Spy Tools Chronometry - Interactive Date and Calendar Conversion:

This page allows you to convert dates in a variety of civil, astronomical, and computer calendars.

Enter a date in any calendar you wish, Press ">> Update Page Dates", and you can read the date in any other calendar!

Enter a date in any calendar you wish, Press ">> Update Page Dates", and you can read the date in any other calendar!

Gregorian Calendar

The Gregorian calendar was proclaimed by Pope Gregory XIII, and took effect in most Catholic states in 1582, in which October 4, 1582 of the Julian calendar was followed by October 15 in the new calendar. When comparing historical dates, it's important to note that the Gregorian calendar, used universally today in Western countries and in international commerce, was adopted at different times by different countries. Britain and her colonies (including what is now the United States), did not switch to the Gregorian calendar until 1752, when Wednesday 2nd September in the Julian calendar dawned as Thursday the 14th in the Gregorian.

The Gregorian calendar is a minor correction to the Julian. In the
Julian calendar every fourth year is a leap year in which February has
29, not 28 days, but in the Gregorian, years divisible by 100 are
*not* leap years unless they are also divisible by 400.
As in the Julian calendar, days are considered to begin at midnight.

Julian Day

Astronomers frequently need to do arithmetic
with dates. Julian days simply enumerate the days
and fraction which have elapsed since the start of the
Modified Julian Day

While any event in recorded human history can be written as
a positive Julian day number, when working with contemporary
events all those digits can be cumbersome. A Julian Calendar

The Julian calendar was proclaimed by Julius Caesar in 46 B.C.
and underwent several modifications before reaching its final
form in 8 C.E. The Julian calendar differs from the Gregorian
only in the determination of leap years, lacking the correction
for years divisible by 100 and 400 in the Gregorian calendar.
In the Julian calendar, any positive year is a leap year if
divisible by 4. (Negative years are leap years if the absolute value
divided by 4 yields a remainder of 1.) Days are considered to
begin at midnight.
In the Julian calendar the average year has a length of 365.25 days. compared to the actual solar tropical year of 365.24219878 days. The calendar thus accumulates one day of error with respect to the solar year every 128 years. Being a purely solar calendar, no attempt is made to synchronise the start of months to the phases of the Moon.

Hebrew Calendar

The Hebrew (or Jewish) calendar attempts to simultaneously
maintain alignment between the months and the seasons and
synchronise months with the Moon--it is thus deemed a
"*luni-solar calendar*". In addition, there are constraints
on which days of the week on which a year can begin and to shift
otherwise required extra days to prior years to keep the
length of the year within the prescribed bounds.
This isn't easy, and the
computations required are correspondingly intricate.

Years are classified as *common* (normal) or
*embolismic* (leap) years which occur in a 19 year
cycle in years 3, 6, 8, 11, 14, 17, and 19. In an
embolismic (leap) year, an extra *month* of 29 days,
"Veadar" or "Adar II", is added to the end of the year after
the month "Adar", which is designated "Adar I" in such
years. Further, years may be *deficient*,
*regular*, or *complete*, having respectively
353, 354, or 355 days in a common year and 383, 384, or 385
days in embolismic years. Days are defined as beginning at
sunset, and the calendar begins at sunset the night before
Monday, October 7, 3761 B.C.E. in the Julian calendar, or
Julian 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 close
to the mean *synodic month* (time from new Moon to
next new Moon) of 29.530588 days. Such is the accuracy that
more than 13,800 years elapse before a single day
discrepancy between the calendar's average reckoning of the
start of months and the mean time of the new Moon.
Alignment with the solar year is better than the Julian
calendar, but inferior to the Gregorian. The average length
of a year is 365.2468 days compared to the actual solar tropical
year (time from equinox to equinox) of 365.24219 days, so
the calendar accumulates one day of error with respect to
the solar year every 216 years.

Islamic Calendar

The Islamic calendar is purely lunar and consists of twelve alternating
months of 30 and 29 days, with the final 29 day month extended to
30 days during leap years. Leap years follow a 30 year cycle
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
on Friday, July 16th, 622 C.E. in the Julian calendar, Julian
day 1948439.5, the day of Muhammad's flight from Mecca to Medina,
with sunset on the preceding day reckoned as the first day of
the first month of year 1 A.H.--"*Anno Hegiræ*"--the Arabic word
for "separate" or "go away". Weeks begin on Sunday, and the
names for the days are just their numbers: Sunday is the first
day and Saturday the seventh.

Each cycle of 30 years thus contains 19 normal years of 354
days and 11 leap years of 355, so the average length of a
year is therefore ((19 ? 354) + (11 ? 355)) / 30 =
354.365... days, with a mean length of month of 1/12 this
figure, or 29.53055... days, which closely approximates the
mean *synodic month* (time from new Moon to next new
Moon) of 29.530588 days, with the calendar only slipping one
day with respect to the Moon every 2525 years. Since the calendar
is fixed to the Moon, not the solar year, the months shift
with respect to the seasons, with each month beginning about
11 days earlier in each successive solar year.

The calendar presented here is the most commonly used civil calendar in the Islamic world; for religious purposes months are defined to start with the first observation of the crescent of the new Moon.

Persian Calendar

The modern Persian calendar was adopted in 1925, supplanting (while retaining the month names of) a traditional calendar dating from the eleventh century. The calendar consists of 12 months, the first six of which are 31 days, the next five 30 days, and the final month 29 days in a normal year and 30 days in a leap year.

As one of the few calendars designed in the era of accurate
positional astronomy, the Persian calendar uses a very complex
leap year structure which makes it the most accurate solar
calendar in use today. Years are grouped into *cycles*
which begin with four normal years after which every fourth
subsequent year in the cycle is a leap year. Cycles are grouped
into *grand cycles* of either 128 years (composed of
cycles of 29, 33, 33, and 33 years) or 132 years, containing
cycles of of 29, 33, 33, and 37 years. A *great grand
cycle* is composed of 21 consecutive 128 year grand cycles
and a final 132 grand cycle, for a total of 2820 years. The
pattern of normal and leap years which began in 1925 will not
repeat until the year 4745!

Each 2820 year great grand cycle contains 2137 normal years of 365 days and 683 leap years of 366 days, with the average year length over the great grand cycle of 365.24219852. So close is this to the actual solar tropical year of 365.24219878 days that the Persian calendar accumulates an error of one day only every 3.8 million years. As a purely solar calendar, months are not synchronised with the phases of the Moon.

Mayan Calendars

The Mayans employed three calendars, all organised as hierarchies
of cycles of days of various lengths. The *Long Count* was
the principal calendar for historical purposes, the *Haab*
was used as the civil calendar, while the *Tzolkin*
was the religious calendar. All of the Mayan calendars
are based on serial counting of days without means for synchronising
the calendar to the Sun or Moon, although the Long Count and Haab
calendars contain cycles of 360 and 365 days, respectively, which
are roughly comparable to the solar year. Based purely on counting
days, the Long Count more closely resembles the
Julian Day system and contemporary computer representations of
date and time than other calendars devised in antiquity.
Also distinctly modern in appearance is that days and
cycles count from zero, not one as in most other calendars,
which simplifies the computation of dates, and that numbers
as 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 the
hierarchy of cycles shown at the right.
Each of the cycles is composed of 20 of the next
shorter 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 maintains
approximate alignment with the solar year over modest
intervals--the calendar comes undone from the
Sun 5 days every *tun*.

The Mayans believed at at the conclusion of each
*pictun* cycle of about 7,885 years the universe is
destroyed and re-created. Those with apocalyptic
inclinations will be relieved to observe that the present
cycle will not end until Columbus Day, October 12, 4772 in
the Gregorian calendar. Speaking of apocalyptic events,
it's amusing to observe that the longest of the cycles in
the Mayan calendar, *alautun*, about 63 million
years, is comparable to the 65 million years since the
impact which brought down the curtain on the dinosaurs--an
impact which occurred near the Yucatan peninsula where,
almost an *alautun* later, the Mayan civilisation
flourished. If the universe is going to be destroyed and
the end of the current *pictun*, there's no point in
writing dates using the longer cycles, so we dispense
with them here.

Dates in the Long Count calendar are written, by convention, as:

*baktun* **.** *katun* **.** *tun* **.** *uinal* **.** *kin*

and thus resemble present-day IPV4 Internet addresses!

For civil purposes the Mayans used the *Haab*
calendar in which the year was divided into 18 named periods
of 20 days each, followed by five *Uayeb* days
not considered part of any period. Dates in this
calendar are written as a day number (0 to 19 for regular
periods and 0 to 4 for the days of *Uayeb*) followed
by the name of the period. This calendar has no concept of
year numbers; it simply repeats at the end of the complete
365 day cycle. Consequently, it is not possible, given a
date in the Haab calendar, to determine the Long
Count or year in other calendars. The 365 day cycle
provides better alignment with the solar year than the 360
day *tun* of the Long Count but, lacking a leap year
mechanism, the Haab calendar shifted one day with
respect to the seasons about every four years.

The Mayan religion employed the *Tzolkin* calendar,
composed of 20 named periods of 13 days. Unlike the
Haab calendar, in which the day numbers increment
until the end of the period, at which time the next period
name is used and the day count reset to 0, the names and numbers
in the Tzolkin calendar advance in parallel. On each
successive day, the day number is incremented by 1, being
reset to 0 upon reaching 13, and the next in the cycle of twenty
names is affixed to it. Since 13 does not evenly divide 20,
there are thus a total of 260 day number and period names before
the calendar repeats. As with the Haab calendar, cycles
are not counted and one cannot, therefore, convert a Tzolkin
date into a unique date in other calendars. The 260 day cycle
formed the basis for Mayan religious events and has no relation
to the solar year or lunar month.

The Mayans frequently specified dates using *both* the Haab
and Tzolkin calendars; dates of this form repeat only
every 52 solar years.

Bahá'í Calendar

The Bahá'í calendar is a solar calendar organised as a
hierarchy of cycles, each of length 19, commemorating the 19
year period between the 1844 proclamation of the Báb in
Shiraz and
the revelation by Bahá'u'lláh in 1863. Days are named in a
cycle of 19 names. Nineteen of these cycles of 19 days,
usually called "months" even though they have nothing
whatsoever to do with the Moon, make up a year, with a
period between the 18th and 19th months referred to as
*Ayyám-i-Há* not considered part of any month; this
period is four days in normal years and five days in leap
years. The rule for leap years is identical to that of the
Gregorian calendar, so the Bahá'í calendar shares its
accuracy and remains synchronised. The same cycle of 19
names is used for days and months.

The year begins at the equinox, March 21, the Feast of
Naw-Rúz; days begin at sunset. Years have their own
cycle of 19 names, called the *Váhid*. Successive cycles of
19 years are numbered, with cycle 1 commencing on March 21, 1844,
the year in which the Báb announced his prophecy.
Cycles, in turn, are assembled into *Kull-I-Shay*
super-cycles of 361 (19?) years. The first *Kull-I-Shay*
will not end until Gregorian calendar year 2205. A week of seven
days is superimposed on the calendar, with the week considered to
begin on Saturday. Confusingly, three of the names of weekdays
are identical to names in the 19 name cycles for days and months.

Indian Civil Calendar

A bewildering variety of calendars have been and continue to be used in the Indian subcontinent. In 1957 the Indian government's Calendar Reform Committee adopted the National Calendar of India for civil purposes and, in addition, defined guidelines to standardise computation of the religious calendar, which is based on astronomical observations. The civil calendar is used throughout India today for administrative purposes, but a variety of religious calendars remain in use. We present the civil calendar here.

The National Calendar of India is composed of 12 months.
The first month, *Caitra*, is 30 days in normal
and 31 days in leap years. This is followed by five
consecutive 31 day months, then six 30 day months. Leap
years in the Indian calendar occur in the same years as
as in the Gregorian calendar; the two calendars thus
have identical accuracy and remain synchronised.

Years in the Indian calendar are counted from the start of the Saka Era, the equinox of March 22nd of year 79 in the Gregorian calendar, designated day 1 of month Caitra of year 1 in the Saka Era. The calendar was officially adopted on 1 Caitra, 1879 Saka Era, or March 22nd, 1957 Gregorian. Since year 1 of the Indian calendar differs from year 1 of the Gregorian, to determine whether a year in the Indian calendar is a leap year, add 78 to the year of the Saka era then apply the Gregorian calendar rule to the sum.

French Republican Calendar

The French Republican calendar was adopted by a
decree of *La
Convention Nationale* on Gregorian date October 5, 1793
and went into effect the following November 24th, on which
day Fabre d'Églantine proposed to the *Convention*
the names for the months. It incarnates the revolutionary
spirit of "Out with the old! In with the relentlessly
rational!" which later gave rise in 1795 to the metric
system of weights and measures which has proven more durable
than the Republican calendar.

The calendar consists of 12 months of 30 days each, followed
by a five- or six-day holiday period, the
*jours complémentaires* or
*sans-culottides*. Months are grouped into four
seasons; the three months of each season end with the same
letters and rhyme with one another. The calendar begins on
Gregorian date September 22nd, 1792, the September
equinox and date of the founding of the First Republic.
This day is designated the first day of the month of
Vendémiaire in year 1 of the Republic. Subsequent years
begin on the day in which the September equinox occurs as
reckoned at the Paris meridian. Days begin at true solar
midnight. Whether the *sans-culottides* period
contains five or six days depends on the actual
date of the equinox. Consequently, there is no leap year rule
*per se*: 366 day years do not recur in a regular
pattern but instead follow the dictates of astronomy. The
calendar therefore stays perfectly aligned with the seasons.
No attempt is made to synchronise months with the phases of
the Moon.

The Republican calendar is rare in that it has no
concept of a seven day week. Each thirty day month
is divided into three *décades* of ten days
each, the last of which, *décadi*, was the
day of rest. (The word "*décade*" may
confuse English speakers; the
French noun denoting ten years is "*décennie*".)
The names of days in the *décade* are derived from
their number in the ten day sequence. The five or
six days of the *sans-culottides* do not bear
the names of the *décade*. Instead, each of these holidays
commemorates an aspect of the republican spirit.
The last, *jour de la Révolution*, occurs only
in years of 366 days.

Napoléon abolished the Republican calendar in favour of the Gregorian on January 1st, 1806. Thus France, one of the first countries to adopt the Gregorian calendar (in December 1582), became the only country to subsequently abandon and then re-adopt it. During the period of the Paris Commune uprising in 1871 the Republican calendar was again briefly used.

The original decree
which established the Republican calendar contained a
contradiction: it defined the year as starting on the day
of the true autumnal equinox in Paris, but further prescribed
a four year cycle called *la Franciade*, the fourth
year of which would end with *le jour de la Révolution*
and hence contain 366 days. These two specifications are
incompatible, as 366 day years defined by the equinox do
not recur on a regular four year schedule. This problem was
recognised shortly after the calendar was proclaimed, but the
calendar was abandoned five years before the first conflict
would have occurred and the issue was never formally resolved. Here
we assume the equinox rule prevails, as a rigid four year
cycle would be no more accurate than the Julian calendar, which
couldn't possibly be the intent of its enlightened Republican
designers.

ISO-8601 Week and Day, and Day of Year

The
International Standards Organisation
(ISO) issued
Standard ISO 8601, "Representation of Dates" in 1988,
superseding the earlier ISO 2015. The bulk of the standard
consists of standards for representing dates in the
Gregorian calendar including the highly recommended
"**YYYY-MM-DD**" form which is unambiguous, free of cultural
bias, can be sorted into order without rearrangement, and is
Y9K compliant. In addition, ISO 8601 formally defines the
"calendar week" often encountered in commercial transactions
in Europe. The first calendar week of a year: week 1, is
that week which contains the first Thursday of the year (or,
equivalently, the week which includes January 4th of the
year; the first day of that week is the previous Monday).
The last week: week 52 or 53 depending on the
date of Monday in the first week, is that which contains
December 28th of the year. The first ISO calendar week of a
given year starts with a Monday which can be as early as
December 29th of the previous year or as late as January
4th of the present; the last calendar week can end as late
as Sunday, January 3rd of the subsequent year.
ISO 8601 dates in year, week, and day form are written
with a "W" preceding the week number, which bears a leading
zero if less than 10, for example February 29th, 2000
is written as 2000-02-29 in year, month, day format and
2000-W09-2 in year, week, day form; since the day number
can never exceed 7, only a single digit is required.
The hyphens may be elided for brevity and the day number
omitted if not required. You will frequently see date of
manufacture codes such as "00W09" stamped on products; this
is an abbreviation of 2000-W09, the ninth week of year 2000.

In solar calendars such as the Gregorian, only days and years have physical significance: days are defined by the rotation of the Earth, and years by its orbit about the Sun. Months, decoupled from the phases of the Moon, are but a memory of forgotten lunar calendars, while weeks of seven days are entirely a social construct--while most calendars in use today adopt a cycle of seven day names or numbers, calendars with name cycles ranging from four to sixty days have been used by other cultures in history.

ISO 8601 permits us to jettison the historical and cultural
baggage of weeks and months and express a date simply by
the year and day number within that year, ranging from 001
for January 1st through 365 (366 in a leap year) for
December 31st. This format makes it easy to do arithmetic
with dates within a year, and only slightly more complicated
for periods which span year boundaries. You'll
see this representation used in project planning and for specifying delivery
dates. ISO dates in this form are written as "**YYYY-DDD**",
for example 2000-060 for February 29th, 2000; leading zeroes
are always written in the day number, but the hyphen may be
omitted for brevity.

All ISO 8601 date formats have the advantages of being
fixed length (at least until the Y10K crisis rolls around) and, when
stored in a computer, of being sorted in date order
by an alphanumeric sort of their textual representations.
The ISO week and day and day of year calendars are
derivative of the Gregorian calendar and share its accuracy.

Unix time():

Development of the Unix operating system began at Bell Laboratories in 1969 by Dennis Ritchie and Ken Thompson, with the first PDP-11 version becoming operational in February 1971. Unix wisely adopted the convention that all internal dates and times (for example, the time of creation and last modification of files) were kept in Universal Time, and converted to local time based on a per-user time zone specification. This far-sighted choice has made it vastly easier to integrate Unix systems into far-flung networks without a chaos of conflicting time settings.

Many machines on which Unix was initially widely deployed
could not support arithmetic on integers longer than 32 bits
without costly multiple-precision computation in software.
The internal representation of time was therefore chosen to be
the number of seconds elapsed since
00:00 Universal time on January 1, 1970 in the Gregorian
calendar (Julian day 2440587.5), with time stored as a 32
bit signed integer (`long` in early C implementations).

The influence of Unix time representation has spread well beyond
Unix since most C and C++ libraries on other systems provide
Unix-compatible time and date functions. The major drawback of
Unix time representation is that, if kept as a 32 bit signed
quantity, on January 19, 2038 it will go negative, resulting in
chaos in programs unprepared for this. Unix and C
implementations wisely (for reasons described below) define the
result of the `time()` function as type `time_t`,
which leaves the door open for remediation (by changing the
definition to a 64 bit integer, for example) before the clock
ticks the dreaded doomsday second.

C compilers on Unix systems prior to 7th Edition lacked the
32-bit `long` type. On earlier systems `time_t`,
the value returned by the `time()` function, was an array
of two 16-bit `int`s which, concatenated, represented the
32-bit value. This is the reason why `time()` accepts a
pointer argument to the result (prior to 7th Edition it returned
a status, not the 32-bit time) and `ctime()` requires a
pointer to its input argument. Thanks to Eric Allman (author
of `sendmail`) for
pointing out these historical nuggets.

Excel Serial Day Number

Spreadsheet calculations frequently need to do arithmetic with date
and time quantities--for example, calculating the interest on a loan
with a given term. When Microsoft Excel was introduced for the PC
Windows platform, it defined dates and times as "serial values", which
express dates and times as the number of days elapsed since midnight
on January 1, 1900 with time given as a fraction of a day. Midnight
on January 1, 1900 is day 1.0 in this scheme. Time zone is
unspecified in Excel dates, with the `NOW()` function returning
whatever the computer's clock is set to--in most cases local time, so
when combining data from machines in different time zones you usually
need to add or subtract the bias, which can differ over the year due
to observance of summer time. Here we assume Excel dates represent
Universal (Greenwich Mean) time, since there isn't any other rational
choice. But don't assume you can always get away with this.

You'd be entitled to think, therefore, that conversion back and
forth between PC Excel serial values and Julian day numbers would
simply be a matter of adding or subtracting the Julian day number
of December 31, 1899 (since the PC Excel days are numbered from 1).
But this is a *Microsoft* calendar, remember, so one must
first look to make sure it doesn't contain one of those bonehead
blunders characteristic of Microsoft. As is usually the case,
one doesn't have to look very far. If you have a copy of PC
Excel, fire it up, format a cell as containing a date, and
type 60 into it: out pops "February 29, 1900". News apparently
travels *very* slowly from Rome to Redmond--ever since
Pope Gregory revised the calendar
in 1582, years divisible
by 100 have *not* been leap years, and consequently the
year 1900 contained no February 29th. Due to this morsel of
information having been lost somewhere between the Holy See and
the Infernal Seattle monopoly,
all Excel day numbers for days subsequent to February 28th, 1900
are one day greater than the actual day count from January 1, 1900.
Further, note that any computation of the number of days in
a period which begins in January or February 1900 and ends in a
subsequent month will be off by one--the day count will be one
greater than the actual number of days elapsed.

By the time the 1900 blunder was discovered, Excel users had
created millions of spreadsheets containing incorrect
day numbers, so Microsoft decided to leave the error in place
rather than force users to convert their spreadsheets, and the
error remains to this day. Note, however, that *only 1900*
is affected; while the first release of Excel probably also
screwed up all years divisible by 100 and hence implemented a
purely Julian calendar, contemporary versions do correctly
count days in 2000 (which is a leap year, being divisible by
400), 2100, and subsequent end of century years.

PC Excel day numbers are valid only between 1 (January 1, 1900) and 2958465 (December 31, 9999). Although a serial day counting scheme has no difficulty coping with arbitrary date ranges or days before the start of the epoch (given sufficient precision in the representation of numbers), Excel doesn't do so. Day 0 is deemed the idiotic January 0, 1900 (at least in Excel 97), and negative days and those in Y10K and beyond are not handled at all. Further, old versions of Excel did date arithmetic using 16 bit quantities and did not support day numbers greater than 65380 (December 31, 2078); I do not know in which release of Excel this limitation was remedied.

Having saddled every PC Excel user with a defective date
numbering scheme wasn't enough for Microsoft--nothing ever is.
Next, they proceeded to come out with a Macintosh version
of Excel which uses an *entirely different* day numbering
system based on the MacOS native time format which counts
seconds elapsed since January 1, 1904. To further obfuscate
matters, on the Macintosh they chose to number days from zero
rather than 1, so midnight on January 1, 1904 has serial
value 0.0. By starting in 1904, they avoided screwing up 1900
as they did on the PC. So now Excel users who interchange data
have to cope with two incompatible schemes for counting days, one
of which thinks 1900 was a leap year and the other which
doesn't go back that far. To compound the fun, you can now
select either date system on either platform, so you can't be
certain dates are compatible even when receiving data from
another user with same kind of machine you're using. I'm
sure this was all done in the interest of the "efficiency"
of which Microsoft is so fond. As we all know, it would take a computer
*almost forever* to add or subtract four in order to make everything
seamlessly interchangeable.

Macintosh Excel day numbers are valid only between 0 (January 1, 1904) and 2957003 (December 31, 9999). Although a serial day counting scheme has no difficulty coping with arbitrary date ranges or days before the start of the epoch (given sufficient precision in the representation of numbers), Excel doesn't do so. Negative days and those in Y10K and beyond are not handled at all. Further, old versions of Excel did date arithmetic using 16 bit quantities and did not support day numbers greater than 63918 (December 31, 2078); I do not know in which release of Excel this limitation was remedied.