TL;DR: Converting a lunar date to a solar date cannot be done with a fixed addition and subtraction table, because lunar months vary in length from about 29.27 to 29.84 days, averaging 29.53 days. The calculation must rely on the new moon point (the no-moon day) computed in each country's legal time, together with the major solar term rule and the leap month rule. As a result, the Vietnamese and Chinese calendars can differ by one day, or even one month, even though they share the same set of rules.
Why can't lunar dates be converted to solar dates with a fixed addition and subtraction table?
No fixed addition and subtraction table can convert lunar dates to solar dates, because the length of a lunar month keeps changing rather than following a regularly repeating cycle. In the solar calendar, November always has 30 days and December always has 31 days, but in the lunar calendar, the twelfth month may have a full 30 days this year, only 29 days next year, and may even stay short for several years in a row before becoming full again. That variation makes every attempt at a fixed table fail after a few years.
According to Mr. Trần Tiến Bình, a former staff member of the Calendar Research Division at the Vietnam Academy of Science and Technology, the length of a lunar month depends on the simultaneous motion of three bodies: the Earth, the Moon and the Sun, not merely on the Moon's cycle as many people assume. This is the root reason the conversion must be recalculated for each moment in time and cannot be looked up in a table.
What is the new moon point, and how does it determine the first day of a lunar month?
The new moon point is the moment when the Earth, the Moon and the Sun lie in a straight line in that order, with the Moon turning its dark half toward the Earth. This is the no-moon day, and it is also the first day of the lunar month. The rule is clear: if the new moon point falls at any time between 0:00 and 24:00 of a given day, that day is counted as the first day of the lunar month.
A lunar month is the interval between two consecutive new moon days, rounded to 29 days (a short month) or 30 days (a full month). The actual length of a month ranges from about 29.27 to 29.84 days, averaging 29.53 days. That average equals 29 days, 12 hours, 44 minutes and 2.8 seconds.
Because the rounding threshold sits right next to the average value, a shift of just a few dozen seconds in the new moon point can flip a month from full to short or the reverse. Computing the Moon's motion is very complex, since it is disturbed by the pull of the Sun, the Earth and other planets, plus the uneven shape of the Earth and the Moon.
Historical errors show how fragile the calculation is
According to a publication released in 2002 by the Purple Mountain Observatory in China, the dates 28 September 2057, 4 September 2089 and 7 August 2097 were once miscalculated to the following day. Specifically, the new moon point on 28 September 2057 fell at 23:59, the one on 4 September 2089 fell at 23:57, and the one on 7 August 2097 fell at 23:59. Just minutes before midnight, yet enough to change the length of the corresponding month. This is the clearest evidence that lunar date conversion cannot rely on a fixed addition and subtraction table.
The lunar calendar rules that Vietnam and China both apply
According to Mr. Trần Tiến Bình, the way the lunar calendar is calculated in Vietnam and China rests on the same set of rules, with four main points. First, the first day of the month is the new moon day. Second, an ordinary year has 12 months and a leap year has 13 months. Third, the winter solstice always falls in the eleventh month. Fourth, in a leap year, the month without a major solar term is the leap month, and it is numbered together with the month before it plus the word leap. If a leap year has two months without a major solar term, the first one after the winter solstice is treated as the leap month.
The only difference lies in the legal meridian used for the calculation. Vietnam uses the 105th meridian east, corresponding to time zone 7. China uses the 120th meridian east, corresponding to time zone 8. This one-hour difference is what creates the occasions when the two calendars fall on different days.
Why does Vietnamese Tet sometimes differ from Chinese Tet?
Vietnamese Tet differs from Chinese Tet because the new moon point computed for the first day of Tet falls in a period when Vietnamese time is still within the day, but Chinese time has already moved to the next day. For example, in 2007, the new moon point computed for the first day of Tet was 16:15:23. Adding 7 hours for Vietnamese time gives 23:15:23, still within the day, so the Vietnamese calendar recorded the first day of Tet as 17 February in the solar calendar. Adding 8 hours for Chinese time moves it to the next day, so the Chinese calendar recorded the first day of Tet as 18 February. The solar date and the sexagenary day were the same in both countries; only the lunar date differed.
Another case is Tết Mậu Thân 1968. 31 December 1967 corresponded to the first day of the twelfth month in both the Vietnamese and Chinese calendars. But the next new moon point occurred at 23:29 Vietnamese time on 29 January 1968, so the twelfth month in the Vietnamese calendar had only 29 days. In Beijing time it was already 0:29 on 30 January, so the Chinese twelfth month had a full 30 days. As a result, the first day of Tết Mậu Thân in Vietnam came one day earlier than in China.
According to Nhân Dân newspaper, at the end of the 20th century there were three occasions when Vietnamese Tet differed from Chinese Tet by one day or one month: Mậu Thân 1968 and Kỷ Dậu 1969 were one day earlier, and Ất Sửu 1985 was one month earlier. In the 21st century, the Lunar New Year in 2007, 2030 and 2053 in Vietnam comes one day before Chinese Tet.
Specific full and short months that show the irregularity
According to data from the Perpetual Calendar of the 20th and 21st Centuries by author Trần Tiến Bình, the years 2014, 2015, 2017, 2018, 2019, 2020 and 2021 all had a twelfth month of a full 30 days. In 2022, the twelfth month was short with 29 days. In 2023 and 2024 it was full again. After that, the twelfth month stayed short for several years in a row until 2033, when it was full again. This shows there is no alternating full-short pattern by year.
| Period | Twelfth month | Number of days |
|---|---|---|
| 2014, 2015 | Full | 30 |
| 2017 to 2021 | Full | 30 |
| 2022 | Short | 29 |
| 2023, 2024 | Full | 30 |
| 2025 to 2032 | Short | 29 |
| 2033 | Full | 30 |
The table above shows that the same twelfth month can be full in some years and short in others, with long full runs suddenly turning into long short runs. This is why no fixed addition and subtraction table can be made for the conversion.
Why is the lunar calendar actually a lunisolar calendar?
The calendar Vietnamese people use every day is not a purely lunar calendar but a lunisolar one. A lunar year has only 354 or 355 days, while the hot and cold weather cycle is about 365 days, leaving 10 to 11 extra days each year, so three consecutive years run more than a month ahead. To stay in step with the agricultural cycle, people in the past added one month in the third year, called the leap month, giving that year 13 months with 384 or 385 days.
According to Professor Trần Ngọc Thêm in the book Foundations of Vietnamese Culture, the lunar calendar originated in the Mesopotamian cultural region based on the Moon's motion with a cycle of 29.53 days, giving 354 days a year. According to Nghien cuu Lich su magazine, the Sumerian civilization beside the Tigris River more than 6000 years ago, in the land that is now Baghdad, Iraq, already knew how to make a calendar based on the Moon's motion. The Roman Empire before Julius Caesar also used this kind of lunar calendar. So the lunar calendar did not originate in China as many people assume.
The legal time zone and legal basis of the Vietnamese calendar
The Vietnamese calendar is calculated by time zone 7, with a central meridian of 105 degrees east, 7 hours ahead of British legal time and 1 hour behind Chinese legal time. The most recent legal basis is Decision No. 134/2002/QD-TTg dated 14 October 2002 of the Prime Minister, whose Article 1 states clearly: the seventh time zone under the international time zone system is taken as the official time of Vietnam. Earlier, Decision No. 121-CP dated 8 August 1967 had stipulated that the official time zone of our country is time zone 7 and that the lunar calendar used in Vietnam is calculated by this official time zone.
According to Nhân Dân newspaper, the State Calendar Board is tasked with researching and managing the State calendar, and each year provides the official calendar tables to all calendar publishers nationwide. Publishers must comply with Circular No. 61/2006/TT-BVHTT dated 15 June 2006 of the Ministry of Culture and Information, which requires printed calendars to take official data from the State Calendar Board. Calendars printed from other sources are only for reference.
Why are there many different lunar calendars on the market?
There are many different lunar calendars on the market because cultural exchange has left many calendars for research and reference in circulation. In 2006, there were 48 publishers printing 15 million calendar copies using calendar tables provided by the State Calendar Board, which are the standard. If calendar information is taken from a source other than the State Calendar Board, it does not match our country's calendar.
