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AAT ICAS 2041 ✧ NC calculation factors

document note: this document is part of the Integrated Chronological Applications System (ICAS). Alliance for the Advancement of Technology (AAT) provides ICAS standards documents subject to terms of use described in document AAT ICAS 9010. please refer to other key AAT ICAS standards documents accessible via the AAT ICAS web site at for important information about ICAS.

this document describes AAT ICAS calculation factors for the New Calendar system. please refer to AAT ICAS 2040 for additional important information about calculation factor guidelines.


New Calendar calculation factors

a number of general and specific methods for formatting and factoring dates and times are described in a variety of other resources including operating system documentation, application documentation, UNIX manual pages, APIs for Java and other languages, ISO 8601, and so forth.

developers and users should consider any scale factors among the New Calendar scale, the New Calendar Day Notation scale, and other scales of years and days. the use of a particular method of calculation or factoring may involve the following considerations: the particular scale that a time, day, or year is derived from; the relationships among particular scale factors; the particular fixed or coordinated implementation of a particular scale to dates in the far past or far future; and whether the designation or observance of a particular date is based on a particular scale.

to calculate a New Calendar Day Notation date from a UCN date for years in a positive scale:

UCN 12000A01 at IDC t500 deka(0) corresponds to NDN 4382911.5 and to JD 2451545 and provides a calculation factor of 1 931 366.5 days between the NDN and JD scales.

Macintosh computer serial dating day 0 at UCN 11904A01 corresponds to NDN 4347847 and to AD 1904 January 01, and provides a calculation factor of 4 347 847 days between the NDN and Macintosh serial dating scales (based on UT time for both scales).

Windows computer serial dating day 1 at UCN 11900A01 corresponds to NDN 4346387 and to AD 1900 January 01, and provides a calculation factor of 4 346 386 days between the NDN and Windows serial dating scales (based on UT time for both scales).


table 2041.1 ✧ some New Calendar formula resources

resource formula
resource formula
for any NC-era year yNC, for any Gregorian-era year yG (AD 1582 or later per Gregorian calendar), for any Julian* BC-era year yBC (*subject to yBC conformance with New Calendar year), for any Julian Day day JD, for any New Calendar Day Notation day NDN, for any Macintosh computer serial date dateMac (based on UT for all scales), for any Windows computer serial date dateWin (based on UT for all scales):
4 and 100 year ruleIF (yNC/4) = INTEGER(yNC/4) AND IF (yNC/100) does NOT EQUAL integer of (yNC/100), THEN yNC is a leap year.
400 year ruleIF (yNC/400) = INTEGER(yNC/400), THEN year is a leap year.
year zero ruleIF yNC = zero, THEN yNC is a leap year.
leap year ruleIF either the 4 and 100 year rule, the 400 year rule, OR the year zero rules is TRUE, THEN a yNC is a leap year.
G to NC calculationyNC = yG + 10 000.
G to NC correspondenceNC 12000 corresponds to AD 2000.
UCA to NC calculationyNC = yUCA + 10 000.
NC to UCA calculationyUCA = yNC - 10 000.
NC to BC calculationyNC = 10 001 - yBC.
BC to NC calculationyBC = 10 001 -yNC.
JD to NDN calculationNDN = JD + 1 931 366.5.
MJD to NDN calculationNDN = MJD + 4331367.
NDN to JD calculationJD = NDN - 1 931 366.5.
NDN to MJD calculationMJD = NDN - 4331367.
dateMac to NDN calculationNDN = dateMac + 4 347 847.
dateWin to NDN calculationNDN = dateWin + 4 346 386.
special note: ensure that numerical expressions are represented to an appropriate number of places, even if the beginning places are leading zeroes.


table 2041.2 ✧ New Calendar Day Notation day factors

UCN date NDN date
UCN date NDN date
UCN 00000A01NDN 001
UCN 00000M36NDN 366
UCN 00001N01NDN 367
UCN 00001Z35NDN 731
UCN 00002A01NDN 732
UCN 00002M35NDN 1096
UCN 00003N01NDN 1097
UCN 00003Z35NDN 1461
UCN 00004A01NDN 1462
UCN 00004M36NDN 1827
UCN 00005N01NDN 1828
UCN 00005Z35NDN 2192
UCN 00006N01NDN 2193
UCN 00006Z35NDN 2557
UCN 00007N01NDN 2558
UCN 00007Z35NDN 2922
UCN 00008A01NDN 2923
UCN 00008M36NDN 3288
UCN 00009N01NDN 3289
UCN 00009Z35NDN 3653
UCN 5287Y28 IDC t500 deka(0)NDN 1931366.5 (JD 1 or BC 4713 January 01)
UCN 11582K17NDN 4230526 (Julian calendar date 1582 October 04 Thursday)
UCN 11582K18NDN 4230527 (Gregorian calendar date 1582 October 15 Friday)
UCN 11800M35NDN 4310227
UCN 11858L21NDN 4331367 (t000 is MJD day 0 or JD 2400000.5)
UCN 11900A01NDN 4346387 (day 1 of Windows serial dating)
UCN 11900M35NDN 4346751
UCN 11904A01NDN 4347847 (day 0 of Macintosh serial dating)
UCN 11909Z35NDN 4350038
UCN 11919Z35NDN 4353690
UCN 11929Z35NDN 4357343
UCN 11939Z35NDN 4360995
UCN 11949Z35NDN 4364648
UCN 11959Z35NDN 4368300
UCN 11969Z35NDN 4371953
UCN 11979Z35NDN 4375605
UCN 11989Z35NDN 4379258
UCN 11999Z35NDN 4382910
UCN 12000M36NDN 4383276
UCN 12001Z35NDN 4383641
UCN 12002M35NDN 4384006
UCN 12003Z35NDN 4384371
UCN 12004M36NDN 4384737
UCN 12005Z35NDN 4385102
UCN 12006M35NDN 4385467
UCN 12007Z35NDN 4385832
UCN 12008M36NDN 4386198
UCN 12009Z35NDN 4386563
UCN 12010M35NDN 4386928
UCN 12011Z35NDN 4387293
UCN 12012M36NDN 4387659
UCN 12013Z35NDN 4388024

top document updated:

system identifiersdatetime
Uniform CalendarUCUCN 12019 S19 Yellow
Inter-Dial ClockIDCzone(UT)t339 tt050
'ICAS in use' can accommodate calendar and clock formatting 'for all people, for all time'.
day of yearD-o-YAD common year day139
Gregorian calendarGG2019 May 19 Sunday
seconds, minutes, hoursSMHUT08:08:14
style legend


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