When the new moon falls near midnight

1 The rule that makes midnight matter

The Chinese calendar has been computed from the true positions of the sun and moon since the reform of 1645. Its rules, now set out in the national standard GB/T 33661-2017, reduce to four:

1. A day runs from midnight to midnight at the meridian 120° East — China Standard Time. (Before 1929, at the meridian of Beijing; see §5.)
2. The day on which a new moon occurs is the first day of a month, whatever the hour.
3. The month containing the winter solstice, 冬至 (Dongzhi, Winter Solstice), is the eleventh month.
4. When thirteen new moons separate one eleventh month from the next, the first month between them that contains no principal solar term — no moment at which the sun’s longitude is a multiple of 30° — is a leap month, and repeats the number of the month before it.

Rules 2 and 4 are where the trouble lives. Neither rounds anything. A new moon at 23:59:59 starts its month a whole day before a new moon at 00:00:01, and a principal term a second after midnight on the day a month begins belongs to that month, not the one before. Every boundary in the calendar is a question of which side of a midnight an instant falls on. Any two implementations that time those instants differently will agree almost everywhere and disagree completely where it counts.

2 Three calendars, compared day by day

The comparison runs over every day from 19 February 1901 to 8 February 2100 — 72,674 days, the full span the Hong Kong Observatory tabulates — and reads three calendars for each:

The Observatory

The Hong Kong Observatory’s Gregorian–Lunar Calendar Conversion Tables, ingested in full and used as the reference throughout. Its tables are the calendar this site publishes.

ICU

ICU 78.3 as shipped in Node.js v24.19.0, read through Intl.DateTimeFormat. This is the calendar a JavaScript program gets when it asks for one.

A rebuild from modern astronomy

The calendar recomputed from the four rules above, with new moons and principal terms from astronomy-engine 2.1.19. Its new-moon times for every contested month were checked against NASA’s catalogue of lunar phases by Espenak and Meeus and agree to within 66 seconds; NASA publishes to the minute, so that is the resolution of the check.

ICU exposes only dates, not the instants it computed them from. To measure its astronomy directly, this note ports ICU’s CalendarAstronomer — the sun, the moon, and the search that finds when each reaches a given angle — line by line from the ICU release-78.3 source. The port reproduces ICU’s first day of the month for 2,474 of 2,474 new moons in the span, which is every one of them, so the instants it reports are the instants ICU used.

3 Where ICU and the Observatory part

Eight of ICU’s eleven errors are a single month starting a day early or late: thirty days on which every date is off by one. Three are worse. When a principal term crosses midnight, the month that lacks one changes, and the leap month moves with it — two consecutive months are then misnumbered, 59 days in all.

Worked example: Lunar New Year 2027

The new moon that begins lunar year 2027 happens at 23:56:47 China Standard Time on 6 February 2027 — 3 min 13 s before midnight. By rule 2 the whole of that day is the first day of the year, and the Observatory says so. ICU computes the same new moon 6 min 44 s later, at 00:03:32 on 7 February 2027, and starts the year a day late.

For anyone born on 6 February 2027 the difference is not cosmetic. By the Observatory the child is born on the first day of 丁未 (Ding-Wei), the year of the Goat; by ICU, on the last day of 丙午 (Bing-Wu), the year of the Horse. Every zodiac lookup, 虚岁 (nominal age) count and lunar birthday built on Intl inherits ICU’s answer. The Lantern Festival that closes the New Year season moves with it, to 21 February 2027 instead of 20 February 2027.

Worked example: the leap month of 1987

In 1987 the principal term 处暑 (Chushu, End of Heat; sun at 150°) falls at 00:09:56 China Standard Time (120°E) on 24 August 1987 — 9 min 56 s after midnight, on the same day as that month’s new moon, so it belongs to the month that begins then. The month before it, beginning 26 July 1987, is left with no principal term and becomes the leap sixth month, 闰六月 (rùn liùyuè, “leap sixth month”).

ICU times the same term 10 min 2 s earlier: at 23:59:54 on 23 August 1987, 6 s before midnight. The month from 26 July 1987 now has a principal term; the first month without one is the next, and ICU makes that the leap month instead — a leap seventh month, 闰七月 (rùn qīyuè). From 26 July 1987 to 22 September 1987 the two calendars name different months. The Qixi festival, the seventh day of the seventh month, falls on 30 August 1987 by the Observatory and on 1 August 1987 by ICU — 29 days apart — and the Ghost Festival on 7 September 1987 against 9 August 1987.

A ten-minute error decided by a margin of seconds is not a coincidence peculiar to 1987. It is what the calendar’s zero tolerance does to any error at all: the only question is how often an event lands within the error of a midnight, and over two centuries the answer is eleven times.

4 Why ICU’s clock is off

ICU’s CalendarAstronomer says in its own documentation that it is modelled on Peter Duffett-Smith’s Practical Astronomy with your Calculator (Cambridge, 1990), and warns that it “basically does just enough” to support the Islamic and Chinese calendars. Three simplifications account for most of its error:

• The sun follows a fixed ellipse. Its longitude comes from a two-body Kepler orbit whose elements are frozen at an epoch of 31 December 1989. The perigee never moves and no planet perturbs the Earth, so the error grows with distance from 1990 in either direction.
• The moon has six corrections. Mean orbital elements plus evection, the annual equation, the equation of the centre, the variation and two further small terms the code leaves unnamed. Modern lunar theories sum hundreds to thousands of periodic terms.
• No ephemeris time. The code carries a comment, “TODO: Convert the time of day portion into ephemeris time”. Orbital positions are evaluated in civil time, ignoring ΔT, the gap between the Earth’s rotation and the uniform time-scale the orbits run on — close to zero in 1900, about 69 s today.

The two errors matter differently. A new moon decides a single month boundary, and ICU’s new moons are good to a few minutes. A principal term decides where a leap month goes, and ICU’s principal terms are routinely out by half an hour or more, and run early by 9.4 minutes on average. The leap-month errors of Table 1 come from this second source.

None of this is a fault in ICU’s calendar rules, which are the standard ones applied correctly. The clearest evidence is 2033, the case that prompted Aslaksen’s paper. The month after the seventh contains no principal term but is not a leap month, because the thirteen new moons of rule 4 fall a year later; every Chinese calendar made it one until the early 1990s. ICU and the Observatory both give 闰十一月 (rùn shíyīyuè, “leap eleventh month”), and agree on every day of that year. The rules are right. The clock that feeds them is not.

5 The meridian before 1929

Rule 1 is younger than the others. China adopted a standard time based on 120° East in 1928, and calendars from 1929 on are computed for it. Before that they were computed for the meridian of Beijing, 116°25′ East — 14 min 20 s behind (Aslaksen 2003, rule 1). ICU’s source is explicit that it does not do this: “Some sources use a different historically accurate offset of GMT+7:45:40 for years before 1929; we do not do this.”

Rebuilding the calendar from modern astronomy three ways shows which meridian the Observatory’s tables use:

The Observatory follows the historical meridian, and so should anyone converting a date from before 1929. That raises a question about ICU: if it ignores the Beijing meridian, why does it agree with the Observatory in the months where the meridian decides the day? There are three such months, and in each of them ICU is right by accident.

One month before 1929 fits neither meridian. In 1906 the new moon falls 7 min 14 s before midnight at Beijing, so the rebuild begins the month on 23 April 1906; the Observatory begins it a day later. 1906 was still under the Qing dynasty’s 时宪历 (Shíxiàn lì, the Shixian calendar), computed with pre-modern astronomy that need not agree with a modern computation to within seven minutes. This note has not checked the printed almanac for that year, and leaves the month unexplained.

The meridian also reproduces a well-known confusion. Aslaksen records that in 1978 Hong Kong and Taiwan, still following the old imperial calendar, kept the Mid-Autumn Festival on a different day from mainland China. The new moon that began the eighth month fell at 00:09:34 on 3 September 1978 at 120°E, 9 min 34 s after midnight, but 4 min 46 s before midnight at Beijing. Computed at Beijing, the eighth month begins on 2 September 1978 and the festival falls on 16 September 1978; at 120°E on 3 September 1978 and 17 September 1978. The Observatory’s table today gives the 120°E answer.

6 Three months no one can date yet

The Observatory’s own page carries a warning: “The uncertainty in the calculation of the time of moon phases and solar terms decades ahead may be up to a few minutes.” It names three new moons whose month might start a day differently — 28 September 2057, 4 September 2089 and 7 August 2097. The uncertainty is not in the moon, whose motion is known far more precisely than that. It is in the Earth.

Orbits run on a uniform time-scale; clocks follow the Earth’s rotation, which is slowing irregularly. The gap between the two, ΔT, is measured for the past and must be forecast for the future. A new moon fixed in uniform time falls earlier by the clock if ΔT turns out larger, and later if it turns out smaller.

The Observatory’s choices can be reproduced exactly. Rebuilding the calendar from 2026 on with the long-term parabola for ΔT — the formula of Morrison and Stephenson, which NASA gives for dates far from the present — matches the Observatory on every day to 2100. Not one day differs. That shows the tables are consistent with a larger ΔT forecast; it does not show that the Observatory used that formula.

Which forecast will prove right is a question about the Earth, and the measurements so far point one way. The US Naval Observatory’s measured ΔT rose steadily for decades, then stopped:

ΔT peaked at 69.36 s in 2020 and has drifted down to 69.11 s since, as the Earth’s rotation has sped up slightly. For the Observatory’s date for 2057 to be right, ΔT must reach 149 s by then — an average gain of 2.6 s a year for three decades. Over the thirty years from 1975 to 2005 it gained 0.6 s a year. On the evidence to date, the ninth month of 2057 is more likely to begin on 29 September 2057, as modern astronomy and ICU have it, than on 28 September 2057 — which would move the Double Ninth Festival from 6 October 2057 to 7 October 2057.

2089 runs the other way. Every calendar here agrees on 4 September 2089, but only while ΔT stays above 66 s in 2089; today it is 69.1 s. The long-term trend of tidal braking makes a fall of that size unlikely, but it is the one flagged month where the agreed answer depends on the Earth not continuing to do what it is doing now. And 2097, whose new moon falls 15 s after midnight on a forecast uncertain by ±45.6 s, is simply open. ICU’s answer for it agrees with the Observatory, but only because ICU’s own error is larger than the margin.

7 What follows

For software, the practical reading is narrow. Intl’s Chinese calendar is right on 99.4% of days, and every one of its errors sits in a month whose deciding event lies within 14 minutes of a midnight. Anything published — a table of dates, a festival calendar, a birth year’s zodiac animal — should come from the published tables instead. This site takes its Chinese dates from the Observatory for that reason; its Lunar New Year table and Chinese age calculator follow the Observatory in all of the months above, including 2057 and 2097.

For the calendar itself, the point is more interesting. The Chinese calendar is exact in principle and, at its edges, cannot be computed in advance: a rule with no tolerance applied to quantities with a nonzero error. Arithmetic calendars avoid this by fixing their rules ahead of time, as the Hebrew calendar does. This one cannot, and so the day a month begins in 2097 is, today, a forecast about the Earth’s rotation.

8 Limits of this note

• One ICU. Every ICU figure is from ICU 78.3 in Node.js v24.19.0. Browsers ship their own calendar code — some a different ICU version, some a different library — and none has been tested here.
• The Observatory as the reference. The Purple Mountain Observatory computes China’s official calendar; this note compares against the Hong Kong Observatory’s tables, which agree with the rules above everywhere a modern computation can check them, but has not compared against printed almanacs.
• The resolution of the rebuild. astronomy-engine agrees with NASA to within 66 seconds on every contested new moon, but NASA publishes to the minute. The rebuild is not used to decide any event closer to midnight than that; those are the months of §6, stated as open.
• One unexplained month. 1906, discussed in §5.

9 Sources and data

The code and data behind this note are public at github.com/esekercioglu/chinese-calendar-icu: the port of ICU’s astronomy, the independent rebuild, the Observatory’s tables and the generator, under the MIT licence. Every figure on this page comes from its findings.json at commit 83ffe65, also served here as findings.json (CC BY 4.0).

To see whether the ICU in your own Node.js behaves like the one tested here, clone the repository and run npm run check; it takes a few seconds and needs no network. This site’s build runs the same comparison, and fails if the ICU it builds with stops producing the disagreements in Table 1, so this page cannot quietly go stale when Node.js updates.

1. Hong Kong Observatory. Gregorian–Lunar Calendar Conversion Table, and its note on uncertain new moons. Tables ingested 18 August 2026.
2. National standard of the People’s Republic of China. GB/T 33661-2017, 农历的编算和颁行 (Calculation and promulgation of the Chinese calendar).
3. Helmer Aslaksen. The Mathematics of the Chinese Calendar. National University of Singapore, 28 August 2003.
4. Unicode ICU, release-78.3: chnsecal.cpp and astro.cpp.
5. Peter Duffett-Smith. Practical Astronomy with your Calculator. Cambridge University Press, 1990 — the edition ICU’s astronomy cites.
6. Don Cross. Astronomy Engine, version 2.1.19.
7. Fred Espenak and Jean Meeus. Phases of the Moon, 1901–2000 and 2001–2100. NASA Goddard Space Flight Center. Read 29 September 2026.
8. Fred Espenak. Uncertainty in Delta T (Huber’s model) and Polynomial expressions for Delta T (Espenak–Meeus; Morrison and Stephenson’s parabola). NASA GSFC.
9. United States Naval Observatory. Measured ΔT. Read 29 September 2026.

Prose last reviewed 29 September 2026. Corrections are welcome at the address below, and matter more on a page like this than most: if a figure here is wrong, it is wrong in a way someone may already have quoted.