Perpetual calendar

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A perpetual calendar is a calendar which is good for a span of many years, such as the Runic calendar.

1 General Information
2 Perpetual Calendar Formulas
3 Patents
4 External links

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.

Common year starting on Mon - Tue - Wed - Thu - Fri - Sat - Sun Leap year starting on Mon - Tue - Wed - Thu - Fri - Sat - Sun

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 mechanism in the watch that displays calendar dates and does not need to be adjusted at the end of each month by the user to take into account the different lengths of different months.

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Perpetual Calendar Formulas

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 begin 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 yeap years.

A table is needed to get the relative day of the first of each month relative to the first day of the year. 1-0 2-3 3-3 4-6 5-1 6-4 7-6 8-2 9-5 10-0 11-3 12-5

Now for the formula (example for 2/15/2006)

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

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