All date formats in this writeup use the Gregorian calendar system.
The examples given are for Tuesday, February 8, 2000 (the local date of when I created this writeup).
Other locations may use the given date format besides the places I list.

my short format (with "checksum")
"year.month.date_of_month.nday_of_week" (the days of week are 0=Sunday, 1=Monday, 2=Tuesday, 3=Wednesday, 4=Thursday, 5=Friday, 6=Saturday) - "2000.02.08.n2"

full or long (USA)
"day_of_week, month date_of_month, year" - "Tuesday, February 8, 2000"

short (USA)
"month_number/date_of_month/year_2_digits" (the final "/" and year may be omitted) - "2/8/00" or "2/8" (note that this is format is not Y2k compliant)

short (Europe)
"date_of_month/month_number/year_2_digits" (the final "/" and year may be omitted) - "8/2/00" or "8/2" (note that this is format is not Y2k compliant)

Note that sometimes short European and USA formats can be confused for each other, so they may be incorrectly read as August 2, 2000.

One that I've seen (popular with Esperantists and such) is

day month year

but with the month expressed in roman numerals. That way, it isn't tied to a particular language (as using month-name abbreviations would be), nor is it liable to be confused for the month-day-year ordering, since the two kinds of numbers are distinct. So today (according to UTC, not my current timezone) would be 11-XII-2000, which could not be confused for a date in November.

It has its advantages and points to recommend it.

ISO 8601:1988 specifies that dates and times should be written in one of the following formats:
YYYY-MM-DD hh:mm:ss

YYYY: Year (0000-9999)
MM: Month (01-12)
DD: Day of the month (01-31)
hh: Hour of the day (00-23)
mm: Minutes of the hour (00-59)
ss: Seconds of the minute (00-59)
W: A Literal 'W'
ww: Week of the year, W01 is the week containing January 4 (01-53)
d: Day of the week, Monday is 1, Sunday is 7 (1-7)
ddd: Day of the year, (001-366)
When storing the dates in a machine readable text format all the punctuation marks may be omitted but ISO recommends placing a 'T' between the date and time. For example 20000204T235959.

Unlike any national conventions for specifying dates the ISO standard avoids all ambiguities. If you see the date 2001-02-04 you can be certain it refers to the fourth day of February in the year 2001.

The Julian date format is available in several flavors:

  • Military:
    For example, today would be 1026, where:
    1 = the current year (2001)
    026 = the current day (the 26th day of a 365-day year).
    The Military has the old records archived, so every ten years it won't matter if the year digit rolls over.

  • Normal Julian:
    For example, Christmas of 2001 would be 2001359, where:
    2001 = the current year (2001)
    359 = the day (Christmas).

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