Leap year

[Why does leap year exist?]

One day is defined by the Earth rotation, and one year by Earth revolution around the Sun. One revolution of the Earth is not 365 days but accurately 365.2422days. It is leap year that adjusts this decimal fraction.

[How to calculate]

If a dominical year can be divided by 4 without remainder, it is a leap year; otherwise, a dominical year is a common year.
In addition, if a dominical year can be divided by 100 without remainder, it is a common year.
If a dominical year can be divided by 400 without remainder, it is a leap year.

[Ground of calculation]

Since the error is 0.2422 day per year, it will accumulate into 0.9688 day for four years. In order to compensate such error, we have a leap year of 366 days once for four years.
There yet remains an error of -0.0312 day (-0.0078 day as an annual average). Since this error of -0.0078 day will accumulate into an error of -3.12 days for 400 years, only three leap years, in place of common years, are to be provided for 400 years.
It is the ground of calculation for leap year, and yet further there remains an error of -0.12 day (-0.0003 day as an annual average) that will in turn accumulate into an error of just one day for 4882 years (that is, 3300 years since 1582 when the leap year system was established). According to the description in some book, "An error of one day in itself does not concern people today." I expect that the human being 49th century will manage to solve this problem.

[History of leap year]