First, determine the exact moments of two consecutive winter solstices.

Count how many new moon moments occur between those two winter solstices (the interval includes the first solstice but excludes the second).

The period between two new moons constitutes one lunar month. The calendar day on which a new moon occurs is designated as the first day of the month. Day boundaries are defined by Beijing Time (UTC+8), with the day starting at 00:00:00.

Calculate the moments of the principal solar terms (中气), which correspond to the instants when the sun's ecliptic longitude reaches exact multiples of 30°.

Check how many new moons occur between the two winter solstices:

· If there are 12 new moons, no leap month is inserted.

· If there are 13 new moons, then examine each month to see whether it contains a principal solar term. If a month has no principal solar term, that month becomes a leap month, and its name is inherited from the previous month. If two months lack a principal solar term, only the first such month is designated as the leap month; the second is not.

In addition, because the Earth moves faster at perihelion and slower at aphelion, and the Moon likewise moves faster at perigee and slower at apogee, the interval between new moons is not constant. It fluctuates roughly between 29.27 and 29.84 days. This variation affects the determination of the first day of each month, giving rise to "long" (30-day) and "short" (29-day) months in the calendar.

In a sense, the Chinese calendar is an attempt to solve a perturbed two-body, three-body, or even many-body problem under specific constraints. It requires extremely precise calculations of the exact times of every solar term and every new moon.

Today, responsibility for compiling the Chinese calendar lies with the Purple Mountain Observatory. The calendar is published about a year in advance; the latest release is for 2026. The astronomical data they use are fully aligned with international standards, including Solar System ephemerides from NASA's Jet Propulsion Laboratory.

The modern calendar also inherits traditions dating back to the Xia and Han dynasties, such as the principle of "establishing Yin as the first month" (建寅为正)—that is, designating the Yin month as the first month of the year.

"Establishing Yin" means that the handle of the Big Dipper points toward the Yin position. If we imagine the celestial equator as a great circle divided into the twelve Earthly Branches, the Big Dipper's handle functions like a pointer. In ancient times, the direction of the handle at dusk was used as the reference.

The winter solstice occurs when the Dipper's handle points due north, toward the Zi position. Because this is extremely easy to observe, the month containing the winter solstice is designated as the Zi month. Since Yin is defined as the first month, even if a leap month occurs—say, a leap month after the eleventh month—that leap month retains the earthly branch of the preceding month. This system ensures that the Yin month is always the first month.

In terms of hexagrams, the winter solstice corresponds to Hexagram 24 (䷗, "Return"), when the first yang energy is born. By the time the calendar reaches the Yin month, the hexagram is Hexagram 11 (䷊, "Peace")—representing "three yangs bringing great fortune"—an auspicious sign.

If you treat the first month as month one and count forward, you'll find that the winter solstice always falls in the eleventh month. For this reason, the eleventh month is also called the winter month. In modern practice, the month containing the winter solstice is directly designated as the eleventh month.

This is easy to understand: there are only twelve Earthly Branches, fixed in number. Counting from Yin to Zi—Yin, Mao, Chen, Si, Wu, Wei, Shen, You, Xu, Hai, Zi—Zi is the eleventh. If the span from one Zi month to the next contains exactly twelve lunar months, they can be perfectly matched to the twelve branches, and no leap month is needed. If an extra lunar month appears in between, a leap month must be inserted; otherwise, there wouldn't be enough branches to assign.

Take the Gui-Chou year (corresponding roughly to 2033-2034 in the Gregorian calendar) as an example. One winter solstice might fall on a certain day of the eleventh month. If the period until the next winter solstice contains thirteen new moons, you'll find one extra month. The first month after a winter solstice that lacks a principal solar term becomes a leap month, inheriting the name of the preceding month—for instance, a leap eleventh month.

The first month does not have to be the Yin month. The Xia dynasty used Yin as the first month; the Shang dynasty used Chou; the Zhou dynasty used Zi; the Qin dynasty used Hai. Emperor Wu of the Han restored Yin as the first month. Wang Mang, invoking ancient precedent, switched back to Chou. During the Wu Zhou period of the Tang dynasty, Empress Wu Zetian followed Zhou precedent and made Zi the first month.

From the Three Dynasties through Qin, each change moved the calendar one month earlier—a fascinating pattern. Changing the calendrical new year was also ritually legitimate.

As stated in The Book of Rites · Great Tradition: "When a sage rules the world facing south, he must begin with human affairs. These include establishing standards of weights and measures, reviewing written culture, changing the beginning of the year, altering dress colors, distinguishing insignia, modifying ritual objects, and differentiating clothing. These are the ways by which he brings reform to the people."

Kong Yingda's commentary explains: "'Changing the beginning of the year'—'beginning' refers to the start of the year, and 'new moon' to the start of the month. When a ruler comes to power, he demonstrates that things begin anew with him, adopting a new system according to Yin, Chou, or Zi. Zhou used Zi, Shang used Chou, Xia used Yin—this is what 'changing the beginning' means. Zhou reckoned the day from midnight, Shang from cockcrow, and Xia from dawn—this is what 'changing the new moon' means."

Update: February 16, 2022

On "Lunar/Lunisolar New Year" vs. "Chinese New Year":

If you celebrate the New Year according to the Chinese Lunar calendar, then it is unquestionably Chinese New Year, because the Chinese calendar is calculated using Beijing Time (UTC+8). Calendars calculated in other time zones may differ, resulting in different New Year dates.

"Chinese New Year" is a subset of "Lunar New Year." Using "Lunar New Year" or "Lunisolar New Year" to refer specifically to Chinese New Year is therefore inaccurate.

People in other countries also celebrate lunar New Year. If they follow the Chinese calendar, they are celebrating Chinese New Year. If they follow their own country's lunar calendar, then they are celebrating that country's lunar New Year.