The Gregorian Calendar

This section describes The Gregorian Calendar, which is a solar calendar with two types of calendar years: Common year with 365 days and Leap year with 366 days.

The Gregorian calendar is a solar calendar. It follows the tropical year with two types calendar years:

• Common year - 365 days.
• Leap year - 366 days.

All years are common years with exceptions defined by the following leap year rules:

• 1. If the year number is divisible by 4, it is a leap year.
• 2. But if the year number is divisible by 100, rule 1 is not used, so it is a common year.
• 3. But if the year number is divisible by 400, rule 2 is not used, so it is a leap year.

Now let's see how closely the Gregorian years are synchronized to the tropical years.

Based on leap year rule 1, 4 Gregorian calendar years are about 0.03124 day more than 4 tropical years.

```4 Gregorian years: 3 * 365 + 366 = 1461 days
4 tropical years:  4 * 365.2421896698 = 1460.9687586792 days
```

Based on leap year rule 2, 100 Gregorian calendar years are about 0.21897 day less than 100 tropical years.

```100 Gregorian years: 76 * 365 + 24 * 366 = 36524 days
100 tropical years:  100 * 365.2421896698 = 36524.21896698 days
```

Based on leap year rule 3, 400 Gregorian calendar years are about 0.12413 day more than 400 tropical years.

```400 Gregorian years: 305 * 365 + 95 * 366 = 146097 days
400 tropical years:  400 * 365.2421896698 = 146096.87586792 days
```

As you can see, there will be about one extra day in about 2500 Gregorian calendar years comparing 2500 tropical years.

A Gregorian year is divided into 12 Gregorian months, named as January, February, March, April, May, June, July, August, September, October, November and December. The number of days in each month varies as shown in the following tables for a common year:

```Month    1    2    3    4    5    6    7    8    9   10   11   12
Days    31   28   31   30   31   30   31   31   30   31   30   31
```

For a leap year, the second month has 29 days.

Note that Gregorian month has no relation with the synodic month cycle.

Gregorian calendar also uses the week cycle, which is a 7-day cycle, with days names as Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, and Saturday. The first day of Gregorian year 1 is a Monday.

Since 400 Gregorian years have 146097 days, which is divisible by 7, the week cycle and the year cycle meets every 400 years.