The Julian day or Julian day number (JDN) is the integer number of days that have elapsed since the initial epoch defined as noon Universal Time (UT) Monday, January 1, 4713 BC in the proleptic Julian calendar ^[1]. That noon-to-noon day is counted as Julian day 0. Thus the multiples of 7 are Mondays. Negative values can also be used, although those predate all recorded history. The Joint Data Network (JDN) is an interconnected network of Joint Tactical Information Distribution System (JTIDS)–based systems, which links air and missile defense command and control and weapons systems across United States armed forces. ... Look up day in Wiktionary, the free dictionary. ... In chronology, an epoch (or epochal date, or epochal event) means an instant in time chosen as the origin of a particular era. ... Noon is the time exactly halfway through the day, written 12:00 in the 24-hour clock and 12:00 noon in the 12-hour clock. ... Universal Time (UT) is a timescale based on the rotation of the Earth. ... This article does not cite any references or sources. ... is the 1st day of the year in the Gregorian calendar. ... // Events 4860 BC - Mount Mazama in Oregon collapses, forming a caldera that later fills with water and becomes Crater Lake, the deepest lake in the United States. ... The proleptic Julian calendar is produced by extending the Julian calendar to dates preceding its official introduction in 45 BC. Historians since Bede have traditionally represented the years preceding AD 1 as 1 BC, 2 BC, etc. ... Ancient history is from the period of time when writing and historical records first appear, roughly 5,500 years before the Common Era. ...

Now at 10:29, Friday October 12, 2007 (UTC) the JDN is 2454385. The remainder of this value divided by 7 is 3, an integer expression for the day of the week with 0 representing Monday. is the 285th day of the year (286th in leap years) in the Gregorian calendar. ... Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st Century. ... ... In computing, the modulo operation finds the remainder of division of one number by another. ... This article is about days of the week. ...

The Julian date (JD) is a continuous count of days and fractions elapsed since the same initial epoch. Currently the JD is 2454385.93681. The integral part (its floor) gives the Julian day number. The fractional part gives the time of day since noon UT as a decimal fraction of one day or fractional day, with 0.5 representing midnight UT. Typically, a 64-bit floating point (double precision) variable can represent an epoch expressed as a Julian date to about 1 millisecond precision. The floor and fractional part functions In mathematics, the floor function of a real number x, denoted or floor(x), is the largest integer less than or equal to x (formally, ). For example, floor(2. ... Decimal, or denary, notation is the most common way of writing the base 10 numeral system, which uses various symbols for ten distinct quantities (0, 1, 2, 3, 4, 5, 6, 7, 8 and 9, called digits) together with the decimal point and the sign symbols + (plus) and − (minus... French decimal clock from the time of the French Revolution Decimal time is the representation of the time of day using units which are decimally related. ... For other uses, see Midnight (disambiguation) Midnight, literally the middle of the night, is a time arbitrarily designated to determine the end of a day and the beginning of the next in some, mainly Western, cultures. ... In computing, a 64-bit component is one in which data are processed or stored in 64-bit units (words). ... A floating-point number is a digital representation for a number in a certain subset of the rational numbers, and is often used to approximate an arbitrary real number on a computer. ... In computing, double precision is a computer numbering format that occupies two storage locations in computer memory at address and address+1. ... In astronomy, an epoch is a moment in time for which celestial coordinates or orbital elements are specified. ... One millisecond is one-thousandth of a second. ...

A Julian date of 2454115.05486 means that the date and Universal Time is Sunday 14 January 2007 at 13:18:59.9. is the 14th day of the year in the Gregorian calendar. ... Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st Century. ...

The decimal parts of a Julian date:
0.1 = 2.4 hours or 144 minutes or 8640 seconds
0.01 = 0.24 hours or 14.4 minutes or 864 seconds
0.001 = 0.024 hours or 1.44 minutes or 86.4 seconds
0.0001 = 0.0024 hours or 0.144 minutes or 8.64 seconds
0.00001 = 0.00024 hours or 0.0144 minutes or 0.864 seconds.

Almost 2.5 million Julian days have elapsed since the initial epoch. JDN 2,400,000 was November 16, 1858. JD 2,500,000.0 will occur on August 31, 2132 at noon UT. This article does not cite any references or sources. ...

The Julian day number can be considered a very simple calendar, where its calendar date is just an integer. This is useful for reference, computations, and conversions. It allows the time between any two dates in history to be computed by simple subtraction. A page from the Hindu calendar 1871-72. ... A date in a calendar is a reference to a particular day represented within a calendar system. ... 5 - 2 = 3 (verbally, five minus two equals three) An example problem Subtraction is one of the four basic arithmetic operations; it is the inverse of addition. ...

The Julian day system was introduced by astronomers to provide a single system of dates that could be used when working with different calendars and to unify different historical chronologies. Apart from the choice of the zero point and name, this Julian day and Julian date are not directly related to the Julian calendar, although it is possible to convert any date from one calendar to the other. The Julian calendar was introduced in 46 BC by Julius Caesar and came into force in 45 BC (709 ab urbe condita). ...

Julian Date

Historical Julian Dates were recorded relative to GMT or Ephemeris Time, but the International Astronomical Union now recommends that Julian Dates be specified in Terrestrial Time, and that when necessary to specify Julian Dates using a different time scale, that the time scale used be indicated when required, such as JD(UT1). The fraction of the day is found by converting the number of hours, minutes, and seconds after noon into the equivalent decimal fraction. Ephemeris Time (ET) is a now obsolete time scale used in ephemerides of celestial bodies, in particular the Sun (as observed from the Earth), Moon, planets, and other members of the solar system. ... Logo of the IAU The International Astronomical Union (French: Union astronomique internationale) unites national astronomical societies from around the world. ... Terrestrial Time (TT) is the modern time standard for time on the surface of the Earth. ...

The term Julian date is also used to refer to:

• Julian calendar dates
• ordinal dates (day-of-year)

The use of Julian date to refer to the day-of-year (ordinal date) is usually considered to be incorrect, however it is widely used that way in the earth sciences and computer programming. The Julian calendar was introduced in 46 BC by Julius Caesar and came into force in 45 BC (709 ab urbe condita). ... ISO 8601 is an international standard for date and time representations issued by the International Organization for Standardization (ISO). ...

Alternatives

• The Heliocentric Julian Day (HJD) is the same as the Julian day, but adjusted to the frame of reference of the Sun, and thus can differ from the Julian day by as much as 8.3 minutes, that being the time it takes the Sun's light to reach Earth. The Julian day is sometimes referred to as the Geocentric Julian Day (GJD) in order to distinguish it from HJD.

Because the starting point is so long ago, numbers in the Julian day can be quite large and cumbersome. A more recent starting point is sometimes used, for instance by dropping the leading digits, in order to fit into limited computer memory with an adequate amount of precision.

• The Modified Julian Day (MJD) is the number of days (with decimal fraction of the day) that have elapsed since midnight at the beginning of Wednesday November 17, 1858. In terms of the Julian day:

MJD = JD − 2,400,000.5

Currently the value is 2454385.93681 − 2400000.5 = 54385.43681.

The day is found by rounding downward, currently giving 54385. This number changes at midnight UT or TT. It is 2,400,001 less than the Julian day number of the afternoon half of the same day (which is the same as the JD at noon). It is a multiple of 7 on Wednesdays.

The MJD was introduced by the Smithsonian Astrophysical Observatory in 1957 to record the orbit of Sputnik via an IBM 704 (36-bit machine) and using only 18 bits until 2576-08-07. MJD is the epoch of OpenVMS, using 63-bit date/time postponing the next Y2K campaign to 31-JUL-31086 02:48:05.47.

• The Reduced Julian Day (RJD) is also used by astronomers and counts days from nearly the same day as the MJD, but lacks the additional offset of 12 hours that MJD has. It therefore starts from the previous noon UT or TT, on Tuesday November 16, 1858. It is defined as:

RJD = JD − 2400000

• The Truncated Julian Day (TJD) was introduced by NASA for the space program. TJD was zero at midnight UT at the beginning of May 24, 1968. It is defined by NASA as:

TJD = JD − 2440000.5

This was chosen so the number would resemble the MJD but be only four digits long. TJD exceeded four digits on October 10, 1995, and NASA now uses five-digit TJDs [1]. NIST, however, defines TJD cyclically so that it never exceeds four digits:

TJD = (JD − 0.5) mod 10000

• The Dublin Julian Day (DJD) is the number of days that has elapsed since the epoch of the solar and lunar ephemerides used from 1900 through 1983, Newcomb's Tables of the Sun and Ernest W. Brown's Tables of the Motion of the Moon (1919). This epoch was noon UT on 0 January 1900, which is the same as noon UT on December 31, 1899. The DJD was defined by the International Astronomical Union at their 1955 meeting in Dublin, Ireland, [2] as:

DJD = JD − 2415020

• The Lilian day number is a count of days of the Gregorian Calendar. It is an integer applied to a whole day; day 1 was October 15, 1582, which was the day the Gregorian calendar went into effect. It uses the local timezone, not UT. It was named for Aloysius Lilius, the principal author of the Gregorian Calendar.

• The ANSI Date defines January 1, 1601 as day 1, and is used as the origin of COBOL integer dates. This epoch is the beginning of the previous 400-year cycle of leap years in the Gregorian Calendar, which ended with the year 2000.

• Rata Die is a system (or more precisely a family of three systems) used in the book Calendrical Calculations. It uses the local timezone, and day 1 is January 1, 1, that is, the first day of the Christian or Common Era in the proleptic Gregorian Calendar.

• Unix Time uses January 1, 1970 as the epoch, but counts by the second, not by the day.

Unix Time = (JD – 2440587.5) × 86400

Sol redirects here. ... This article is about Earth as a planet. ... 17 November is also the name of a Marxist group in Greece, coinciding with the anniversary of the Athens Polytechnic uprising. ... Year 1858 (MDCCCLVIII) was a common year starting on Friday (link will display the full calendar) of the Gregorian Calendar (or a common year starting on Wednesday of the 12-day slower Julian calendar). ... Year 1957 (MCMLVII) was a common year starting on Tuesday (link displays the 1957 Gregorian calendar). ... Sputnik 1 (Russian: , Satellite-1, or literally Co-traveler-1 byname ПС-1 (PS-1, i. ... OpenVMS[1] (Open Virtual Memory System or just VMS) is the name of a high-end computer server operating system that runs on the VAX[2] and Alpha[3] family of computers developed by Digital Equipment Corporation of Maynard, Massachusetts (DIGITAL was then purchased by Compaq, and is now owned... This article is about the millennial computer glitch. ... is the 320th day of the year (321st in leap years) in the Gregorian calendar. ... Year 1858 (MDCCCLVIII) was a common year starting on Friday (link will display the full calendar) of the Gregorian Calendar (or a common year starting on Wednesday of the 12-day slower Julian calendar). ... This article is about the American space agency. ... is the 144th day of the year (145th in leap years) in the Gregorian calendar. ... Year 1968 (MCMLXVIII) was a leap year starting on Monday (link will display full calendar) of the Gregorian calendar. ... is the 283rd day of the year (284th in leap years) in the Gregorian calendar. ... Year 1995 (MCMXCV) was a common year starting on Sunday (link will display full 1995 Gregorian calendar). ... As a non-regulatory agency of the United States Department of Commerce’s Technology Administration, the National Institute of Standards (NIST) develops and promotes measurement, standards, and technology to enhance productivity, facilitate trade, and improve the quality of life. ... An ephemeris (plural: ephemerides) (from the Greek word ephemeros= daily) was, traditionally, a table providing the positions (given in a Cartesian coordinate system, or in right ascension and declination or, for astrologers, in longitude along the zodiacal ecliptic), of the Sun, the Moon, and the planets in the sky at... Newcombs Tables of the Sun is the short title for a work by the American astronomer and mathematician Simon Newcomb entitled Tables of the Motion of the Earth on its Axis and Around the Sun on pages 1-169 of volume VI of the serial publication Astronomical Papers prepared... Ernest William Brown (November 29, 1866 – July 22, 1938) was a British astronomer. ... This article does not cite any references or sources. ... Äž: For the film, see: 1900 (film). ... is the 365th day of the year (366th in leap years) in the Gregorian calendar. ... Year 1899 (MDCCCXCIX) was a common year starting on Sunday (link will display the full calendar) of the Gregorian calendar (or a common year starting on Friday [1] of the 12-day-slower Julian calendar). ... Logo of the IAU The International Astronomical Union (French: Union astronomique internationale) unites national astronomical societies from around the world. ... Dublin city centre at night WGS-84 (GPS) Coordinates: , Statistics Province: Leinster County: Dáil Éireann: Dublin Central, Dublin North Central, Dublin North East, Dublin North West, Dublin South Central, Dublin South East European Parliament: Dublin Dialling Code: +353 1 Postal District(s): D1-24, D6W Area: 114. ... The Gregorian calendar is the most widely used calendar in the world. ... is the 288th day of the year (289th in leap years) in the Gregorian calendar. ... Gregorian Calendar switch: Year 1582 involved conversion to the Gregorian calendar. ... Aloysius Lilius (Luigi Lilio, 1510 – 1576) was a physician from Calabria in Italy (at that time part of the kingdom of Naples). ... The American National Standards Institute or ANSI (pronounced an-see) is a nonprofit organization that oversees the development of standards for products, services, processes and systems in the United States. ... is the 1st day of the year in the Gregorian calendar. ... Events February 8 - Robert Devereux, 2nd Earl of Essex, rebels against Elizabeth I of England - revolt is quickly crushed February 25 - Robert Devereux beheaded Jesuit Matteo Ricci arrives in China Bad harvest in Russia due to rainy summer Dutch troops drive Portuguese from Málaga Battle of Kinsale, Ireland Births... COBOL (pronounced //) is a third-generation programming language, and one of the oldest programming languages still in active use. ... In chronology, an epoch (or epochal date, or epochal event) means an instant in time chosen as the origin of a particular era. ... Rata Die (RD) is a system for assigning numbers to calendar days (optionally with time of day), independent of any calendar, for the purposes of calendrical calculations. ... is the 1st day of the year in the Gregorian calendar. ... This article is about the year 1. ... Anno Domini (Latin: In the year of the Lord), or more completely Anno Domini Nostri Jesu Christi (in the year of our Lord Jesus Christ), commonly abbreviated AD or A.D., is the designation used to number years in the dominant Christian Era in the world today. ... “BCE” redirects here. ... The proleptic Gregorian calendar is produced by extending the Gregorian Calendar to dates preceding its official introduction in 1582. ... Unix time passed 1000000000 seconds in 2001-09-09T03:46:40. ... is the 1st day of the year in the Gregorian calendar. ... Year 1970 (MCMLXX) was a common year starting on Thursday (link shows full calendar) of the Gregorian calendar. ...

History

The Julian day number is based on the Julian Period proposed by Joseph Scaliger in 1583, at the time of the Gregorian calendar reform, but it is the multiple of three calendar cycles used with the Julian calendar: Joseph Justus Scaliger (1540-1609) was the tenth child and third son of Julius Caesar Scaliger and Andiette de Roques Lobejac. ... The Gregorian calendar is the most widely used calendar in the world. ... A page from the Hindu calendar 1871-72. ... The Julian calendar was introduced in 46 BC by Julius Caesar and came into force in 45 BC (709 ab urbe condita). ...

15 (indiction cycle) × 19 (Metonic cycle) × 28 (Solar cycle) = 7980 years

Its epoch falls at the last time when all three cycles were in their first year together — Scaliger chose this because it pre-dated all historical dates. An indiction is any of the years in a 15-year cycle used to date medieval documents. ... The Metonic cycle or Enneadecaeteris in astronomy and calendar studies is a particular approximate common multiple of the year (specifically, the seasonal tropical year) and the synodic month. ... The solar cycle is a 28-year cycle of the Julian calendar with respect to the week. ... In chronology, an epoch (or epochal date, or epochal event) means an instant in time chosen as the origin of a particular era. ...

Note: although many references say that the "Julian" in "Julian day" refers to Scaliger's father, Julius Scaliger, in the introduction to Book V of his Opus de Emendatione Temporum (Work on the Emendation of Time) he states: "Iulianum vocauimus: quia ad annum Iulianum dumtaxat accomodata est" which translates more or less as "We have called it Julian merely because it is accommodated to the Julian year". This "Julian" refers to Julius Caesar, who introduced the Julian calendar in 46 BC. Julius Caesar Scaliger (1484-1558), humanist scholar. ... For other uses, see Julius Caesar (disambiguation). ...

In his book Outlines of Astronomy, first published in 1849, the astronomer John Herschel wrote: John Herschel Sir John Frederick William Herschel (7 March 1792 – 11 May 1871) was an English mathematician and astronomer. ...

The first year of the current Julian period, or that of which the number in each of the three subordinate cycles is 1, was the year 4713 B.C., and the noon of the 1st of January of that year, for the meridian of Alexandria, is the chronological epoch, to which all historical eras are most readily and intelligibly referred, by computing the number of integer days intervening between that epoch and the noon (for Alexandria) of the day, which is reckoned to be the first of the particular era in question. The meridian of Alexandria is chosen as that to which Ptolemy refers the commencement of the era of Nabonassar, the basis of all his calculations.

Astronomers adopted Herschel's Julian Days in the late nineteenth century, but used the meridian of Greenwich instead of Alexandria, after the former was made the Prime Meridian by international conference in 1884. This has now become the standard system of Julian days. Julian days are typically used by astronomers to date astronomical observations, thus eliminating the complications resulting from using standard calendar periods like eras, years, or months. They were first introduced into variable star work by Edward Charles Pickering, of the Harvard College Observatory, in 1890.^[2] An astronomer or astrophysicist is a person whose area of interest is astronomy or astrophysics. ... Location of the Prime Meridian Prime Meridian in Greenwich A GPS receiver at the Greenwich Meridian Laser projected from the Royal Observatory in Greenwich marking the Prime Meridian The Royal Observatory, Greenwich (today a museum) The 24-hour clock at Greenwich The Prime Meridian, also known as the International Meridian... For other uses, see Astronomy (disambiguation). ... A page from the Hindu calendar 1871-72. ... This article or section contains a plot summary that is overly long or excessively detailed. ... Edward Charles Pickering (July 19, 1846 – February 3, 1919) was an American astronomer and physicist, brother of William Henry Pickering. ... Harvard College Observatory, about 1900. ...

Julian days begin at noon because when Herschel recommended them, the astronomical day began at noon (it did so until 1925). The astronomical day had begun at noon ever since Ptolemy chose to begin the days in his astronomical periods at noon. He chose noon because the transit of the Sun across the observer's meridian occurs at the same apparent time every day of the year, unlike sunrise or sunset, which vary by several hours. Midnight was not even considered because it could not be accurately determined using water clocks. Nevertheless, he double-dated most nighttime observations with both Egyptian days beginning at sunrise and Babylonian days beginning at sunset. This would seem to imply that his choice of noon was not, as is sometimes stated, made in order to allow all observations from a given night to be recorded with the same date. This article is about the geographer, mathematician and astronomer Ptolemy. ... A water clock or clepsydra is a device for measuring time by letting water regularly flow out of a container usually by a tiny aperture. ... Babylonia was an ancient state in Iraq), combining the territories of Sumer and Akkad. ...

Calculation

The Julian day number can be calculated using the following formulas:

The months January to December are 1 to 12. Astronomical year numbering is used, thus 1 BC is 0, 2 BC is −1, and 4713 BC is −4712. In all divisions (except for JD) the floor function is applied to the quotient (for dates since 1 March −4800 all quotients are non-negative, so we can also apply truncation). Astronomical year numbering is based on BCE/CE (or BC/AD) year numbering, but follows normal decimal integer numbering more strictly. ... The floor and fractional part functions In mathematics, the floor function of a real number x, denoted or floor(x), is the largest integer less than or equal to x (formally, ). For example, floor(2. ... is the 60th day of the year (61st in leap years) in the Gregorian calendar. ... In mathematics, truncation is the term used for reducing the number of digits right of the decimal point, by discarding the least significant ones. ...

For a date in the Gregorian calendar (at noon):

For a date in the Julian calendar (at noon):

The constants used at the end of the Gregorian and Julian formulas are required to return the same JDN for the same date in both calendars between March 1, 200 and February 28, 300. The constants are the JDNs of February 29, −4800 in each calendar. In the proleptic Gregorian calendar the Julian Day zero is November 24, 4714 BC which is 32045 days apart from the start of the Gregorian quadricentennial cycle (i.e. 400 years cycle starting and ending in a year divisible by 400) containing the Julian Day zero, which begins on March 1 4801 BC in the proleptic Gregorian calendar. is the 60th day of the year (61st in leap years) in the Gregorian calendar. ... For other uses, see number 200. ... February 28 is the 59th day of the year in the Gregorian calendar. ... Franks penetrate into northern Belgium (approximate date). ... February 29 is a day added into a leap year of the Gregorian calendar. ... The proleptic Gregorian calendar is produced by extending the Gregorian Calendar to dates preceding its official introduction in 1582. ... is the 328th day of the year (329th in leap years) in the Gregorian calendar. ... // Events 4860 BC - Mount Mazama in Oregon collapses, forming a caldera that later fills with water and becomes Crater Lake, the deepest lake in the United States. ... is the 60th day of the year (61st in leap years) in the Gregorian calendar. ... // Events 4860 BC - Mount Mazama in Oregon collapses, forming a caldera that later fills with water and becomes Crater Lake, the deepest lake in the United States. ... The proleptic Gregorian calendar is produced by extending the Gregorian Calendar to dates preceding its official introduction in 1582. ...

For the full Julian Date, not counting leap seconds (divisions are real numbers): A leap second is a one-second adjustment to civil time in order to keep it close to the mean solar time. ...

So, for example, 1 January 2000 at midday corresponds to JD = 2451545.0

The day of the week can be determined from the Julian day number by calculating it modulo 7, where 0 means Monday. For more details on each day of the week, see days of the week. ... Modular arithmetic (sometimes called modulo arithmetic, or clock arithmetic because of its use in the 24-hour clock system) is a system of arithmetic for integers, where numbers wrap around after they reach a certain value — the modulus. ...

Gregorian calendar from Julian day number

• Let J be the Julian day number from which we want to compute the date components.
• With J, compute a relative Julian day number j from a Gregorian epoch starting on March 1 −4800 (i.e. March 1 4801 BC in the proleptic Gregorian Calendar), the beginning of the Gregorian quadricentennial 32,044 days before the epoch of the Julian Period.
• With j, compute the number g of Gregorian quadricentennial cycles elapsed (there are exactly 146,097 days per cycle) since the epoch; subtract the days for this number of cycles, it leaves dg days since the beginning of the current cycle.
• With dg, compute the number c (from 0 to 4) of Gregorian centennial cycles (there are exactly 36,524 days per Gregorian centennial cycle) elapsed since the beginning of the current Gregorian quadricentennial cycle, number reduced to a maximum of 3 (this reduction occurs for the last day of a leap centennial year where c would be 4 if it were not reduced); subtract the number of days for this number of Gregorian centennial cycles, it leaves dc days since the beginning of a Gregorian century.
• With dc, compute the number b (from 0 to 24) of Julian quadrennial cycles (there are exactly 1,461 days in 4 years, except for the last cycle which may be incomplete by 1 day) since the beginning of the Gregorian century; subtract the number of days for this number of Julian cycles, it leaves db days in the Gregorian century.
• With db, compute the number a (from 0 to 4) of Roman annual cycles (there are exactly 365 days per Roman annual cycle) since the beginning of the Julian quadrennial cycle, number reduced to a maximum of 3 (this reduction occurs for the leap day, if any, where a would be 4 if it was not reduced); subtract the number of days for this number of annual cycles, it leaves da days in the Julian year (that begins on March 1).
• Convert the four components g, c, b, a into the number y of years since the epoch, by summing their values weighted by the number of years that each component represents (respectively 400 years, 100 years, 4 years, and 1 year).
• With da, compute the number m (from 0 to 11) of months since March (there are exactly 153 days per 5-month cycle, however these 5-month cycles are offset by 2 months within the year, i.e. the cycles start in May, and so the year starts with an initial fixed number of days on March 1, the month can be computed from this cycle by a Euclidian division by 5); subtract the number of days for this number of months (using the formula above), it leaves d days past since the beginning of the month.
• You can then deduce the Gregorian date (Y, M, D) by simple shifts from (y, m, d).

We can then develop these formulas into a single inlined formula per component, computed as above. All this computing requires only integers and so is not sensitive to rounding errors caused by floating point approximations (most decimal fractions have an inexact representation within the binary format used by floating point arithmetic used by most computer software, so using them would produce false results on some dates because of roundoff errors). is the 60th day of the year (61st in leap years) in the Gregorian calendar. ... is the 60th day of the year (61st in leap years) in the Gregorian calendar. ... is the 60th day of the year (61st in leap years) in the Gregorian calendar. ...

The formulae below (which use Euclidian division — integer division (div) and modulo (mod) — without any negative numbers) are valid for the whole range of dates since −4800. For dates before 1582, the resulting date components are valid only in the Gregorian proleptic calendar. This is based on the Gregorian calendar but extended to cover dates before its introduction, including the pre-Christian era. For dates in that era (before year 1 CE), astronomical year numbering is used. This includes a year zero, which immediately precedes 1 CE. Astronomical year zero is 1 BCE in the proleptic Gregorian calendar and, in general, year n BCE = astronomical year 1 − n, and for astronomical year A (A < 1), the BCE year is 1 + abs(A). “BCE” redirects here. ... Astronomical year numbering is based on BCE/CE (or BC/AD) year numbering, but follows normal decimal integer numbering more strictly. ... BCE is a TLA that may stand for: Before the Common Era, date notation equivalent to BC (e. ...

J = Julian day number

j = J + 32044

g = j div 146097

dg = j mod 146097

c = (dg div 36524 + 1) × 3 div 4

dc = dg − c × 36524

b = dc div 1461

db = dc mod 1461

a = (db div 365 + 1) × 3 div 4

da = db − a × 365

y = g × 400 + c × 100 + b × 4 + a

m = (da × 5 + 308) div 153 − 2

d = da − (m + 4) × 153 div 5 + 122

Y = y − 4800 + (m + 2) div 12

M = (m + 2) mod 12 + 1

D = d + 1

See also

• Julian year (astronomy)
• Julian year (calendar)
• Decimal time
• Epoch (reference date)
• Epoch (astronomy)
• Era
• Time
• Time scales
• Ordinal date

In astronomy, a Julian year is a unit of time defined as exactly 365. ... A Julian year is on average 365. ... French decimal clock from the time of the French Revolution Decimal time is the representation of the time of day using units which are decimally related. ... In chronology, an epoch (or epochal date, or epochal event) means an instant in time chosen as the origin of a particular era. ... In astronomy, an epoch is a moment in time for which celestial coordinates or orbital elements are specified. ... An era is a long period of time with different technical and colloquial meanings, and usages in language. ... Look up time in Wiktionary, the free dictionary. ... A time scale specifies divisions of time. ... The ordinal date within a year together with the year form the full ISO 8601 ordinal date. ...

Footnotes

1. ^ This equals November 24, 4714 BC in the proleptic Gregorian calendar.
2. ^ An Introduction to the Study of Variable Stars by Caroline Ellen Furness page 206.

The proleptic Gregorian calendar is produced by extending the Gregorian Calendar to dates preceding its official introduction in 1582. ...

References

• Gordon Moyer, "The Origin of the Julian Day System," Sky and Telescope 61 (April 1981) 311−313.
• Explanatory Supplement to the Astronomical Almanac, edited by P. Kenneth Seidelmann. University Science Books, 1992. ISBN 0-935702-68-7

External links

• U.S. Naval Observatory Julian Date Converter
• Julian Day and Civil Date calculator
• U.S. Naval Observatory Time Service article on Modified Julian Date
• U.S. Naval Observatory current MJD service
• MJD explanation (18 bits for dates)
• Peter Baum's date algorithms cover Rata Die
• Outlines of Astronomy by John Herschel
• International Astronomical Union Resolution 1B: On the Use of Julian Dates
• Open-source date conversion software
• Calendrica
• Another Julian Day calculator with conversions to many other calendars valid from 1 January 100 proleptic Gregorian calendar