Leap Years: Why Some Years Have 366 Days and How to Find the Next One
Years divisible by 4 are leap years, except century years that are not divisible by 400. The extra day keeps the calendar close to the seasons.
Also called
Leap day (the extra day, February 29)
A simplified model
The drawings are computed from the numbers in the sources. They simplify the real sky. For exact times and dates, use official tables.
Most years have 365 days. Every so often a year has 366, with one extra day on the calendar. Many people know that this happens about every four years, but the real rule has two exceptions. They explain why 1900 had no leap day while 2000 did.
This guide explains what a leap year is, why the calendar needs them, how to test any year with the Gregorian rule, and where the rule came from. It ends with a short task in the Clock Dial.
What a leap year is
A calendar year is the period between two dates with the same name, and the U.S. Naval Observatory glossary says it is either 365 or 366 days long. In an ordinary year, NASA Space Place says, you would count 365 days from January to December. In a leap year, February has 29 days instead of 28, so the year has 366 days. The extra day is called the leap day.
NASA Space Place gives a simple run of example years. The years 2017, 2018 and 2019 are ordinary, and 2020 is a leap year. The rings below show a common year, 2026, and a leap year, 2028.
Why the calendar needs them
Earth takes approximately 365 days and 6 hours to orbit the Sun, according to NASA Space Place, so a year is not an exact number of days. The calendar rounds down to 365. Each year that leaves about 6 hours, a quarter of a day, unaccounted for, and the leftovers are gathered into one extra day roughly every four years. NASA adds that without leap years, the missing hours would pile up into days, weeks and even months.
The Naval Observatory gives a more exact figure. The cycle of the seasons, the tropical year, is approximately 365.2422 days. A 365-day calendar would therefore fall short by about 0.2422 days each year, and over a century the calendar and the seasons would part by about 24 days. The guide to the solar calendar tells that story in full.
Notice that the two numbers differ a little. NASA Space Place rounds to a quarter of a day, and the Observatory gives the tropical year to four decimals. A leap day every fourth year assumes exactly a quarter, which is slightly too much. That small excess is the reason for the exceptions in the rule.
The Gregorian rule, step by step
The Naval Observatory states the Gregorian rule this way: years divisible by 4 are leap years, with the exception of century years that are not divisible by 400. Put as a short test:
- Is the year divisible by 4? If not, it is a common year with 365 days.
- If it is, does it end in 00? If not, it is a leap year with 366 days.
- If it ends in 00, is it divisible by 400? If yes, it is a leap year. If not, it is a common year.
The Observatory lists the years that show the exception at work. The years 1700, 1800, 1900 and 2100 are not leap years, while 1600, 2000 and 2400 are.
| Year | Divisible by 4 | Ends in 00 | Divisible by 400 | Leap year |
|---|---|---|---|---|
| 1600 | Yes | Yes | Yes | Yes |
| 1700, 1800, 1900 | Yes | Yes | No | No |
| 2000 | Yes | Yes | Yes | Yes |
| 2100 | Yes | Yes | No | No |
| 2400 | Yes | Yes | Yes | Yes |
Now apply the test to the years just ahead of us. The divisions below are our own arithmetic.
| Year | Test | Result |
|---|---|---|
| 2026 | 2026 ÷ 4 = 506.5, not a whole number | Common year, 365 days |
| 2027 | 2027 ÷ 4 = 506.75, not a whole number | Common year, 365 days |
| 2028 | 2028 ÷ 4 = 507, and it does not end in 00 | Leap year, 366 days |
How the rule keeps the average honest
Under the old rule of a leap day every fourth year, the average year was 365.25 days. The Gregorian rule drops some of those leap days. The Observatory says 97 leap days are introduced every 400 years instead of one every fourth year, which makes the average Gregorian year 365.2425 days. That agrees with the tropical year to within half a minute.
You can rebuild the average from the 400-year cycle. Four hundred years of 365 days make 146,000 days, and the 97 leap days bring the total to 146,097. NASA's reprint of the Explanatory Supplement to the Astronomical Almanac divides 146097 by 400 and gets the same average, 365.2425 days.
The result is very good but not perfect. The Observatory says it will take about 3,300 years before the Gregorian calendar is a full day out of step with the seasons. NASA's reprint says the calendar accumulates an error of one day in about 2,500 years. The two estimates differ, and both are measured in thousands of years.
A short history of the rule
The Naval Observatory glossary says Julius Caesar introduced the Julian calendar in 46 B.C. (another Observatory page says 45 B.C., so the sources differ on the year). In that calendar a common year has 365 days and every fourth year is a leap year with 366 days. The average is 365.25 days, which runs about 0.0078 days long, and over a century that builds up to a little over three quarters of a day.
In 1582, Pope Gregory XIII instituted the Gregorian calendar. NASA's Astronomy Picture of the Day describes the fine-tuning: leap days should not occur in years ending in 00, unless the year is divisible by 400. NASA's reprint of the Explanatory Supplement records the jump of that reform, 1582 October 4 followed by 1582 October 15. The Observatory notes that the Gregorian calendar is now used as the civil calendar in most countries.
Common mistakes
- Believing every fourth year is a leap year. Century years need to be divisible by 400. That is why 1900 and 2100 are not leap years and 2000 was.
- Thinking 2000 was skipped because it ends in 00. It is divisible by 400, so the exception does not apply. The Observatory glossary says plainly that 2000 was a leap year.
- Adding four forever. By the rule above, the leap year after 2096 is 2104, not 2100.
- Reading "about every four years" as "exactly every four years". NASA Space Place words it as approximately every four years, and the Gregorian rule has gaps of eight years at century marks such as 2100.
- Assuming leap years fix the calendar for good. The Gregorian average is within half a minute of the tropical year, so the drift is tiny, but it is not zero.
Try it in the instrument
Open the Clock Dial and set the sky to the next leap year after 2026. The target is 2028. You can work it out with the rule. The year 2027 is not divisible by 4, because 2027 ÷ 4 leaves 3 over, so it is a common year. The year 2028 is divisible by 4, since 2028 ÷ 4 = 507, and it does not end in 00, so no century exception applies.
Use the ring figures as a check. A common year such as 2026 fills the ring with 365 days, and a leap year such as 2028 fills it with 366. Stepping forward from 2028 by four gives 2032, 2036 and so on, until the century exception arrives in 2100.
Questions people ask
Is 2100 a leap year?
No. The Naval Observatory lists 2100 among the years that are not leap years. It ends in 00 and is not divisible by 400.
Was 2000 a leap year?
Yes. It ends in 00 but is divisible by 400. The Observatory glossary puts it this way: 2000 was a leap year, but 1900 and 2100 are not.
How many leap years are there in 400 years?
The Naval Observatory says 97 leap days are introduced every 400 years. That is three fewer than one every fourth year would give, and it brings the average year to 365.2425 days.
Do other planets have leap years?
Mars does, according to NASA Space Place. A Martian year is 668 sols, or Martian days, but one trip around the Sun takes 668.6 sols. In a 10-year stretch, NASA says four years would have 668 sols and six would be leap years with 669, so Mars has more leap years than regular years.
Sources
- Leap Years, U.S. Naval Observatory, Astronomical Applications Department. https://aa.usno.navy.mil/faq/leap_years. Opened November 10, 2026.
- What Is a Leap Year?, NASA Space Place. https://spaceplace.nasa.gov/leap-year/en/. Opened November 10, 2026.
- Glossary, U.S. Naval Observatory, Astronomical Applications Department. https://aa.usno.navy.mil/faq/asa_glossary. Opened November 10, 2026.
- Calendars and their History, NASA Eclipse Web Site, NASA Goddard Space Flight Center (reprint from the Explanatory Supplement to the Astronomical Almanac, L. E. Doggett). https://eclipse.gsfc.nasa.gov/SEhelp/calendars.html. Opened November 10, 2026.
- APOD: 2024 February 29 - Julius Caesar and Leap Days, NASA Science (Astronomy Picture of the Day). https://science.nasa.gov/image-article/apod-2024-february-29-julius-caesar-and-leap-days/. Opened November 10, 2026.
- Introduction to Calendars, U.S. Naval Observatory, Astronomical Applications Department. https://aa.usno.navy.mil/faq/calendars. Opened November 10, 2026.
We opened each source ourselves on the date shown. The drawings are our own and were checked against the numbers in these sources.
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