00 · QUICK ORIENTATION
A calendar manages a remainder
- 1The tropical year is about 365.2422 days, so a calendar of exactly 365 days drifts against the seasons.
- 2The Gregorian calendar inserts 97 leap days in 400 years, producing an average calendar year of 365.2425 days.
- 3Leap years and leap seconds solve different problems.
01 · THE FRACTION
The seasons refuse to fit whole days
The tropical year is about 365.2422 days, so a calendar of exactly 365 days drifts against the seasons.
The relevant interval is tied to the seasonal cycle, such as one March equinox to the next. A civil calendar must approximate that continuous motion with whole dates.
02 · DRIFT
A small annual error becomes history
A 365-day calendar falls behind the seasons by nearly a quarter day each year. After a few years the mismatch is obvious; after centuries it shifts seasonal dates.
Leap days are not bonus astronomical time. They are bookkeeping that changes the labels attached to Earth’s continuous rotation and orbit.
365-day calendar
Loses about 0.2422 day each year.
365Julian correction
Adds slightly too many leap days.
365.25Gregorian correction
Skips three century leap days per 400 years.
365.242503 · THE JULIAN SOLUTION
Every fourth year corrects too much
The Julian calendar averages 365.25 days by adding one day every four years. That is close, but longer than the tropical year by about eleven minutes.
The residual error accumulates to roughly a day in 128 years, enough to matter for a calendar tied to equinoxes and religious observance.
04 · THE GREGORIAN FILTER
Century years pass a second test
The Gregorian calendar inserts 97 leap days in 400 years, producing an average calendar year of 365.2425 days.
A year divisible by four is normally leap; a century year is not unless divisible by 400. Thus 2000 was leap, while 2100 will not be.
A rule can be simple to use because a more careful approximation was built into its exceptions.
The tropical year is about 365.2422 days, so a calendar of exactly 365 days drifts against the seasons.
The tropical year changes slowly, and 365.2425 is still an approximation. The Gregorian rule is extraordinarily useful, not mathematically eternal.
05 · REFORM IS POLITICAL TIME
Changing the rule also changed dates
The Gregorian reform of 1582 removed accumulated calendar drift and altered the future leap rule. Adoption then spread at different times across states and religious communities.
A date is therefore both an astronomical approximation and a social agreement. Historical dates require knowing which calendar a source used.
The calendar counts whole days; the seasons do not. A leap year is a carefully imperfect correction that stops dates from slowly walking through the seasons.
One year
The fractional day remains.
36506 · NOT THE SAME AS A LEAP SECOND
Calendar days and atomic seconds solve different mismatches
Leap years keep dates aligned with the seasonal year. Leap seconds, when used, keep atomic civil time near irregular Earth rotation.
The similar names hide different scales, authorities and causes. One adjusts a calendar pattern; the other adjusts a time scale by a second.
07 · EVIDENCE TRAIL
Orbit, rule and historical adoption
A seasonal year is not 365 whole days. Leap-year rules keep a civil calendar close to Earth’s orbit without adding a day every four years forever.
- 01US Naval Observatory · Leap YearsOFFICIAL EXPLAINER ↗
USNO explanation and numerical calendar averages.
- 02US Naval Observatory · Introduction to CalendarsOFFICIAL REFERENCE ↗
USNO calendar history and definitions.
- 03Library of Congress · Inter Gravissimas and the Gregorian reformHISTORY SOURCE ↗
Library of Congress account of the 1582 reform.
- 04BIPM · Time metrologyMETROLOGY REFERENCE ↗
BIPM distinction between atomic time and Earth rotation.