Islamic, Hebrew and Chinese Calendars: Lunar vs Lunisolar

A lunar calendar counts months by the phases of the moon and ignores the solar year. A lunisolar calendar also counts lunar months, but adds an extra "leap" month every two or three years so that its year stays in step with the seasons. The Islamic (Hijri) calendar is purely lunar. The Hebrew and Chinese calendars are lunisolar. That one difference explains why Ramadan moves through every season, while Passover always falls in the northern spring and Chinese New Year always falls in late January or February.

Key Takeaways

• All three calendars use months of 29 or 30 days that follow the moon.
• Twelve lunar months last about 354 days, about 11 days short of a solar year. The Islamic calendar accepts the gap; the Hebrew and Chinese calendars close it with a 13th month.
• The Hebrew calendar adds a second month of Adar in 7 years of every 19. The Chinese calendar adds a leap month, about 7 times in 19 years, wherever its solar-term rule requires one.
• Result: Ramadan circles the seasons in about 33 years, while Passover and Chinese New Year stay within about a month-long window.

Lunar and lunisolar: the definitions

The US Naval Observatory's introduction to calendars draws the line clearly. A lunar calendar bases each month on a full cycle of the moon's phases, without regard to the solar year. Lunisolar calendars, in the Observatory's words, "try to remain synchronous with both the solar year and the moon phases."

The difficulty is that the two cycles do not divide into each other. NASA's eclipse website gives the mean synodic month, from one new moon to the next, as 29.53059 days. Royal Museums Greenwich gives the solar year as 365.2422 days.

A calendar of 12 lunar months falls about 11 days behind the sun each year. After about three years the shortfall reaches roughly 33 days, more than a month. A lunisolar calendar inserts a 13th month at about that point. A lunar calendar does not.

The 19-year Metonic cycle

Both lunisolar calendars in this article rely on a near-coincidence between the two cycles. The USNO page explains that 235 lunar months are almost exactly 19 years, so after 19 years the same phase of the moon returns to the same date. This is the Metonic cycle, named after Meton of Athens.

The arithmetic shows how close it is. 235 × 29.53059 = 6,939.69 days, and 19 × 365.2422 = 6,939.60 days. The difference is about 0.09 of a day, roughly two hours, which matches the Observatory's description. Nineteen years of 12 months would hold 228 months, so the cycle needs 235 − 228 = 7 extra months.

The Hebrew calendar: a second Adar, 7 times in 19 years

The Hebrew calendar is lunisolar, "regulated by the positions of both the moon and the sun," in the words of Encyclopaedia Britannica. Its ordinary year has 12 months of 29 or 30 days and totals 353, 354 or 355 days. Britannica explains that leap years are added "in order to assure that the major festivals fall in their proper season."

In a leap year an extra 30-day month called First Adar is placed before the regular month of Adar, which then becomes Second Adar. A leap year has 383, 384 or 385 days, and according to Britannica it occurs seven times in every 19-year cycle.

The calendar is fixed by calculation. The USNO calendars page describes it as "based on calculation rather than observation" and dates the fixed calendar to Hillel II in 359 CE. Britannica adds that in late Second Temple times a new month was proclaimed on the testimony of witnesses who had seen the new moon, before calculation gradually replaced observation.

Which Hebrew years are leap years

Within each 19-year cycle, the leap years are years 3, 6, 8, 11, 14, 17 and 19. We confirmed this pattern by listing every Hebrew year from 5761 to 5861 that contains a Second Adar in the Hebrew calendar built into Node.js. For example, 5787, which begins in September 2026, is year 11 of its cycle and has 13 months.

Because the leap month always sits in the same place, just before Nisan, it keeps Passover (15 Nisan) in spring. Britannica's month table places Nisan in March–April.

The Chinese calendar: a leap month set by the solar terms

The Chinese calendar is also lunisolar. An article on the University of California, Berkeley's Calendar in the Sky site notes that it "may have begun as a lunar calendar, but in current use it is lunisolar." The USNO describes it as based on calculations of the positions of the sun and moon.

The Hong Kong Observatory's explainer What year is it today? sets out the main rules:

• Each month has 29 or 30 days, following the phases of the moon.
• The 24 solar terms come from the solar year, and one cycle of the 24 terms corresponds to one year.
• A year has 12 months, or 13 in a leap year; the extra one is called a leap month.
• Lunar New Year's Day is the day of the second new moon after the winter solstice, not counting a leap month.
• The Observatory says the Metonic cycle of 7 leap months in 19 years is adopted.

Where the leap month goes

The Hebrew leap month always falls before Adar. The Chinese leap month can follow almost any month. The Berkeley article gives the rule: the winter solstice must always fall in the 11th month, and in a leap year "the first month where there is no principle solar term is designated as the leap month." The leap month takes the number of the month before it, so a leap month after the sixth month is called a leap sixth month.

A recent example comes from the Shanghai municipal government's English site, which explains the Leap Sixth Month of 2025. The lunar month from 25 July to 22 August 2025 contained only a minor solar term and no major one, so it became a leap sixth month of 29 days.

Calculated with the Chinese calendar built into Node.js, the next seven leap months fall in 2028 (after month 5), 2031 (month 3), 2033 (month 11), 2036 (month 6), 2039 (month 5), 2042 (month 2) and 2044 (month 7). That is seven leap months in the 19 Chinese years from 2026 to 2044, matching the Metonic average, though the Chinese calendar reaches it through its solar-term rule rather than a fixed list of leap years.

The Islamic calendar: twelve months and no leap month

The Hijri calendar keeps 12 lunar months every year. The USNO Islamic calendar page describes it as based on lunar months that begin when the thin crescent is sighted. It adds that 12 lunar months are on average 11 days shorter than the civil year, so the Islamic year shifts earlier by about that amount.

The number twelve comes from the Quran. In the translation of the meaning by Dr. Mustafa Khattab (The Clear Quran) on quran.com, Surah At-Tawbah 9:36 says "the number of months ordained by Allah is twelve," four of them sacred. The next verse, 9:37, condemns the pre-Islamic practice of nasi', reallocating the sanctity of months. The Prophet ﷺ said, as recorded in Sahih al-Bukhari 3197, that time "has turned to its original form" and that the year "is of twelve months." The version in Sahih Muslim 1679a places these words in the Farewell Address. Scholars and historians discuss exactly what nasi' involved; the sister post on nasi and the end of the leap month covers those views. In practice, the Islamic calendar adds no 13th month.

Many Islamic months are still set by sighting the crescent, so the start of Ramadan or Eid can differ by a day between communities. The Hebrew and Chinese calendars are fixed by calculation in advance.

How the three calendars compare

What this means for festival dates

The effect shows up as soon as you line up the dates. The table gives the first day of Ramadan (1 Ramadan), the first day of Passover (15 Nisan) and Chinese New Year (1st day of the 1st month) for nine Gregorian years.

Islamic dates are calculated from the Umm al-Qura tables in the open-source hijri-converter library that this site uses; local announcements may differ by a day. Hebrew dates were calculated with the hebrew calendar built into Node.js through its Intl API. Chinese New Year dates follow the Hong Kong Observatory's Gregorian-Lunar calendar conversion tables, which also confirm the leap months and the 2001-2100 range given below.

Three patterns stand out:

• Ramadan moves steadily earlier, by 10 to 12 days a year. In 2030 it begins twice, in January and again in December. The same calculation puts 1 Ramadan on 26 July in 2044, so in under two decades it moves from late winter in the northern hemisphere to high summer.
• Passover jumps later in a leap year. From 2 April 2026 it moves 20 days later, to 22 April 2027, because 5787 has a Second Adar. It then drifts about 11 days earlier each year until the next leap year pulls it back.
• Chinese New Year behaves the same way. It moves earlier from 6 February 2027 to 26 January 2028, then jumps to 13 February 2029 after the leap fifth month of 2028.

Across the whole century from 2001 to 2100, the same calculation keeps 15 Nisan between 26 March and 25 April, and Chinese New Year between 21 January and 19 February. No such window exists for Ramadan. It returns to roughly the same Gregorian dates after about 33 years, as the USNO calendars page notes, and the sister post on why Islamic dates move each year works through that cycle.

Common questions

Is the Chinese calendar lunar or lunisolar?

Lunisolar. Its months follow the moon, but its leap months and its solar terms tie the year to the sun, with the winter solstice fixed in the 11th month. "Lunar New Year" names the festival; it does not mean the calendar ignores the sun.

Why doesn't the Islamic calendar add a leap month?

Because the Quran fixes the year at twelve months (9:36) and condemns nasi' (9:37). Calculated forms of the Hijri calendar do have leap days: the tabular calendar described on the USNO Islamic calendar page adds a day in 11 years of every 30. Those days only keep the months in line with the moon. They do not bring the year back to the sun.

Do Ramadan and Passover ever fall at the same time?

Yes, for a few years at a time. Using the same calculations as the table above, some of the eight days of Passover (15 to 22 Nisan) fell within Ramadan in 2022 and 2023, and they will again in 2054, 2055 and 2056. The gap of about three decades reflects Ramadan's journey through the seasons while Passover stays in March and April.

Compare the calendars yourself

To see where any Gregorian date falls in the Hijri calendar, use the Hijri date converter. The Islamic months page lists the twelve months, and the Ramadan 1448 calendar shows the calculated days of Ramadan 1448, which is calculated to begin on 8 February 2027. For the Hebrew or Chinese date of the same day, consult a calendar published by those communities, since their festival dates follow their own fixed rules.