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© J R Stockton, ≥ 2012-05-13

Date and Time Scales.

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Except as indicated, this page deals with English or British convention.

The Positioning of Dates

ISO 8601 describes the nature of the Gregorian Calendar. ISO 8601:2000 assigned 1875 to the signing of the "Convention du mètre" in Paris, thereby only loosely indicating the positioning of the sequence of dates on the sequence of natural days. ISO 8601:2004 assigns 1875-05-20 to the signing of the Convention.

In this respect, the Papal Bull of Pope Gregory XIII only said, in effect, "omit ten dates"; it relied otherwise on the existing positioning. Likewise for the British Calendar (New Style) Act (1750 c.23), which omitted eleven dates.

Dionysius Exiguus positioned the Anno Domini numbering on the sequence of natural years.

Julius Caesar decreed, via the length of the Year of Confusion (B.C. 46; 445 days (432?); annis confusionis), the exact positioning of the year boundaries of the Julian Calendar on the sequence of natural days, though it seems possible that the positioning got nudged by the Augustine month-length changes about four decades later (according to the Calendar FAQ that reform is, anyway, a fabrication).

The positioning of a calendar should be defined either by reference to another calendar (which must itself be well-defined) or by reference to an event for which the moment of occurrence (to within a few hours or better) can be determined whenever it may be required. The latter means an astronomical event defined by orbital mechanics; I suggest the famous Total Solar Eclipse of 1999-08-11.

The Beginnings of Dates

The date, in Gregorian and other calendars past and present, can change at different times of the Local or legal GMT (=UT) day. Here the times are given in signed form hh:mm with zero being at midnight, either Local or Greenwich. Local times may be affected by Summer Time.

TimeBasisUsage
-??:?? ¤GMT Date first appears, in the Far East (South Pacific)
-12:00 ¶GMT Date appears, in Zone +12, Standard Time
-12:00Local Royal Navy Date, until change ordered on 1805-10-11
-08:21GMT Jewish Moon prediction, -0600 @ Jerusalem
-06:00Local ¤ Jewish/Islamic conventions
Sunset §n/a Islamic/Jewish conventions; also Roman
  00:00Local ¤
GMT
GMT
Gregorian Date, customary civil usage
GMT Date - by UK Law from 1880
þ Astronomers' GMT Date, from 1925-01-01 GMT
+03:00Local ¤ Some transport may operate internally on 03:00-27:00,
so that the working day has a constant date
+04:30Local ¤ Transport for London, Oyster day, 00:00/04:30-28:29+
+06:00Local ¤ Broadcasting may operate internally on 06:00-30:00,
so that the working day has a constant date
+10:00 ¤GMT Date finally appears, in the Far West, Zone -10
+12:00GMT þ Astronomers' GMT Date, before 1925-01-01 GMT
+12:00 ¶GMT Date would appear, in Zone -12, Standard Time
Notes § : Sunset definitions vary
¤ : Summer Time may affect this
¶ : Zones ±12 are not the actual limits
þ : or Astronomical Date (GMAT)

In earlier times, European conventions varied considerably, including starting the day at noon. I know nothing about conventions in regions not mentioned or implied.

The Beginnings of Years

Here only Gregorian/Julian based calendars are considered.

Year TypeFirst Day of Year
Present Civil January 1st
Astronomers', before 1925 January 1.5 GMT (London noon Jan 1st) *
English, c12 to 1751 March 25th - Lady Day, Annunciation
Present UK Financial April 6th - Lady Day + 12 sic
Old Celtic November 1st - All-Hallows' Day
Roman Catholic Church First Sunday in Advent (Nov 27th - Dec 3rd)
English, c7 to c12 December 25th - Christmas Day
Roman Catholic ecclesiastical, to 1910 December 25th - January 1st from 1911
British Regnal Anniversary of the Accession of the Monarch
Royal Navy, at sea December 31st, local noon (to 1805)
Other Financial Various
Other Civil Various
* Maybe beginning with Jan 0 starting at London noon Dec 31st.

Likewise, conventions varied elsewhere.

See the Calendar FAQ, Sec 2.9, for more.

Regnal Years

British legislation is dated by Regnal Year, counting from the day of the Accession of the Monarch.

For a list, see Harvey, via Date and Time Index and Links.

Zeroes of Date/Time Scales

For more on Date scales, see Date Miscellany I and CritDate (ZIP); these have more about some of the scales starting on these dates.

These are Zeroes of Day or Time; in many cases, Day scales are actually defined by Day 1 being the logically-following day. There is advantage in being free to use 0 to represent undefined / null / escape, in scales that do not need to extend back befor Day 1.

Where the origin is not given as GMT (=UT) or local, it merely means that I do not know; it may well be defined somewhere. The Calendar column applies to the date of origin.

To be checked, especially if yellow
OriginatorScaleUnit  Zero Date       Time     Calendar
[0]Chronological JDday BC 4713-01-01local 00:00Julian
J J ScaligerJulian Period7980 years BC 4713-01-01 Julian
John HerschelJulian Day Countday BC 4713-01-0112:00 GMTJulian
JRSprogram longcalcsecond AD 0000-03-0100:00 localGregorian
Microsoft.NET Framework Class Lib100 ns AD 0001-01-0100:00 GMT+localGregorian
BorlandDelphi 1 TDateTimeday AD 0001-01-0000:00 localGregorian
Mike CowlishawRexx1 µs AD 0001-01-0100:00Gregorian
Rexx Base Formatday AD 0001-01-00 ?-Gregorian
?Paradoxms AD 0001-01-01 ?00:00Gregorian
MS WindowsTTimeStamp100 ns AD 0001-01-0100:00Gregorian
Dr Luigi LilioLilian Day Countday AD 1582-10-14-Gregorian
?SPSSsecond AD 1582-10-1400:00Gregorian
ANSICOBOL 85day AD 1601-01-00-Gregorian
MicrosoftWindows File Time100 ns AD 1601-01-01 ?00:00 GMTGregorian
MicrosoftAD Integer8100 ns AD 1601-01-01 ?00:00 GMTGregorian
ANSI ?MUMPS $Horolog [3]day AD 1841-01-0000:00Gregorian
?Modified Julian Dateday AD 1858-11-1700:00 GMTGregorian
?Chronological MJDday AD 1858-11-1700:00 localGregorian
DECVMS100 ns AD 1858-11-1700:00 GMTGregorian
Lotus123, Excel, etc.day AD 1899-12-3000:00 localGregorian
BorlandDelphi 2+ TDateTimeday AD 1899-12-3000:00 localGregorian
ICLGeorge 3day AD 1899-12-31-Gregorian
IBMMVS CICS DB2day AD 1899-12-31-Gregorian
IAU [4]Dublin Julian Dateday AD 1900-01-0012:00 GMT?Gregorian
Net RFCNTPsecond AD 1900-01-0100:00 GMTGregorian
Common LispUniversal Timesecond AD 1900-01-0100:00 GMTGregorian
AppleOld Mac Long Timesecond AD 1904-01-0100:00 GMTGregorian
AppleMac Excelday AD 1904-01-01-Gregorian
?SASsecond AD 1960-01-0100:00Gregorian
PickPickday AD 1967-12-31 ?-Gregorian
IBMC, etc.day AD 1969-12-31-Gregorian
?UNIX, C, Perl, etc.second AD 1970-01-0100:00 GMTGregorian
?Java, JSmillisecond AD 1970-01-0100:00 GMTGregorian
MicrosoftDOSday AD 1980-01-01localGregorian
Apollo (now HP)OS[1] AD 1980-01-01?Gregorian
USAGPSweek [2] AD 1980-01-0600:00 GMTGregorian
Steltor UNIAPI_TIMEminute AD 1991-01-0100:00 GMTGregorian
[0] Chronological Julian Date : historians seem to treat Julian Day Number as starting at 0000h local time on Julian BC 4713-01-01, rather than the proper noon GMT
[1] About quarter-seconds, but true unit must be (220µs)/4 = 262144 µs
[2] No leap-seconds; always 86400 SI secs/day
[3] ISO 11756, InterSystems Caché Objectscript.
[4] Dublin 1955
[*] Units : ns = nanoseconds ; µs = microseconds
Astronomers' GMT used a 12-hour offset from legal GMT before 1925

The above are all, more or less, counts of units, although some are often subdivided.

Outlines of astronomy (4th edition) by Sir John F. W. Herschel, 1851, p.635, has further ancient dates.

See also in Wikipedia.

Timescale Interconverter

From above, it is possible to drag'n'drop Zero Date & Time together into the Date 1 field. In the calculation, Summer Time is inapplicable and Leap Seconds are ignored; rounding errors were possible.

Enter Gregorian Dates in any form acceptable to JavaScript after converting - to / ;
Interval accepts spaces and expressions, and 0x### Hex.
    Date 1
    Date 2  
    Interval
Interval shown as : Dec Hex Sci
Time unit : 100 ns 1 µs 1 ms 1 s   minute hour day week

Parallel Dates

The dates below are selected solely for their numerical significance.

The standard Julian Date, JD, changes at noon GMT. Modified Julian Date, MJD, is JD-2400000.5, and changes at midnight GMT.

Below, days are to be assumed as GMT 0000h - 2400h unless otherwise indicated. They can be taken to move round the world as daylight does; see Time Zone and Summer Time. Thus some MJD entries below are strictly CMJD.

Some Dates of Some Days
  * Hebrew days start at the 6 p.m. or sunset previous to the MJD and Julian/Gregorian dates given here.
  ~ Islamic Religious days start at sunset.
Dating Creation - Wikipedia
MJDDoWGregorianJulianEvent
-2400001MonBC 4714-11-24BC 4713-01-01Julian Date Zero (from noon GMT)
-2052005SatBC 3761-09-05BC 3761-10-05* Hebrew, Day 0
-2052003MonBC 3761-09-07BC 3761-10-07* Hebrew, 1 Tishri, Year A.M. 1 starts
??BC 3760-08-??BC 3760-09-??* Hebrew, Start of Creation,
-2051649FriBC 3760-08-27BC 3760-09-26* Hebrew, Creation of Adam, 8am (local?); A.M. 1 ends
-678578FriBC 0001-12-29BC 0001-12-31BC Julian ends
-678577SatBC 0001-12-30AD 0001-01-01AD Julian begins
-678576SunBC 0001-12-31AD 0001-01-02BC Gregorian ends
-678575MonAD 0001-01-01AD 0001-01-03AD Gregorian begins
-605833SatAD 0200-03-01AD 0200-03-01Gregorian and Julian agreement, first day
-569310WedAD 0300-02-28AD 0300-02-28Gregorian and Julian agreement, last day
-451561FriAD 0622-07-19AD 0622-07-16~ Moslem, MuHarram 1, 1 A.H. starts
-100841Thu                         AD 1582-10-04Rome: Julian ends
-100841ThuAD 1582-10-14                         Lilian Date Zero
-100840FriAD 1582-10-15 Rome: Gregorian begins
-38780Wed AD 1752-09-02Britain: Julian ends
-38779ThuAD 1752-09-14 Britain: Gregorian begins
0WedAD 1858-11-17AD 1858-11-05Modified Julian Date Zero
+15018SatAD 1899-12-30.Civil: Delphi 2+
+15018SatAD 1899-12-30.Civil: PC Excel
+15019SunAD 1899-12-31.Civil?: George 3
+16840FriAD 1904-01-01.Civil: Mac Excel
+44239TueAD 1980-01-01.Civil: MS-DOS internal Day 0
+50000TueAD 1995-10-10AD 1995-09-27Civil: Certain Birthdays
.Civil: Today
7×NWed  Each Wednesday
10227×NWed AD xxxx-11-05Year (28×N+1858)
146097×NWedAD xx58-11-17 Year (400×N+1858)
 TueAD xx00-02-29 4/100/400 year rules

BC dates are standard notation, for which BC 1 is followed by AD 1. Astronomers should subtract 1 from BC years, and replace "BC " with "-". Italic entries are subsidiary.

Gregorian / Julian Date Difference

The tabulated differences change when a date wrongly occurs or is omitted in the "other" calendar. The safe algorithm for converting between Gregorian and Julian dates is by way of the daycount from some day in a year when the calendars were in agreement, AD 201-299.

Gregorian - Julian Date Difference in Days
 B.C.A.D.
Years
from/to
...500300200100  101201301501601701 901
...302202102  99199299499599699899 999
Days...-5-4-3 -2 -1012345
 A.D.
Years
from/to
10011101130114011501 1701180119012101220123012501...
10991299139914991699 1799189920992199229924992599...
Days6 7891011121314 151617...

In intermediate years (the non-Leap century-ending ones), look left for Jan and Feb and right for Mar to Dec.

Note that the difference was 10 days in 1582, when the Gregorian Calendar was first introduced; it was 11 days in 1752, when Britain made the change; and 13 days in 1918, when Russia changed to the Fregorian Calendar.

For the 99 years after the year AD N×100, the difference D is given by something including N - N Div 4. Note that 0 is not special for this Div function. The code using |0 will err when N+85 is negative.

See also in JavaScript Date and Time 8 : Enhancing the Object, which now includes a form for Julian/Gregorian Calendar Date Conversion, including CMJD and covering over ±275000 years.

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