Perpetual calendar

A perpetual calendar from Sweden to compute the easter 1140-1671 according to the Julian calendar. Notice the runic writing.

A 50 year "pocket calendar" that is adjusted by turning the dial to place the name of the month under the current year. You can then deduce the day of the week, or the date.

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

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 14 one-year calendars consists of two sets of seven calendars, seven for each common year (year that does not have a February 29) that starts on each day of the week, and seven for each leap year that starts on each day of the week, totaling fourteen.

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 the 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.

The internal mechanism will move the dial to the next 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:

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:

Following centuries continue the cyclic sequence.

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.

3. The month: For the month number, add as follows, except in case of January and February during a leap year.

The Leap Year Rule: a) If the year is divisible by 4 but not 100. b) If the year is divisible by 400.

4. Add the day number.

5. The total is divided by 7 and the remainder will be the day of the week, Sunday being the first day.

Example 1: September 11, 2001

Step 1. 2000s corresponds to 6

Step 2. 01 plus 1/4 of 01 is 1

Step 3. September corresponds to number 6

Step 4. The day of the month 11

Step 5. The sum of 24 divided by 7 leaves 3 remainder. Number 3 correponds to Tuesday.

Example 2: December 7, 1941

1. 1900s corresponds to 0

2. 41 plus 10 is 51

3. Dec corresponds to 6

4. The 7th day, add 7

5. Sum of 64 divided by 7 is 9 with 1 remainder. The first day of the week is SUNDAY.

General Information

Prior to September 14, 1752, Great Britain (and her American colonies) observed the Julian calendar. For purposes of the formula, a century year is treated as belonging to the century which it precedes (e.g. for purposes of the formula, 2000 is considered to be part of the 21st century). Under the current (Gregorian) calendar, century years are not leap years unless exactly divisible by 400. This makes the calendar accurate to one day in 3,323 years. A slight modification, in which century years are not leap years unless they give remainder 200 or 700 on division by 900 makes the calendar accurate to one day in 44,000 years. Under this scheme, the next centennial leap year will be 2500 (instead of 2400).

Source: Funk & Wagnall’s College Standard Dictionary (1939 ed.)

Perpetual Julian and Gregorian calendar table

For Julian dates before 1000 and after 1699 use the year in the table which differs by an exact multiple of 700 years. For Gregorian dates after 2799 convert to Julian. To find how many days the Gregorian date is ahead of the Julian, add 300 to the year, multiply the hundreds by 7, divide by 9 and subtract 4. Ignore any fraction of a day. When the difference between the calendars changes the calculated value applies from March 1 (Gregorian date).

To use the table, add together the numbers in the far right hand column on the same line as the hundreds, remaining digits and month. Add the day of the month to the total and divide the grand total by 7. Find the remainder from this division in the far right hand column. The day of the week is beside it. Bold figures (e.g. 04) denote leap year. If a year ends in 00 and its hundreds are in bold it is a leap year. Thus 19 indicates that 1900 is not a leap year, 20 indicates that 2000 is a leap year. Use January and February only in leap years.

Example: On what day does June 6, 6666 (Gregorian) fall? Convert to Julian: 6666+300=6966. 69x7=483. 483/9=53 remainder 6. 53-4=49. June 6 equates to May 37 or April 67. The corresponding Julian date is April (67-49) = April 18. Use 1066, which is exactly 8x700=5600 years earlier. From the table, 2 (for hundreds) + 5 (for remaining digits) + 6 (for month) + 18 (for day of the month) = 31. 31/7=4 remainder 3. The weekday is Tuesday.

See also

• Antikythera Mechanism
• Calculating the day of the week
• Doomsday (weekday)
• Perpetual Calendar of 800 Years
• Long Now Foundation
• Year 10,000 problem

External links

• Perpetual Calendar 1753-2199 in 11 languages.
• Perpetual Calendar 1901-2001 (just click on the year)
• A Perpetual Calendar showing the day of any month corresponding to any day of the week, for the year 1775, to the year 2025
• A perpetual calendar
• U.S. Patent 248,872, "Calendar".

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