Welcome to Fourmilab's calendar converter!This page allows you to interconvert dates in a variety ofcalendars, both civil and computer-related. Allcalculations are done in JavaScript executed in your ownbrowser; complete source code is embedded in or linked tothis page, and you're free to downloadthese files to your owncomputer and use them even when not connected to theInternet. To use the page, your browser must supportJavaScript and you must not have disabled execution of thatlanguage. Let's see…
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If the box above says “Your browser supports JavaScript”, you're in business;simply enter a date in any of the boxes below and press the “Calculate”button to show that date in all of the other calendars.Gregorian Calendar
The Gregorian calendar wasproclaimedby Pope Gregory XIII and tookeffect in most Catholic states in 1582, in which October 4, 1582 ofthe Julian calendar was followed by October 15 in the new calendar,correcting for the accumulated discrepancy between the Julian calendarand the equinox as of that date. When comparing historical dates,it's important to note that the Gregorian calendar, used universallytoday in Western countries and in international commerce, wasadopted at different times by different countries. Britain and her colonies (including what is now the United States), did not switchto the Gregorian calendar until 1752, when Wednesday 2nd Septemberin the Julian calendar dawned as Thursday the 14th in the Gregorian.
The Gregorian calendar is a minor correction to the Julian. In theJulian calendar every fourth year is a leap year in which February has29, not 28 days, but in the Gregorian, years divisible by 100 arenot leap years unless they are also divisible by 400. Howprescient was Pope Gregory! Whatever the problems of Y2K, they won'tinclude sloppy programming which assumes every year divisible by 4 isa leap year since 2000, unlike the previous and subsequent yearsdivisible by 100, is a leap year. As in the Julian calendar,days are considered to begin at midnight.
The average length of a year in the Gregorian calendar is 365.2425days compared to the actual solar tropical year (time from equinox toequinox) of 365.24219878 days, so the calendar accumulates one day oferror with respect to the solar year about every 3300 years. As a purelysolar calendar, no attempt is made to synchronise the start of monthsto the phases of the Moon.
While one can't properly speak of “Gregorian dates” prior tothe adoption of the calendar in 1582, the calendar can beextrapolated to prior dates. In doing so, thisimplementation uses the convention that the year prior toyear 1 is year 0. This differs from the Julian calendar inwhich there is no year 0—the year before year 1 in the Juliancalendar is year −1. The date December 30th, 0 in the Gregoriancalendar corresponds to January 1st, 1 in the Julian calendar.
A slight modification of the Gregorian calendar would make it even moreprecise. If you add the additional rule that years evenly divisibleby 4000 are not leap years, you obtain an average solar yearof 365.24225 days per year which, compared to the actual mean yearof 365.24219878, is equivalent to an error of one day over a periodof about 19,500 years; this is comparable to errors due to tidalbraking of the rotation of the Earth.
Julian Day
Astronomers, unlike historians, frequently need to do arithmeticwith dates. For example: a double star goes into eclipse every1583.6 days and its last mid-eclipse was measured to be onOctober 17, 2003 at 21:17 UTC. When is the next? Well, you couldget out your calendar and count days, but it's far easierto convert all the quantities in question to Julian day numbersand simply add or subtract. Julian days simply enumerate the daysand fraction which have elapsed since the start of theJulian era, which is defined as beginning at noonon Monday, 1st January of year 4713 B.C.E. in the Juliancalendar. This date is defined in terms of a cycle of years,but has the additional advantage that all known historical astronomicalobservations bear positive Julian day numbers, and periods canbe determined and events extrapolated by simple addition andsubtraction. Julian dates are a tad eccentric in starting atnoon, but then so are astronomers (and systems programmers!)—whenyou've become accustomed to rising after the “crack of noon” anddoing most of your work when the Sun is down, you appreciaterecording your results in a calendar where the date doesn't changein the middle of your workday. But even the Julian day convention bears witness to the eurocentrism of 19th century astronomy—noonat Greenwich is midnight on the other side of the world. But the Julianday notation is so deeply embedded in astronomy that it is unlikelyto be displaced at any time in the foreseeable future. It is an idealsystem for storing dates in computer programs, free of cultural biasand discontinuities at various dates, and can be readily transformedinto other calendar systems, as the source code for this page illustrates.Use Julian days and fractions (stored in 64 bit or longer floatingpoint numbers) in your programs, and be ready for Y10K, Y100K,and Y1MM!
While any event in recorded human history can be written asa positive Julian day number, when working with contemporaryevents all those digits can be cumbersome. A ModifiedJulian Day (MJD) is created by subtracting 2400000.5from a Julian day number, and thus represents the number ofdays elapsed since midnight (00:00) Universal Time onNovember 17, 1858. Modified Julian Days are widely used tospecify the epoch in tables of orbital elements ofartificial Earth satellites. Since no such objects existedprior to October 4, 1957, all satellite-related MJDs arepositive.
Julian Calendar
The Julian calendar was proclaimed by Julius Cæsar in 46 B.C.and underwent several modifications before reaching its finalform in 8 C.E. The Julian calendar differs from the Gregorianonly in the determination of leap years, lacking the correctionfor years divisible by 100 and 400 in the Gregorian calendar.In the Julian calendar, any positive year is a leap year ifdivisible by 4. (Negative years are leap years if the absolute valuedivided by 4 yields a remainder of 1.) Days are considered tobegin at midnight.
In the Julian calendar the average year has a length of 365.25 days.compared to the actual solar tropical yearof 365.24219878 days. The calendar thus accumulates one day oferror with respect to the solar year every 128 years.Being a purely solar calendar, no attempt is made to synchronise thestart of months to the phases of the Moon.
Hebrew Calendar
The Hebrew (or Jewish) calendar attempts to simultaneouslymaintain alignment between the months and the seasons andsynchronise months with the Moon—it is thus deemed a“luni-solar calendar”. In addition, there are constraintson which days of the week on which a year can begin and to shiftotherwise required extra days to prior years to keep thelength of the year within the prescribed bounds.This isn't easy, and thecomputations required are correspondingly intricate.
Years are classified as common (normal) orembolismic (leap) years which occur in a 19 yearcycle in years 3, 6, 8, 11, 14, 17, and 19. In anembolismic (leap) year, an extra month of 29 days,“Veadar” or “Adar II”, is added to the end of the year afterthe month “Adar”, which is designated “Adar I” in suchyears. Further, years may be deficient,regular, or complete, having respectively353, 354, or 355 days in a common year and 383, 384, or 385days in embolismic years. Days are defined as beginning atsunset, and the calendar begins at sunset the night beforeMonday, October 7, 3761 B.C.E. in the Julian calendar, orJulian day 347995.5. Days are numbered with Sunday as day 1,through Saturday: day 7.
The average length of a month is 29.530594 days, extremely closeto the mean synodic month (time from new Moon tonext new Moon) of 29.530588 days. Such is the accuracy thatmore than 13,800 years elapse before a single daydiscrepancy between the calendar's average reckoning of thestart of months and the mean time of the new Moon.Alignment with the solar year is better than the Juliancalendar, but inferior to the Gregorian. The average lengthof a year is 365.2468 days compared to the actual solar tropicalyear (time from equinox to equinox) of 365.24219 days, sothe calendar accumulates one day of error with respect tothe solar year every 216 years.
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Islamic Calendar
The Islamic calendar is purely lunar and consists of twelvealternating months of 30 and 29 days, with the final 29 day monthextended to 30 days during leap years. Leap years follow a 30 yearcycle and occur in years 1, 5, 7, 10, 13, 16, 18, 21, 24, 26, and 29.Days are considered to begin at sunset. The calendar begins onFriday, July 16th, 622 C.E. in the Julian calendar, Julian day1948439.5, the day of Muhammad's flight from Mecca to Medina, withsunset on the preceding day reckoned as the first day of the firstmonth of year 1 A.H.—“AnnoHegiræ”—the Arabic word for“separate” or “go away”. The names for thedays are just their numbers: Sunday is the first day and Saturday theseventh; the week is considered to begin on Saturday.
Each cycle of 30 years thus contains 19 normal years of 354days and 11 leap years of 355, so the average length of ayear is therefore ((19 × 354) + (11 × 355)) / 30 =354.365… days, with a mean length of month of 1/12 thisfigure, or 29.53055… days, which closely approximates themean synodic month (time from new Moon to next newMoon) of 29.530588 days, with the calendar only slipping oneday with respect to the Moon every 2525 years. Since the calendaris fixed to the Moon, not the solar year, the months shiftwith respect to the seasons, with each month beginning about11 days earlier in each successive solar year.
The calendar presented here is the most commonly usedcivil calendar in the Islamic world; for religious purposesmonths are defined to start with the first observation ofthe crescent of the new Moon.
Persian Calendar
The modern Persian calendar was adopted in 1925, supplanting(while retaining the month names of) a traditionalcalendar dating from the eleventh century. The calendarconsists of 12 months, the first six of which are 31days, the next five 30 days, and the final month 29days in a normal year and 30 days in a leap year.
Each year begins on the day in which the March equinox occurs at orafter solar noon at the reference longitude for Iran Standard Time(52°30' E). Days begin at midnight in the standard timezone. There is no leap year rule; 366 day years do not recur in aregular pattern but instead occur whenever that number of days elapsebetween equinoxes at the reference meridian. The calendar thereforestays perfectly aligned with the seasons. No attempt is made tosynchronise months with the phases of the Moon.
There is some controversy about the reference meridian at which theequinox is determined in this calendar. Various sources citeTehran, Esfahan, and the central meridian of Iran Standard Time asthat where the equinox is determined; in this implementation, theIran Standard Time longitude is used, as it appears that this isthe criterion used in Iran today. As this calendar is proleptic for allyears prior to 1925 C.E., historicalconsiderations regarding the capitals of Persia and Iran do notseem to apply.
Persian Algorithmic Calendar
Ahmad Birashk proposed an alternative means of determining leap yearsfor the Persian calendar. His technique avoids the need to determinethe moment of the astronomical equinox, replacing it with a verycomplex leap year structure. Years are grouped into cycleswhich begin with four normal years after which every fourth subsequentyear in the cycle is a leap year. Cycles are grouped into grandcycles of either 128 years (composed of cycles of 29, 33, 33, and33 years) or 132 years, containing cycles of of 29, 33, 33, and 37years. A great grand cycle is composed of 21 consecutive 128year grand cycles and a final 132 grand cycle, for a total of 2820years. The pattern of normal and leap years which began in 1925 willnot repeat until the year 4745!
This is not the calendar in use in Iran! It ispresented here solely because there are many computer implementationsof the Persian calendar which use it (with which users may wish tocompare results), and because its baroque complexity enthrallsprogrammers like myself.
Each 2820 year great grand cycle contains 2137 normalyears of 365 days and 683 leap years of 366 days,with the average year length over the great grand cycleof 365.24219852. So close is this to the actualsolar tropical year of 365.24219878 days thatthis calendar accumulates an error of one dayonly every 3.8 million years. As a purely solarcalendar, months are not synchronised with thephases of the Moon.
Mayan Calendars
The Mayans employed three calendars, all organised as hierarchiesof cycles of days of various lengths. The Long Count wasthe principal calendar for historical purposes, the Haabwas used as the civil calendar, while the Tzolkinwas the religious calendar. All of the Mayan calendarsare based on serial counting of days without means for synchronisingthe calendar to the Sun or Moon, although the Long Count and Haabcalendars contain cycles of 360 and 365 days, respectively, whichare roughly comparable to the solar year. Based purely on countingdays, the Long Count more closely resembles theJulian Day system and contemporary computer representations ofdate and time than other calendars devised in antiquity.Also distinctly modern in appearance is that days andcycles count from zero, not one as in most other calendars,which simplifies the computation of dates, and that numbersas opposed to names were used for all of the cycles.
| Cycle | Composed of | Total Days | Years (approx.) |
|---|---|---|---|
| kin | 1 | ||
| uinal | 20 kin | 20 | |
| tun | 18 uinal | 360 | 0.986 |
| katun | 20 tun | 7200 | 19.7 |
| baktun | 20 katun | 144,000 | 394.3 |
| pictun | 20 baktun | 2,880,000 | 7,885 |
| calabtun | 20 piktun | 57,600,000 | 157,704 |
| kinchiltun | 20 calabtun | 1,152,000,000 | 3,154,071 |
| alautun | 20 kinchiltun | 23,040,000,000 | 63,081,429 |
The Long Count calendar is organised into thehierarchy of cycles shown at the right.Each of the cycles is composed of 20 of the nextshorter cycle with the exception of the tun,which consists of 18 uinal of 20 days each.This results in a tun of 360 days, which maintainsapproximate alignment with the solar year over modestintervals—the calendar comes undone from theSun 5 days every tun.
The Mayans believed at at the conclusion of eachpictun cycle of about 7,885 years the universe isdestroyed and re-created. Those with apocalypticinclinations will be relieved to observe that the presentcycle will not end until Columbus Day, October 12, 4772 inthe Gregorian calendar. Speaking of apocalyptic events,it's amusing to observe that the longest of the cycles inthe Mayan calendar, alautun, about 63 millionyears, is comparable to the 65 million years since theimpact which brought down the curtain on the dinosaurs—animpact which occurred near the Yucatan peninsula where,almost an alautun later, the Mayan civilisationflourished. If the universe is going to be destroyed andthe end of the current pictun, there's no point inwriting dates using the longer cycles, so we dispensewith them here.
Dates in the Long Count calendar are written, by convention,as:
baktun.katun.tun.uinal.kin
and thus resemble present-day Internet IP addresses!
For civil purposes the Mayans used the Haabcalendar in which the year was divided into 18 named periodsof 20 days each, followed by five Uayeb daysnot considered part of any period. Dates in thiscalendar are written as a day number (0 to 19 for regularperiods and 0 to 4 for the days of Uayeb) followedby the name of the period. This calendar has no concept ofyear numbers; it simply repeats at the end of the complete365 day cycle. Consequently, it is not possible, given adate in the Haab calendar, to determine the LongCount or year in other calendars. The 365 day cycleprovides better alignment with the solar year than the 360day tun of the Long Count but, lacking a leap yearmechanism, the Haab calendar shifted one day withrespect to the seasons about every four years.
The Mayan religion employed the Tzolkin calendar,composed of 20 named periods of 13 days. Unlike theHaab calendar, in which the day numbers incrementuntil the end of the period, at which time the next periodname is used and the day count reset to 0, the names and numbersin the Tzolkin calendar advance in parallel. On eachsuccessive day, the day number is incremented by 1, beingreset to 0 upon reaching 13, and the next in the cycle of twentynames is affixed to it. Since 13 does not evenly divide 20,there are thus a total of 260 day number and period names beforethe calendar repeats. As with the Haab calendar, cyclesare not counted and one cannot, therefore, convert a Tzolkindate into a unique date in other calendars. The 260 day cycleformed the basis for Mayan religious events and has no relationto the solar year or lunar month.
The Mayans frequently specified dates using both the Haaband Tzolkin calendars; dates of this form repeat onlyevery 52 solar years.
Indian Civil Calendar
A bewildering variety of calendars have been and continue to beused in the Indian subcontinent. In 1957 the Indiangovernment's Calendar Reform Committee adopted the NationalCalendar of India for civil purposes and, in addition,defined guidelines to standardise computation of thereligious calendar, which is based on astronomicalobservations. The civil calendar is used throughout Indiatoday for administrative purposes, but a variety ofreligious calendars remain in use. We present the civilcalendar here.
The National Calendar of India is composed of 12 months.The first month, Caitra, is 30 days in normaland 31 days in leap years. This is followed by fiveconsecutive 31 day months, then six 30 day months. Leapyears in the Indian calendar occur in the same years asas in the Gregorian calendar; the two calendars thushave identical accuracy and remain synchronised.
Years in the Indian calendar are counted from the start ofthe Saka Era, the equinox of March 22nd of year 79 in theGregorian calendar, designated day 1 of monthCaitra of year 1 in the Saka Era. The calendar wasofficially adopted on 1 Caitra, 1879 Saka Era, orMarch 22nd, 1957 Gregorian. Since year 1 of the Indiancalendar differs from year 1 of the Gregorian, todetermine whether a year in the Indian calendar is a leapyear, add 78 to the year of the Saka era thenapply the Gregorian calendar rule to the sum.
French Republican Calendar
The French Republican calendar was adopted by adecree of LaConvention Nationale on Gregorian date October 5, 1793and went into effect the following November 24th, on whichday Fabre d'Églantine proposed to the Conventionthe names for the months. It incarnates the revolutionaryspirit of “Out with the old! In with the relentlesslyrational!” which later gave rise in 1795 to the metricsystem of weights and measures which has proven more durablethan the Republican calendar.
The calendar consists of 12 months of 30 days each, followedby a five- or six-day holiday period, thejours complémentaires orsans-culottides. Months are grouped into fourseasons; the three months of each season end with the sameletters and rhyme with one another. The calendar begins onGregorian date September 22nd, 1792, the Septemberequinox and date of the founding of the First Republic.This day is designated the first day of the month ofVendémiaire in year 1 of the Republic. Subsequent yearsbegin on the day in which the September equinox occurs asreckoned at the Paris meridian. Days begin at true solarmidnight. Whether the sans-culottides periodcontains five or six days depends on the actualdate of the equinox. Consequently, there is no leap year ruleper se: 366 day years do not recur in a regularpattern but instead follow the dictates of astronomy. Thecalendar therefore stays perfectly aligned with the seasons.No attempt is made to synchronise months with the phases ofthe Moon.
The Republican calendar is rare in that it has noconcept of a seven day week. Each thirty day monthis divided into three décades of ten dayseach, the last of which, décadi, was theday of rest. (The word “décade” mayconfuse English speakers; theFrench noun denoting ten years is “décennie”.)The names of days in the décade are derived fromtheir number in the ten day sequence. The five orsix days of the sans-culottides do not bearthe names of the décade. Instead, each of these holidayscommemorates an aspect of the republican spirit.The last, jour de la Révolution, occurs onlyin years of 366 days.
Napoléon abolished the Republican calendar in favourof the Gregorian on January 1st, 1806. Thus France, oneof the first countries to adopt the Gregorian calendar(in December 1582), became the only country to subsequentlyabandon and then re-adopt it. During the period of theParis Commune uprising in 1871 the Republican calendarwas again briefly used.
The original decreewhich established the Republican calendar contained acontradiction: it defined the year as starting on the dayof the true autumnal equinox in Paris, but further prescribeda four year cycle called la Franciade, the fourthyear of which would end with le jour de la Révolutionand hence contain 366 days. These two specifications areincompatible, as 366 day years defined by the equinox donot recur on a regular four year schedule. This problem wasrecognised shortly after the calendar was proclaimed, but thecalendar was abandoned five years before the first conflictwould have occurred and the issue was never formally resolved. Herewe assume the equinox rule prevails, as a rigid four yearcycle would be no more accurate than the Julian calendar, whichcouldn't possibly be the intent of its enlightened Republicandesigners.
ISO-8601 Week and Day, and Day of Year
TheInternational Standards Organisation(ISO) issuedStandard ISO 8601, “Representation of Dates” in 1988,superseding the earlier ISO 2015. The bulk of the standardconsists of standards for representing dates in theGregorian calendar including the highly recommended“YYYY-MM-DD” form which is unambiguous, free of culturalbias, can be sorted into order without rearrangement, and isY9K compliant. In addition, ISO 8601 formally defines the“calendar week” often encountered in commercial transactionsin Europe. The first calendar week of a year: week 1, isthat week which contains the first Thursday of the year (or,equivalently, the week which includes January 4th of theyear; the first day of that week is the previous Monday).The last week: week 52 or 53 depending on thedate of Monday in the first week, is that which containsDecember 28th of the year. The first ISO calendar week of agiven year starts with a Monday which can be as early asDecember 29th of the previous year or as late as January4th of the present; the last calendar week can end as lateas Sunday, January 3rd of the subsequent year.ISO 8601 dates in year, week, and day form are writtenwith a “W” preceding the week number, which bears a leadingzero if less than 10, for example February 29th, 2000is written as 2000-02-29 in year, month, day format and2000-W09-2 in year, week, day form; since the day numbercan never exceed 7, only a single digit is required.The hyphens may be elided for brevity and the day numberomitted if not required. You will frequently see date ofmanufacture codes such as “00W09” stamped on products; thisis an abbreviation of 2000-W09, the ninth week of year 2000.
In solar calendars such as the Gregorian, only days andyears have physical significance: days are defined by therotation of the Earth, and years by its orbit about the Sun.Months, decoupled from the phases of the Moon, are but amemory of forgotten lunar calendars, while weeks of seven daysare entirely a social construct—while most calendars in usetoday adopt a cycle of seven day names or numbers, calendarswith name cycles ranging from four to sixty days have beenused by other cultures in history.
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ISO 8601 permits us to jettison the historical and culturalbaggage of weeks and months and express a date simply bythe year and day number within that year, ranging from 001for January 1st through 365 (366 in a leap year) forDecember 31st. This format makes it easy to do arithmeticwith dates within a year, and only slightly more complicatedfor periods which span year boundaries. You'llsee this representation used in project planning and for specifying deliverydates. ISO dates in this form are written as “YYYY-DDD”,for example 2000-060 for February 29th, 2000; leading zeroesare always written in the day number, but the hyphen may beomitted for brevity.
All ISO 8601 date formats have the advantages of beingfixed length (at least until the Y10K crisis rolls around) and, whenstored in a computer, of being sorted in date orderby an alphanumeric sort of their textual representations.The ISO week and day and day of year calendars arederivative of the Gregorian calendar and share its accuracy.
Unix time() value
Development of the Unix operating system began at Bell Laboratoriesin 1969 by Dennis Ritchie and Ken Thompson, with the firstPDP-11 version becoming operational in February 1971. Unix wiselyadopted the convention that all internal dates and times (for example,the time of creation and last modification of files) were kept inUniversal Time, and converted to local time based on a per-usertime zone specification. This far-sighted choice has made itvastly easier to integrate Unix systems into far-flung networkswithout a chaos of conflicting time settings.
Many machines on which Unix was initially widely deployedcould not support arithmetic on integers longer than 32 bitswithout costly multiple-precision computation in software.The internal representation of time was therefore chosen to bethe number of seconds elapsed since00:00 Universal time on January 1, 1970 in the Gregoriancalendar (Julian day 2440587.5), with time stored as a 32bit signed integer (long in early C implementations).
The influence of Unix time representation has spread well beyondUnix since most C and C++ libraries on other systems provideUnix-compatible time and date functions. The major drawback ofUnix time representation is that, if kept as a 32 bit signedquantity, on January 19, 2038 it will go negative, resulting inchaos in programs unprepared for this. Unix and Cimplementations wisely (for reasons described below) define theresult of the time() function as type time_t,which leaves the door open for remediation (by changing thedefinition to a 64 bit integer, for example) before the clockticks the dreaded doomsday second.
C compilers on Unix systems prior to 7th Edition lacked the32-bit long type. On earlier systems time_t,the value returned by the time() function, was an arrayof two 16-bit ints which, concatenated, represented the32-bit value. This is the reason why time() accepts apointer argument to the result (prior to 7th Edition it returneda status, not the 32-bit time) and ctime() requires apointer to its input argument. Thanks to Eric Allman (authorof sendmail) forpointing out these historical nuggets.
Excel Serial Day Number
Spreadsheet calculations frequently need to do arithmetic with dateand time quantities—for example, calculating the interest on a loanwith a given term. When Microsoft Excel was introduced for the PCWindows platform, it defined dates and times as “serial values”, whichexpress dates and times as the number of days elapsed since midnighton January 1, 1900 with time given as a fraction of a day. Midnighton January 1, 1900 is day 1.0 in this scheme. Time zone isunspecified in Excel dates, with the NOW() function returningwhatever the computer's clock is set to—in most cases local time, sowhen combining data from machines in different time zones you usuallyneed to add or subtract the bias, which can differ over the year dueto observance of summer time. Here we assume Excel dates representUniversal (Greenwich Mean) time, since there isn't any other rationalchoice. But don't assume you can always get away with this.
You'd be entitled to think, therefore, that conversion back andforth between PC Excel serial values and Julian day numbers wouldsimply be a matter of adding or subtracting the Julian day numberof December 31, 1899 (since the PC Excel days are numbered from 1).But this is a Microsoft calendar, remember, so one mustfirst look to make sure it doesn't contain one of those boneheadblunders characteristic of Microsoft. As is usually the case,one doesn't have to look very far. If you have a copy of PCExcel, fire it up, format a cell as containing a date, andtype 60 into it: out pops “February 29, 1900”. News apparentlytravels very slowly from Rome to Redmond—ever sincePope Gregory revised the calendarin 1582, years divisibleby 100 have not been leap years, and consequently theyear 1900 contained no February 29th. Due to this morsel ofinformation having been lost somewhere between the Holy See andthe Infernal Seattle monopoly,all Excel day numbers for days subsequent to February 28th, 1900are one day greater than the actual day count from January 1, 1900.Further, note that any computation of the number of days ina period which begins in January or February 1900 and ends in asubsequent month will be off by one—the day count will be onegreater than the actual number of days elapsed.
By the time the 1900 blunder was discovered, Excel users hadcreated millions of spreadsheets containing incorrectday numbers, so Microsoft decided to leave the error in placerather than force users to convert their spreadsheets, and theerror remains to this day. Note, however, that only 1900is affected; while the first release of Excel probably alsoscrewed up all years divisible by 100 and hence implemented apurely Julian calendar, contemporary versions do correctlycount days in 2000 (which is a leap year, being divisible by400), 2100, and subsequent end of century years.
PC Excel day numbers are valid only between 1 (January 1, 1900) and2958465 (December 31, 9999). Although a serial day counting schemehas no difficulty coping with arbitrary date ranges or days beforethe start of the epoch (given sufficient precision in the representationof numbers), Excel doesn't do so. Day 0 is deemed the idioticJanuary 0, 1900 (at least in Excel 97), and negative days andthose in Y10K and beyond are not handled at all. Further, oldversions of Excel did date arithmetic using 16 bit quantitiesand did not support day numbers greater than 65380 (December31, 2078); I do not know in which release of Excel this limitation was remedied.
Having saddled every PC Excel user with a defective datenumbering scheme wasn't enough for Microsoft—nothing ever is.Next, they proceeded to come out with a Macintosh versionof Excel which uses an entirely different day numberingsystem based on the MacOS native time format which countsdays elapsed since January 1, 1904. To further obfuscatematters, on the Macintosh they chose to number days from zerorather than 1, so midnight on January 1, 1904 has serialvalue 0.0. By starting in 1904, they avoided screwing up 1900as they did on the PC. So now Excel users who interchange datahave to cope with two incompatible schemes for counting days, oneof which thinks 1900 was a leap year and the other whichdoesn't go back that far. To compound the fun, you can nowselect either date system on either platform, so you can't becertain dates are compatible even when receiving data fromanother user with same kind of machine you're using. I'msure this was all done in the interest of the “efficiency”of which Microsoft is so fond. As we all know, it would take a computeralmost forever to add or subtract four in order to make everythingseamlessly interchangeable.
Macintosh Excel day numbers are valid only between 0(January 1, 1904) and 2957003 (December 31, 9999). Althougha serial day counting scheme has no difficulty coping witharbitrary date ranges or days before the start of the epoch(given sufficient precision in the representation ofnumbers), Excel doesn't do so. Negative days and those inY10K and beyond are not handled at all. Further, oldversions of Excel did date arithmetic using 16 bitquantities and did not support day numbers greater than63918 (December 31, 2078); I do not know in which release ofExcel this limitation was remedied.
References
| Click on titles to order books on-line from |
- Meeus, Jean.Astronomical Algorithms 2nd ed.Richmond: Willmann-Bell, 1998.ISBN 0943396-61-1.
- The essential reference for computational positionalastronomy.
- P. Kenneth Seidelmann (ed.)Explanatory Supplement to the Astronomical Almanac .Sausalito CA: University Science Books,[1992] 2005. ISBN 1-891389-45-9.
- Authoritative reference on a wealth of topics related to computational geodesy and astronomy. Various calendars are described in depth, including techniques for interconversion.
- The Institut de mécanique céleste et de calcul des éphémérides in Paris provides excellent on-line descriptions of a variety of calendars.
by John Walker
September, MMXV