TL;DR: The Vietnamese calendar is lunisolar because its months follow the Moon's cycle (the new moon marks day one), but its years must stay aligned with the Sun's cycle through the solar terms, so a leap month is inserted every few years. That is why Tet falls on a different date each year, and why the Vietnamese calendar sometimes differs from China's by one day, since it is calculated along the 105 degrees east meridian.
What kind of calendar is the Vietnamese calendar, and why is it not purely lunar?
The Vietnamese calendar is a lunisolar calendar: months are counted by the Moon's cycle, while the year is anchored to the Sun's cycle so the four seasons do not drift. According to the classification of the United States Naval Observatory, a lunisolar calendar "tries to keep in sync with both the solar year and the phases of the Moon", and because a solar year does not contain a whole number of lunar months, such calendars must adjust the lengths of years and months[1].
If it followed the Moon alone, each year would have only about 354 days, roughly 11 days shorter than the tropical year. After a few decades, the first lunar month would fall in mid-autumn, and Tet would wander through all four seasons. That is unacceptable for an agriculture that uses solar terms as markers for planting and rituals. People in East Asia therefore attached a solar marker to the lunar calendar, turning it into a dual calendar.
The mechanism: new moon days, major solar terms, and the rule for inserting leap months
The new moon day is the first of the month
The first day of a lunar month is the day containing the new moon point: the moment when the Earth, Moon and Sun are aligned, with the Moon in between, so the angle between the Moon and the Sun is 0 degrees and we cannot see the Moon[2]. The average new moon cycle is about 29.53 days, varying between 29.27 and 29.84 days, so lunar months are rounded to 29 days (short month) or 30 days (full month)[3].
Major solar terms are the solar markers
Major solar terms are points dividing the ecliptic into 12 equal parts, of which four are important: the spring equinox, summer solstice, autumn equinox and winter solstice[2]. Each major solar term is tied to a fixed lunar month: however long or short the months are, the spring equinox always falls in the second lunar month, the summer solstice in the fifth, the autumn equinox in the eighth and the winter solstice in the eleventh. That is how the seasons stay fixed.
The rule for inserting a leap month
The rule is summarized in four points[2]:
- The first day of a lunar month is the day containing the new moon point.
- An ordinary year has 12 months; a leap year has 13 months.
- The winter solstice always falls in the 11th lunar month.
- In a leap year, if a month contains no major solar term, that month is the leap month; if several months contain no major solar term, only the first one after the winter solstice is treated as the leap month.
A leap month carries the name of the month before it plus the word "leap", for example a leap second month stands right after the ordinary second month. Technically, two new moon points are calculated: new moon A just before the first winter solstice and new moon B just before the second winter solstice. If the interval from A to B is under 365 days, that year is ordinary; if over 365 days, it is a leap year[2].
Why must local time zones be used?
New moon points and major solar terms are moments, not days. To know which day a moment falls on, it must be converted to the time zone of the place making the calendar. NASA's astronomy book states clearly: a calendar is a social contract, not a scientific treatise[4], so choosing a time zone is an administrative decision. Vietnam chose the 105 degrees east meridian, that is, time zone 7[2].
Why does Tet in Vietnam differ from China's in some years?
Because Vietnam calculates along the 105 degrees east meridian, while China calculates along 120 degrees east, a difference of one time zone[2]. When the new moon point falls around 11 p.m. Hanoi time, it is already 0 a.m. the next day in Beijing, so the two countries celebrate Tet one day apart. This is not an error but an inevitable consequence of each country using its own official time zone as the standard.
A recorded example: Tet Mau Than 1968, Vietnam celebrated Tet one day earlier than China, because the next new moon point fell at 23:29 Vietnam time on 29 January 1968, while by Beijing time it was already 30 January[3].
The twelfth month, sometimes full and sometimes short: why no fixed cycle?
A familiar question each Tet: which year has a 30th day of the twelfth month, and which does not? The answer is that there is no fixed cycle, because the length of a lunar month depends on the actual motion of the three bodies Earth, Moon and Sun, not just the Moon[3]. The Moon's motion is disturbed by the pull of the Sun, the Earth, other planets, and even the irregular shape of the sphere, so month lengths fluctuate continuously[3].
Mr. Tran Tien Binh, a former staff member of the Calendar Research Division of the Vietnam Academy of Science and Technology, said that the years 2014, 2015, 2017, 2018, 2019, 2020 and 2021 all had a twelfth month of 30 days, but in 2022 the twelfth month was short, then 2023 and 2024 were full again, after which it was short consecutively until 2033, when a 30th day of the twelfth month appears again[3].
A few seconds off changes the whole day
Because the new moon point only needs to fall at any moment between 0 and 24 hours of a day for that day to become the first of the month, a calculation error of a few dozen seconds can turn a full month into a short month[3]. A publication from the Purple Mountain Observatory (China) in 2002 recorded that 28 September 2057, 4 September 2089 and 7 August 2097 were once miscalculated to the next day, because the new moon point fell between 23:57 and 23:59[3].
A comparison table of three calendar types
| Criterion | Solar calendar | Purely lunar calendar (e.g. Islamic) | Lunisolar calendar (Vietnam, China, Jewish) |
|---|---|---|---|
| Main basis | Earth's orbit around the Sun | Moon phase cycle | Both |
| Ordinary year length | About 365 days | 12 lunar months, about 354 days | 12 lunar months, about 353 to 355 days |
| Adjustment | Add leap days | No adjustment | Add leap months |
| Consequence | Fixed seasons | Months drift through four seasons | Fixed seasons, months still follow the Moon |
| Example | Gregorian calendar | Islamic calendar | Vietnamese, Chinese, Jewish calendars |
The table shows the key point: a lunisolar calendar is not "a lunar calendar plus a bit of solar", but a separate system with complex leap month rules, which cannot be derived from the Gregorian calendar by subtracting a fixed number.
Why can the Vietnamese calendar not be calculated with a simple formula?
The Vietnamese calendar is an astronomical calendar, calculated from the actual motion of the Sun, Earth and Moon, not a fixed-rule calendar like the Gregorian[2]. As a result, to look up any lunar date, one must calculate nearby new moon points and major solar terms, and cannot simply add or subtract on a 19-year Metonic cycle. The Metonic cycle (235 lunar months approximating 19 solar years) is a classic tool for making lunisolar calendars, but it itself is off by about two hours per cycle[1], so modern calendars still have to recalculate each year.
This also explains why printed perpetual calendars can differ by a few days in the far future: they rely on different theoretical versions of the Moon's motion, and a small error at the new moon point changes the whole month.
Where are Tet Nguyen Dan and other holidays anchored?
Tết Nguyên Đán is the first day of the first lunar month. Because the winter solstice always falls in the eleventh month[2], Tết usually falls on the second new moon after the winter solstice, or the third if a leap month intervenes that year. Therefore Tet always falls between late January and mid-February in the solar calendar, never drifting into summer. This is the benefit of anchoring to the Sun: the festival keeps its correct season.
Other holidays such as Tet Doan Ngo (the 5th day of the 5th month) and Tet Trung Thu (the 15th day of the 8th month) follow the same principle, always staying within a fixed season. If the Vietnamese calendar were purely lunar, these days would gradually drift through the seasons within a few decades.
So what is the short answer to the original question?
The Vietnamese calendar is lunisolar because it must satisfy two constraints at once: months counted by the Moon to preserve the meaning of the new moon, full moon and first day; and years tied to the Sun so the four seasons and solar terms do not drift. The leap month mechanism based on major solar terms is the technical solution to that two-constraint problem. Choosing the 105 degrees east meridian is an administrative decision, which sometimes makes the Vietnamese calendar differ from China's by one day, and that is normal in calendrics.
