Perpetual calendar

General information[]

Perpetual calendar formula[]

How to construct a perpetual calendar table[]

External links[]

Month correspondences - red month for leap year[]

Dominical letters - days of the week in color[]

Julian centuries 00-20[]

Gregorian centuries 16-35[]

Year correspondences for Gregorian calendar[]

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

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.

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

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

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

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

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

Jan Apr Jul

Feb Mar Nov

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