The Earth’s rotation around the sun is 365.24219 days long. The time it takes for a complete cycle is called a tropical year. Since ancient times, people have attempted to fit an integer number of this length into the solar (tropical) year.

Such attempts include 360 days (Hipparchus), 365 days (Aristotle), 365.25 days (Ptolemy), and 365 1/4 days (Islamic astronomers consulted by Gerbert).

However, none of these attempts is accurate enough to match astronomical events such as the vernal equinox, which occur on a particular day each year. Thus, Jean Meeus suggests that adding one day every 4 years (with 29 February as the extra day) will yield an error of only about 0.0078 days or fewer than four minutes per year.

This is close enough to the real value of the tropical year that leap days are required to match astronomical events more closely (by having a calendar that runs exactly 365 days with no February 29).

There are 12 months of 30 days and one month of 31 days in a year.

12 x 30 = 360 (an approximation of 365)

1 x 31 = 31 (for a total of the correct number, 365)

The ancient Egyptians used a calendar with 12 months with 30 days each. The ancient Egyptians didn’t recognize a leap day, so their calendar drifted out of alignment with the Sun at a rate of one day every 4 years.

The months in this calendar were known by their number within the year.

This calendar was eventually reformed around 1000 BC to allow leap days to be inserted, synchronizing it more closely with the solar year. Still, its usage persisted into the time of the Persians who conquered Egypt in 525 BC.

The Babylonians used a lunisolar calendar that ran for about 19 years. There were 7 months with 29 days and 5 months with 30 days, plus an extra month inserted between the end of one year and the beginning of the next (which contained 27 or 28 days depending on whether the year was an odd or even number).

In general, there are 365.2 days, 12 months, and 52 weeks to complete the cycle.