a solar month is slightly longer than a lunar month.

Here are the other months for 2025. Notice the month I have given a blue color.

As you see there is a lunar month that doesn’t contain a solar center point!. When that happens, that month is considered a leap month. It just duplicates the earlier month. The result is that a lunisolar leap year contains 13 lunar months.

Notice how after the leap month the solar center point is at the beginning of the lunar month. Each lunar month it will advance 1-2 days, so after 2-3 years there will be another leap month. Not necessarily the sixth month, like this year. See Appendix 4.

In the Chinese lunisolar calendar, a lunar month is a leap month when it does NOT contain a solar center point.

Appendix 1 About a leap year in the Gregorian Calendar

A leap day is added when the year is divisible by 4. This makes the length of a year 365 + 1/4 = 365.25 days. But the solar year is actually 365.2422 days, slightly less. Therefore, the Gregorian calendar has a second rule: when the year is divisible by 100, it is NOT a leap year; This makes the average year length 365 +1/4 -1/100 = 365.244 days. A better approximation, but it can be made even better by a third rule: when the year is divisible by 400, it IS a leap year; making the average year length 365 + ¹⁄₄ − ¹⁄₁₀₀ + ¹⁄₄₀₀ = 365.2425 days. More information about leap years can be found here.

Appendix 2: Why do the dates for solar terms vary, while the events are fixed.

Because a normal year is 6 hours short of a solar year, the solar terms will shift 6 hours! Take for example Li Chun. In 2025 it falls on 3 Fberuary at 22:10, but in 2026 on 4 February at 4:02. Six hours later, so next year Li Chun will fall on 4 February. Another cause of variability is the time zone system we are using on Earth. All dates and times in this post are in China/Malaysia time (UTC + 8). in that timezone the Summer Solstice falls in 2025 on 21 June at 2:42. New York is using Eastern Time (UTC-4), the Summer Solstice in that timezone is 12 hours earlier and falls on 20 June 22:42, one day earlier.

Appendix 3 About Dong Zi, Qing Ming and Li Chun

The Chinese festivalls follow the Lunar calendar , with three exceptions. Around Qing Ming (Cheng Beng) Chinese families visite the graves of their ancestors. `And around Dong Zhi, Chinese celebrate the harmony in the family. Li Chun is of special imporatnce for the believers in Feng shui. All three belong to the solar calendar, they don’t move around.

Appendix 4: How to find a leap month

You don’t need mathematics to find a leap month, just the tables for moon phases and solar terms as given above. Solar Center Points advance relative to lunar months, so we must find a lunar month where the Solar Center point falls on the first day of that month. We have to continue until 2028 before we find a month that fits that condition. Here is the relevant part of the table for 2028

I2028 will be a leap year, the 5th month will be duplicated.