🐸Is it a leap year?

Try one of these too

Most people know the rule as “every four years”, which is right for 397 years out of every 400. The other three are the interesting part, and they are where software, spreadsheets and hand-written date code quietly break.

The rule, in the order it must be applied

1. Does the year divide by 400? If yes, it is a leap year. 1600, 2000 and 2400 stop here.
2. Does it divide by 100? If yes and it failed the first test, it is a common year. 1700, 1800, 1900 and 2100 stop here.
3. Does it divide by 4? If yes, it is a leap year. This is where 2028, 2032 and 2036 are decided.
4. Otherwise it is a common year of 365 days.

Run in that order the rule never needs a special case. Run in the reverse order — the way it is usually remembered — step 3 answers “yes” for 1900 and nothing later corrects it.

Century years, 1700 to 2400

Seven century years in a row, and only two of them carry a 29 February:

Three skips for every one that survives. Across a full 400-year cycle that leaves 97 leap days rather than 100, which is the entire mechanism of the Gregorian correction: 400 calendar years come to 146,097 days, or exactly 20,871 weeks.

How wrong the rule still is

Dividing 146,097 by 400 gives a mean calendar year of 365.2425 days. The mean tropical year — the one the seasons actually keep — is close to 365.2422. The calendar therefore runs about 26 seconds long per year, which accumulates to a full day roughly every 3,200 years.

That is worth comparing with what it replaced. The Julian calendar’s flat leap day every four years gives a mean year of 365.25 days, which drifts a day every 128 years or so; by the 1580s the spring equinox had moved ten days from where the church calendar expected it, and correcting that is why ten dates in October 1582 do not exist in the Catholic states at all.

Three ways software still gets this wrong

Testing only for divisibility by 4. The commonest bug, and one you cannot detect by testing — every test date between 1901 and 2099 gives the right answer anyway. It surfaces in 2100.

Assuming 2000 proved the code correct. A routine that checks only year % 4 and a routine that implements the full rule agree on every year from 1901 to 2099, including 2000. The year-2000 rollover tested nothing about this.

Adding a year to 29 February. Anniversary and renewal logic has to decide between 28 February and 1 March, and different systems in the same organisation often decide differently. Pick one, write it down, and check what your database does when it is handed 29 February 2027.

Where the leap day changes an answer

A leap day inside a span adds a day to it, which is why the same pair of dates can be 365 days apart one year and 366 the next — days between dates counts them as ordinary days. It changes how many working days a year holds, though not always in the direction people expect; working days in a year has the counts. It moves the halfway point of the year by twelve hours, which year progress shows, and it stretches the first quarter by a day in quarter dates.