Leap years, the 400-year rule, and the eleven days Britain lost

Last reviewed 12 August 2026

The rule most people remember — every four years — is right about 97% of the time. The other 3% is where the calendar's whole design lives.

A year is the time the Earth takes to go round the Sun, and it is not a whole number of days. That single inconvenience is responsible for leap years, for the Gregorian reform, for eleven days vanishing from the British calendar in 1752, and for the fact that your birthday moves forward one weekday each year — except when it moves two.

The number that causes all the trouble

The tropical year — the interval between successive spring equinoxes, which is what a calendar needs to track if the seasons are to stay put — is about 365.24219 days. Not 365, and not 365.25.

The Julian calendar, introduced in 46 BC, used 365.25 by adding a leap day every four years without exception. That overshoots by about 11 minutes and 14 seconds per year, which sounds negligible and amounts to one full day every 128 years. By the sixteenth century the accumulated error was around ten days: the spring equinox, which the Council of Nicaea had fixed at 21 March for the purpose of computing Easter, was actually falling on 11 March.

The Gregorian rule

The reform promulgated by Pope Gregory XIII in 1582 did two things. It dropped ten days to bring the equinox back to 21 March — Thursday 4 October 1582 was followed directly by Friday 15 October, with the weekday cycle deliberately left unbroken. And it changed the leap rule to stop the drift recurring:

1. Every year divisible by 4 is a leap year;
2. except years divisible by 100, which are not;
3. except years divisible by 400, which are.

So 1996 and 2024 are leap years. 1900 and 2100 are not. 2000 was — which is why anyone who wrote date-handling code in the 1990s using the naive divisible-by-four rule got away with it, and why the same bug lay dormant until 2100 for anyone who used the divisible-by-100 rule without the 400 exception.

The result is 97 leap years every 400 years instead of 100, giving a mean year of exactly 365.2425 days. Compared with the tropical year that is an overshoot of about 27 seconds — one day of drift every 3,200 years or so. Good enough that no further correction is scheduled, and good enough that any correction would be swamped by the gradual slowing of the Earth's rotation anyway.

The eleven days Britain lost

Catholic Europe adopted the new calendar in 1582. Protestant and Orthodox states did not, and for a century and a half Europe ran on two calendars simultaneously — dates from the period are often annotated O.S. and N.S., Old Style and New Style, precisely because a letter posted in London and received in Paris could appear to arrive before it was sent.

Britain and its colonies switched in 1752, by which point the gap had grown to eleven days: Wednesday 2 September 1752 was followed by Thursday 14 September. The same Act moved the start of the legal year from 25 March to 1 January, which is why dates in early-year British records from before 1752 are sometimes written with a double year, as in “12 February 1731/2”.

The popular story that crowds rioted demanding “give us our eleven days” appears to be largely a later embellishment, though there was real and rational grievance about rents and wages being charged for a shortened month. Russia held out until 1918, and Greece until 1923 — which is why the October Revolution happened in November.

For anyone doing genealogy this is a live problem, not a curiosity. A birth recorded in a British parish register in 1740 is an Old Style date. Comparing it directly with a French date from the same year introduces an eleven-day error, and any weekday you compute from it with modern rules is the proleptic Gregorian weekday, not the day the parish clerk would have called it.

Why the calendar repeats every 400 years

Here is a consequence of the Gregorian rule that is genuinely useful. A 400-year cycle contains 400 × 365 + 97 = 146,097 days. Divide that by seven and you get 20,871 exactly, with no remainder.

Because the cycle is a whole number of weeks, the Gregorian calendar is perfectly periodic with a period of 400 years. The pattern of weekdays in 2026 is identical to 1626 and will be identical to 2426. Every weekday algorithm — Zeller's congruence, the doomsday method, the modular arithmetic our day of the week calculator uses — is ultimately exploiting that fact.

It also explains the smaller pattern you may have noticed: a fixed date advances one weekday per common year (365 = 52 weeks + 1 day) and two across a leap year. So a birthday on a Tuesday falls on a Wednesday next year, unless a 29 February intervenes, in which case it jumps to Thursday. And a curiosity that follows from the 400-year cycle: the 13th of the month falls on a Friday slightly more often than on any other weekday.

Leap seconds are a different thing entirely

Leap seconds are frequently confused with leap years and have nothing to do with them. A leap year corrects the calendar against the Earth's orbit. A leap second corrects the clock against the Earth's rotation.

Atomic clocks keep time far more steadily than the planet does. The Earth's rotation is gradually slowing — chiefly through tidal friction — and also fluctuates unpredictably. Since 1972, leap seconds have been inserted into UTC to keep it within 0.9 seconds of astronomical time. Twenty-seven have been added, all as an extra second at the end of June or December; the most recent was on 31 December 2016.

They are unpredictable — announced only about six months in advance — and they have caused enough disruption to computer systems that in 2022 the General Conference on Weights and Measures resolved to stop using them by 2035. Unix time, the timestamp system underlying most software, simply pretends they do not exist: it defines every day as exactly 86,400 seconds and repeats or smears a second when one is inserted.

For everyday date arithmetic this is a non-issue. Twenty-seven seconds over five decades is not going to affect your age, your due date or your project schedule. It matters for satellite navigation, for financial timestamping and for anyone synchronising distributed systems — and it is worth knowing that a “seconds lived” figure of the kind our age calculator shows is technically a Unix-time count and therefore ignores those 27 seconds. So does every other clock you own.