General information

For the Gregorian calendar, a perpetual calendar often consists of 14 one-year calendars, plus a table to show which one-year calendar is to be used for any given year. Note that such a perpetual calendar fails to indicate the dates of moveable feasts such as Easter.

The Perpetual Calendar has 14 one-year calendars, one for each common year (year that does not have a February 29) that starts on each day of the week, and one for each leap year that starts on each day of the week.

Also certain calendar reforms may be considered to be perpetual calendars, such as The World Calendar, International Fixed Calendar and Pax Calendar. These calendars have each year and each month within the year, always beginning on the same day of week.

The term perpetual calendar is also used in watchmaking to describe a calendar mechanism in a watch that displays the date correctly 'perpetually', taking into account the different lengths of the months as well as leap year's day.

Perpetual calendar formula

Following is a formula for calculating the day of the week given the date.

The formula uses the fact that each year begins one day later than the previous except for leap years. The days in a leap year are 2 days later except for January and February where it is one day later. Since the year values increase by one we can create a sequence by adding the year to the year divided by 4 dropping the fraction. This sequence increases by 1 every year except every 4 years where it increases by 2. This sequence will work for the years 1901 through 2099 only since 1900 and 2100 are not leap years.

A table is needed to get the relative day of week of the first of each month relative to the first day of a year.

Now for the formula (example for 2006-02-15).

Add the following: The 4 digit year (2006). The integer portion of the year divided by 4 (501). The relative month code (3). The day of the month (15). If it is a leap year and January or February then subtract 1 (0). Adjust the relative week day by subtracting 2 (2525-2). Divide by 7 keeping the remainder (3).

Use this number to find the day as follows:
0-Sunday 1-Monday 2-Tuesday 3-Wednesday 4-Thursday 5-Friday 6-Saturday. Thus, February 15, 2006 is a Wednesday.

Alternate Version

A Perpetual Calendar formula for finding the day of the week for any given year since the inception of the Gregorian Calendar (>1751).

1. Begin with the century:

2. The year: Take the last two figures of the year date and 1/4 of the number formed by them, ignoring the remainder. For example, for the year 1963, 63 divided by 4 is 15 with no remainder. So, 63 plus 15 totals 78.