Why do we have leap years?
The short answer
Leap years exist because a full orbit around the Sun takes 365.242189 days, so we add extra days to keep our calendar aligned with the seasons. The Gregorian calendar uses specific leap year rules to stay closely synced with the solar year, skipping three leap years every 400 years for better accuracy.
The long answer
It takes 365 days for the Earth to travel around the Sun, right?
Wrong. It actually takes 365.242189 days for a full orbit, or about 5 hours, 48 minutes, and 56 seconds longer than the common, Gregorian calendar year.
If we didn't account for this extra 1/4ish of a day, our calendar would be way off after a while. Over 700 years, this discrepancy would add ~169 days, eventually shifting Northern Hemisphere summers into December.
Not to scale
Adding an extra day in years divisible by four (e.g. 2024) helps compensate for the roughly 1/4-day difference between the common year (no leap year) and the solar year (actual orbit). But simply adding an extra day every four years is not precise enough...
Why are three leap years skipped every 400 years?
If we held to a "have a leap year every four years" protocol, we'd still end up pretty out of sync with the solar year after a while.
That's because adding a day every four years makes the average length of a year 365.25 days, which is ~11 minutes and 15 seconds longer than the true solar year. So after four years, we'd have an extra ~45 minutes, and after 129 years, we'd be off by ~1 day. That's closer to the solar year than no leap years at all but still not close enough.
When the Gregorian calendar was introduced in 1582, it got closer to solving this problem by instituting three rules for leap years:
Leap years occur in years divisible by four (e.g. 2028).
Leap years are skipped in years divisible by 100 (e.g. 1900).
But leap years do occur if they are divisible by 100 and 400 (e.g. 2000).
That means that every 400 years, three leap years are skipped. So from 2000-2400, leap years will be skipped on 2100, 2200, and 2300.
Each dot represents the date of the northern summer solstice (in GMT) from 1750 to 2250. You can see the 4-year pattern created by leap years, where the calendar catches up a bit by adding an extra day. But the overall trend still drifts downward: the Gregorian calendar runs about ~0.24 days too fast each year.
“Gregoriancalendarleap solstice" by BasZoetekouw is licensed under CC BY 3.0.
It isn't a perfect solution though. Following these rules over 400 years will make the average year length 365.2425 days, a tiny bit longer but pretty darn close to the true solar year of 365.242189 days. It'll take thousands of years for us to need more calendar tinkering.
🧠 Bonus brain points
Do other calendars have leap years?
Yes, but they don't operate on the same Gregorian system. The Chinese calendar runs on the lunar cycle, so each month is 29 or 30 days. Every 2-3 lunar years, a leap month is added to keep up with the Gregorian calendar. The Hebrew calendar also runs on the lunar cycle and includes a leap month.
The Hindu calendar is lunisolar calendar, tracking both the Earth's orbit around the Sun and the Moon's orbit around the Earth. Both leap months and days are added to correct for any misalignment.
Many other calendars have also included leap days and months to adjust against the solar year cycle.
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Sources
Baker, H. (2024, March 1). Why do we have leap years? And how did they come about?. LiveScience. https://www.livescience.com/human-behavior/why-do-we-have-leap-years-and-how-did-they-come-about
Bikos, K. (n.d.). Leap Months and Leap Days in the Hindu Calendar. Time and Date. https://www.timeanddate.com/date/hindu-leap-year.html
China Highlights. (n.d.). Chinese Calendar 2025. China Highlights. https://www.chinahighlights.com/travelguide/guidebook/chinese-calendar.htm
Craddock, B. (2020, February 27). The Science of Leap Year. National Air and Space Museum. https://airandspace.si.edu/stories/editorial/science-leap-year
Langowitz, E. (n.d.). Is there a leap day on the Jewish calendar?. Reform Judaism. https://reformjudaism.org/learning/answers-jewish-questions/there-leap-day-jewish-calendar
Yates, K. (2024, February 28). The mathematical muddle created by leap years. BBC News. https://www.bbc.com/future/article/20240228-leap-year-the-imperfect-solution-to-fix-the-calendar
It’s like an American accent but with calendars.