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Weekdate Dating System
© Copyright 2012, Rick McCarty

Weekdate specifies dates using week numbers rather than months. Monday is day 1 of each seven-day week, Sunday is day 7. Every year in weekdate begins on Monday of week one. Common years have 52 weeks, leap years have 53.

The long, thin table at right represents the current Gregorian
year, with weeks beginning on Monday, and with a
column of weekdate week numbers in red.

Below is a comparison of the Gregorian and weekdate dating systems. In the weekdate system, the weekday is specified first, then the week number, then the year. The week number should always have two digits; so the year's first weeks should be represented as 01-09. When the weekdate is specified as a string of numbers, the weekday number can be preceded optionally by a lower case "d" (or the initial of the word for day in the local language). This is only to distinguish the numerically specified weekdate from the numerically specified Gregorian date.

The above table of the current Gregorian month, with Sundays first,
presents weekdates in red, as a supplemental dating system.
The week numbers can be seen to change every Monday.

Weekdate Calendar

The weekdate dating system is independent of the Gregorian Calendar, though the two share an important basis. Both systems observe the same 400-year cycle, called a "quadricentennium." The cycle contains 146,097 days, which is 20,871 whole weeks. The average year-length within the cycle is 365.2425 days. This compares favorably to the mean tropical year (365.2423 days), providing for a one-day discrepancy in 3,300 years.

The Gregorian year contains 365 days in common years, and 366 days in leap years. Gregorian years also contain one or two week fragments. In weekdate, common years contain 364 days, or 52 whole weeks, while leap years contain 371 days, or 53 whole weeks. Weekdate is independent of the Gregorian calendar precisely because its leap-year rule is different.

For leap years in the Gregorian calendar an extra day is added to February in each year whose number is divisible by four, unless it is divisible by 100, except if it is divisible by 400. In weekdate, a 53rd week is added in every year whose number is divisible by five, with two or three exceptions per century. These are computed using a leap-year exception matrix.

quarters exception matrix  exception years
 2000  +       35  85=  2035   2085
 2100        25  702125   2170
 2200        10  552210   2255
 2300          0  45  902300   2345   2390

Centesimal quarters for the 2000 quadricentennium,
when added to the leap-year exception matrix,
generate the nine exception years.

The five-year leap rule, with the 9 exceptions generated by the matrix, provides for 71 leap weeks in 400 years, and so for a quadricentennium of 20,871 weeks.


Coincidence of Weekdate and Gregorian Systems

The weekdate and Gregorian systems coincide every four hundred years. Gregorian Jan. 1, 2001 and Jan. 1, 2401 fall on 1/01/2001 and 1/01/2401 in weekdate. Between these parameters, the two systems coincide on New Year's day in 55 additional years, and never vary more than six days. Week 01 of the weekdate year can begin as early as Gregorian Dec. 26, and as late as Jan. 6—a 12-day spread. Sixty percent of weekdate years begin on the five Gregorian dates from Dec. 30 to Jan. 3.

Weekdate and ISO8601

ISO8601 is a dating system comparable to weekdate, but it is not independent of the Gregorian calendar. It includes no distinct leap-year rule. ISO8601 specifies that the first week of the year is the week containing the first Thursday of the Gregorian year. So at the end of the year it is necessary to consult the Gregorian calendar to determine whether the week number following 52 should be 01, or 53. This is not the case with weekdate. Whether the year contains a 53rd week in weekdate is determined by an independent leap-year rule. Usually, if its number ends in 0 or 5, the year contains 53 weeks.

Advantages of the Weekdate System

  1. Fewer data are required to specify dates, compared with the Gregorian calendar. Weekdate's three data—weekday, week, year—completely specify each date. Specifying Gregorian dates completely requires four data—weekday, month, ordinal day, year (e.g., Friday, January 3rd, 2020).

  2. Intervals between dates are easier to calculate, since weekdates are specified independently of variable month-lengths. How many days from March 19 to June 10? In weekdate the question would be, How many days from 1/12 to 7/23? Answer: six days, eleven weeks, obviously. Or 83 days.

  3. Weekdate is compatible with the Gregorian calendar, and can be used concurrently as an alternative dating system. Most other calendar systems introduce variations on the Gregorian monthly structure, so implementing them requires abruptly setting that calendar aside.

  4. No costly software corrections are required for weekdate's implementation. As it becomes more popular, software developers will choose to overlay the weekdate on the Gregorian date. As the latter gradually falls out of use, weekdate will transition to the default calendar. The prospect of vital computer systems crashing because of outdated calendar programming is nil.

  5. The Weekdate calendar is perennial, apart from the leap week. The year always begins on the same weekday, so weekday events like the start of school terms or holidays can be fixed on the same dates every year. Autumn school terms, in the northern hemisphere, can begin every year on Monday 34, for example.

  6. There is no interruption of the seven-day cycle of the week, as in other methods of establishing a perennial calendar. Those methods designate one or two days each year as falling outside the week-cycle. In weekdate, every day of the year has a weekday designation consistent with the seven-day cycle.

  7. Weekdate is independent of any other calendar system; with its own leap-year rule, weekdate is a stand-alone calendar. Dating by weeks with ISO8601 depends upon the Gregorian calendar. In order to follow ISO8601 it is necessary to determine the first Thursday of each Gregorian year.

Some Disadvantages

  1. The weekdate leap-year rule is more complicated than most alternatives. Its quintennial rule—leap years end in 0 or 5—is a bit simpler than the Gregorian's quadrennial rule. But computing the quintennial rule's exceptions, 2 or 3 per century, is not as easy as computing the Gregorian rule's exceptions.

  2. Seasonal variance of dates is greater, because of the seven-day leap-year correction. Solstices and equinoxes will fall on a wider range of dates (11 days) than in the Gregorian calendar (3 days).

  3. Leap years do not divide easily into quarters, because of their inclusion of a 53rd week. Most years, however, break down into 13-week regular quarters, each with the same number of workdays and weekends.

  4. The seven dates in the leap week are not annual occurrences, whereas only one date, Feb. 29, is like this in the Gregorian calendar. So a larger number of birthdays and anniversaries must be celebrated on analogous dates.

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