There is a single year in the next century where lunar calendar apps disagree with each other, and it is 2033. Ask one when the leap month falls and you will get either the seventh month or the eleventh, depending on which rule the developer implemented. One of those answers is wrong, and the year is a good test because almost nothing else in two hundred years exposes the difference.
The rule everyone repeats
The Chinese calendar keeps the lunar month in step with the solar year by inserting a thirteenth month every few years. The usual one-line explanation is that a leap month is any lunar month containing none of the twelve major solar terms (中氣), which include the solstices and equinoxes.
That is memorable, it is what most explanations give you, and it is incomplete in a way that only shows up occasionally. This rule identifies a potential leap month, but not whether the year requires one.
What actually happens in 2033
The Hong Kong Observatory publishes its conversion tables as plain text, one file per year, and 2033 is worth reading directly because the answer is printed on the page. Two lines in that file both say 11th Lunar Month: one beginning 22 November 2033, another beginning 22 December. A repeated month number is how a leap month appears in the table.
The problem becomes clear when you set the months of that autumn against the major solar terms they contain:
- The month from 26 July holds End of Heat on 23 August.
- The month from 25 August holds nothing at all.
- September and October hold the Autumnal Equinox and Frost.
- The month from 22 November holds two — Light Snow on 22 November and the Winter Solstice on 21 December.
- The month from 22 December holds nothing.
Two empty months in one autumn, and one month carrying two major terms. Apply the one-line rule and you take the first empty month you meet, the one starting 25 August, and call it a leap seventh month. That is precisely what Chinese calendars printed for 2033 until the early 1990s.
The half of the rule that goes missing
The full procedure begins one step earlier. First you find the two lunar months that contain successive winter solstices — those are the eleventh months, by definition. Then you count the months between them. If there are twelve, the year needs no leap month and any empty month you find is a coincidence. Only if there are thirteen do you go looking, and then you take the first empty month inside that span.
For 2033 the span from the eleventh month of one winter to the eleventh month of the next contains thirteen months, so a leap month is required. The empty month of 25 August is outside that span. The empty month of 22 December is inside it. The leap month is the eleventh, and the calendar runs 22 November, then a second eleventh month from 22 December.
The shortcut usually works because a year needing a leap month almost always has just one empty month inside the solstice-to-solstice span. In those cases, scanning the whole year gives the same answer. 2033 is the exception.
How to test the app in your hand
Ask it for the leap month of 2033. If it says the eleventh, it implements the full rule. If it says the seventh, it is running the shortcut and inherited a thirty-year-old error.
There are two things a wrong answer does not mean. Nothing else in the app is necessarily broken, because for every other year in the range the two rules agree. And 2033 is not a date most people have business with, so a wrong answer is a signal about how the software was built rather than a problem you are going to hit next month.
Our own lunar / solar date converter faces the same test, which seemed only fair to apply here. It returns the eleventh month for 2033, the fifth for 2028 and none for 2027, all matching the Observatory.
Why nobody noticed for so long
A leap eleventh month is unusual. Across the Observatory's full published range, from 1901 to 2100, there are seventy-three leap months, and 2033 is the only one that falls on the eleventh. Leap fourth and fifth months are common, a dozen or more each. A leap first month and a leap twelfth never occur at all in those two centuries.
So a developer implementing the shortcut can test every other year in a century and see nothing wrong. The rule and its abbreviation agree everywhere except this one year, which is a bad place to discover the abbreviation is incomplete.
The correct procedure is written down. China published it as a national standard, GB/T 33661-2017, drafted by the Purple Mountain Observatory and in force since September 2017, and the full text is free to read. But you do not have to take the standard's word for it, which is the appealing part of this particular problem — the Observatory's tables settle it on their own, and anyone can read them.
Where this comes from, and what will date
The month boundaries and solar terms above were read from the Hong Kong Observatory's published conversion tables for 2033 and 2034, and the two-hundred-year leap-month distribution was counted from the same series across its full range. The rule is stated in GB/T 33661-2017.
None of this expires. The leap-month placement for 2033 has been settled since the calculation was corrected in the early 1990s, and the arithmetic behind it does not change. Any given app can be updated. A wrong answer today may be corrected tomorrow, so this is a test to repeat, not a verdict to memorise.
One caution about the test itself. Some apps do not expose leap months in an obvious way, and a converter that simply refuses to answer for 2033 is not the same as one that answers wrongly. Check that it can name the leap month for a year you already know — 2028 has a leap fifth month — before reading anything into what it says about 2033.
