Leap Year Calendar Checker

Under the Gregorian calendar system established in 1582 by Pope Gregory XIII, a year is evaluated for leap year status using three sequential mathematical rules: 1. Divisibility by 4: If $\text{Year} \% 4 === 0$, the year is a potential leap year. If false, it is a standard 365-day year. 2. Century Exception (Divisibility by 100): If $\text{Year} \% 100 === 0$, it is an end-of-century year and is NOT a leap year, UNLESS... 3. 400-Year Exception: If $\text{Year} \% 400 === 0$, it IS a leap year. Examples: • 2024 is a leap year ($2024 \% 4 = 0$ and $2024 \% 100 \neq 0$). • 2000 was a leap year ($2000 \% 400 = 0$). • 1900 was NOT a leap year ($1900 \% 100 = 0$ but $1900 \% 400 \neq 0$). • 2100 will NOT be a leap year for the same reason.

Earth takes approximately 365.24219 solar days (365 days, 5 hours, 48 minutes, and 45 seconds) to complete one full tropical orbit around the Sun. Adding an extra day every 4 years adds $0.25$ days per year ($365.25$ average days), which overcompensates by approximately $0.0078$ days (11 minutes and 15 seconds) each year. Over 400 years, this slight overcorrection accumulates to roughly 3 extra days. By omitting 3 leap days every 400 years (skipping century years not divisible by 400), the Gregorian calendar achieves an average year length of $365.2425$ days, closely matching astronomical reality.

Without leap years, our calendar would drift out of alignment with Earth’s astronomical seasons by approximately 1 calendar day every 4 years (about 24 days per century). Over several centuries, the Northern Hemisphere’s summer solstice would drift from June into July, August, and eventually December. Leap years anchor the calendar so that the vernal equinox consistently falls on or around March 21.