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

## General information Edit

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 Edit

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.

```Month   1  2  3   4  5  6   7  8  9  10 11 12
Rel day 0  3  3   6  1  4   6  2  5   0  3  5
```

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

## How to construct a perpetual calendar tableEdit

 Jan Oct Jan Apr Jul Sep Dec Jun Feb Mar Nov Feb Aug May 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
##### Month correspondences - red month for leap yearEdit
 DL Jan Oct Jan Apr Jul Sep Dec Jun Feb Mar Nov Feb Aug May G Mon Tue Wed Thu Fri Sat Sun F Tue Wed Thu Fri Sat Sun Mon E Wed Thu Fri Sat Sun Mon Tue D Thu Fri Sat Sun Mon Tue Wed C Fri Sat Sun Mon Tue Wed Thu B Sat Sun Mon Tue Wed Thu Fri A Sun Mon Tue Wed Thu Fri Sat 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
##### Dominical letters - days of the week in colorEdit
 00 07 14 Sat Thu Tue Sun Fri Wed Mon 01 08 15 Fri Wed Mon Sat Thu Tue Sun 02 09 16 Thu Tue Sun Fri Wed Mon Sat 03 10 17 Wed Mon Sat Thu Tue Sun Fri 04 11 18 Tue Sun Fri Wed Mon Sat Thu 05 12 19 Mon Sat Thu Tue Sun Fri Wed 06 13 20 Sun Fri Wed Mon Sat Thu Tue 01 05 09 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97
##### Julian centuries 00-20Edit
 16 20 24 28 32 Mon Sat Thu Tue Sun Fri Wed 17 21 25 29 33 Sat Thu Tue Sun Fri Wed Mon 18 22 26 30 34 Thu Tue Sun Fri Wed Mon Sat 19 23 27 31 35 Tue Sun Fri Wed Mon Sat Thu 01 05 09 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97
##### Gregorian centuries 16-35Edit
 1 Sun Fri Wed Mon Sat Thu Tue 2 Mon Sat Thu Tue Sun Fri Wed 3 Tue Sun Fri Wed Mon Sat Thu 4 Thu Tue Sun Fri Wed Mon Sat

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