The problem is a remainder
The earth does not take a whole number of days to go round the sun. It takes 365 days, 5 hours, 48 minutes and 45 seconds — 365.2422 days. A calendar can only deal in whole days, so every ordinary year runs about six hours fast, and the seasons slide.
- Add a day every 4 yearsCorrects for 0.25, but the true figure is 0.2422 — so this now runs slow by about 11 minutes a year.
- Skip it in century yearsRemoves three leap days every 400 years, which overcorrects slightly the other way.
- Except when divisible by 400Puts one back. 1900 was not a leap year; 2000 was. The average lands at 365.2425 days.
Why Julian and Gregorian are thirteen days apart
The Julian calendar uses step one and stops. Eleven minutes a year is nothing in a lifetime and a great deal over sixteen centuries: by 1582 the spring equinox had drifted ten days from where the church had fixed it, and Easter was being calculated against a date that no longer matched the sky.
The Gregorian reform deleted ten days outright and changed the rule so it would not happen again. Not everyone adopted it at once — Britain waited until 1752, by which point the gap was eleven days — and several Orthodox churches keep the Julian reckoning still, which is why Orthodox Christmas falls on 7 January.
Other calendars, other corrections
Every solar calendar faces the same remainder, and they do not all solve it arithmetically.
| Calendar | How it handles the quarter-day |
|---|---|
| Gregorian | Arithmetic: every 4 years, not centuries, unless divisible by 400 |
| Julian | Arithmetic: every 4 years, no exceptions — hence the drift |
| Persian (Solar Hijri) | Observation: the year begins at the actual spring equinox in Tehran |
| Ethiopian & Coptic | Arithmetic: a 13th month of 5 days, 6 in a leap year |
| Baháʼí | Observation: Ayyám-i-Há flexes to hold Naw-Rúz at the equinox |