How did the Julian and Gregorian calendars differ by 13 days?

The discrepancy between the Julian and Gregorian calendars arises from how each system accounts for the length of the solar year. The Julian calendar assumed a year length of 365.25 days, which overestimated the actual tropical year by approximately 11 minutes and 14 seconds. Over centuries, this error caused the calendar to drift out of alignment with the seasons.123

By 1582, this drift had accumulated to 10 days, prompting Pope Gregory XIII to introduce the Gregorian calendar. To correct the error, he mandated that 10 days be skipped in October 1582. Furthermore, the Gregorian system refined the leap year rule: while the Julian calendar designated every fourth year as a leap year, the Gregorian calendar excludes centennial years unless they are divisible by 400 (e.g., 1700, 1800, and 1900 were not leap years).134

Because the Julian calendar continued to add leap days in those centennial years, the gap between the two systems grew over time. The current difference is 13 days, though it will increase to 14 days in the year 2100.2