A lunisolar calendar is a type of calendar that uses both the monthly cycles of the Moon and the solar year. Like all calendars that divide the year into months, it must have a whole number of months each year. Most years have twelve months, but every second or third year has an embolismic year, which includes an extra month called an intercalary or leap month.

Lunisolar calendars are used in many different cultures. Unlike purely lunar calendars, such as the Islamic calendar, lunisolar calendars include special rules for adding months. These rules help the calendar stay roughly aligned with the solar year and the changing seasons.

Reconciling lunar and solar cycles

A tropical year is about 365.2422 days long, and a synodic month is about 29.5306 days long. This means a tropical year is about 12.36826 synodic months long. Since 0.36826 is between 1/3 and 1/2, a typical year of 12 months needs an extra, or leap, month added every 2 to 3 years. More accurately, 0.36826 is very close to 7/19 (about 0.3684211). Some lunisolar calendars include 7 leap months in every cycle of 19 years, called the "Metonic cycle." The Babylonians used this 19-year cycle as early as the late sixth century BCE.

Adding leap months is often guided by the "epact," which is the difference between the lunar and solar years (about 11 days). The classic Metonic cycle can be created by starting with an epact value of 1 in the last year of the cycle and increasing it by 11 each year. Between the end of one cycle and the start of the next, the increase is 12, called the "saltus lunae" (Latin for "leap of the moon"). This causes the epact values to repeat every 19 years. When the epact reaches 30 or more, a leap month is added, and 30 is subtracted from the total. The Metonic cycle states that 7 out of 19 years will include an extra leap month, and these years are numbered: 3, 6, 8, 11, 14, 17, and 19. Both the Hebrew and Julian calendars use this pattern.

The Buddhist and Hebrew calendars limit the leap month to one specific month each year. This means there are usually 36 common months between leap months, but sometimes only 24. The Chinese and Hindu lunisolar calendars allow the leap month to occur before or after any month, depending on the calendar. These calendars use the actual movement of the Sun, so their leap months rarely appear near perihelion, the point in Earth's orbit where the Sun appears to move fastest (now around January 3). This causes the usual number of common months between leap months to be about 34 when two common years occur together, or about 29 when only one common year occurs.

Another way to handle the mismatch between the solar year and lunar months is to leave some time unassigned to a named month. Some Coast Salish groups used this method. For example, the Chehalis counted 10 lunar months starting with the arrival of spawning chinook salmon (in October of the Gregorian calendar) and left the remaining time uncounted until the next salmon run.

List of lunisolar calendars

Many calendars, including the Chinese, Buddhist, Burmese, Assyrian, Hebrew, Jain, traditional Nepali, Hindu, Japanese, Korean, Mongolian, Tibetan, and Vietnamese calendars (from the East Asian cultural area), as well as the ancient Hellenic, Coligny, and Babylonian calendars, are lunisolar. Some ancient calendars in south Arabia before Islam also used a lunisolar system. The Chinese, Coligny, and Hebrew lunisolar calendars follow the tropical year, while the Buddhist and Hindu lunisolar calendars follow the sidereal year. This means the first three calendars help people understand the seasons, while the last two help track the position of the full moon among the stars.

Lunisolar calendars are grouped by their families or origins.

The Gregorian calendar, used worldwide, is a solar calendar. However, the date of Easter in Western Christianity is linked to the date of Passover in the Hebrew calendar. A method based on the moon is used to calculate Easter and related holidays. This method uses the ecclesiastical full moon after the ecclesiastical equinox in March. These calculations rely on the Metonic cycle, not direct astronomical observations. Eastern Christian churches use a similar method based on the Julian calendar.

The Chinese lunisolar calendar, also called the Agricultural Calendar or Yin Calendar, uses the movements of the sun (Yang) and moon (Yin) to track time. It influenced calendars in neighboring countries like Vietnam and Korea.

Over time, observations of the sky, clocks, and natural events helped improve how years, months, and days were measured. Scientists worked to mathematically connect the solar and lunar cycles, though some approximations were needed.

The earliest written record of the Chinese lunisolar calendar dates back to the Zhou dynasty (around 1050 BC to 771 BC). Throughout history, the calendar changed with each dynasty, becoming more accurate. Examples include the "six ancient calendars" from the Warring States period, the Qin calendar, the Han calendar, the Taichu calendar, the Shoushi calendar, and the Daming calendar. Since 1912, China has used the western solar calendar alongside the lunisolar calendar.

Important Chinese holidays, such as Chinese New Year, Lantern Festival, Mid-Autumn Festival, and Dragon Boat Festival, are based on the Chinese lunisolar calendar. The Chinese zodiac, a system that assigns an animal and traits to each year in a 12-year cycle, also follows this calendar. The traditional calendar uses a system called the sexagenary cycle, which repeats patterns of Heavenly Stems and Earthly Branches every 60 years.