Convert Gregorian and Julian dates to Julian day numbers

Calculating with dates is easier if days are numbered consecutively, instead of being identified by year, month and day. In order to number them, some date must be picked as day number zero. A proposal made in 1582 by a French scholar,¹ Joseph Justus Scaliger (1540–1609), is still the basis of the way we number days.

In Scaliger's time, every year bore three major designations:

**1. **Its place in the solar cycle of 28
years. In the Julian calendar, in any year the days fall on the same day of the week as they did 28
years ago.

**2.** Its place in the lunar or Metonic cycle
of 19 years. In any year the phases of the moon fall on very nearly the same days of the month
as they did 19 years ago.

If every year is described by its place in these lunar and solar cycles (e.g., “this year is the 23rd year of the solar cycle and the 7th year of the lunar cycle”), 532 years can pass before two years will have the same description (19 × 28 = 532). See Great Paschal period.

The 532-year period was old news in Scaliger's time. He added a third cycle, of fiscal instead of astronomical significance:

**3.** The Roman emperor Diocletian (245?–313?;
reigned 284–305 ce)
had established a practice of taking tax censuses every 15 years, a period that
became known as the cycle of indiction. In the
early middle ages these cycles were taken to have begun with the accession of
Constantine in 312, and until the 13th
century were widely used to date correspondence, charters and other documents–even
later for public documents in Spain. (To find the year of indiction for a year *anno
domine*, add 3, then divide by 15. A non-zero remainder is the year of
indiction; a zero remainder indicates year 15.)

Combining the three cycles, Scaliger got a period of 7,980 years (19 × 28 × 15) in which no two years would have identical numbers for all three cycles. Unlike the 532-year Great Paschal period, this period was long enough to take in all of human history as then conceived, and then some. Scaliger named the period the Julian period (after the Julian year²) and proposed it be used to keep track of such things as astronomical occurrences.

To set day one of the first Julian period, Scaliger calculated backwards to find the date on which all three of the cycles began on the same day (the beginning of the world?). The day he come up with was 1 January 4713 bc, which conveniently is about the time medieval Christians believed the Creation occurred, and before any historical events one might wish to date. Not surprisingly, Scaliger missed: the three cycles don't start on that date, since, among other complications, the lunar cycle is not exactly 19 years. And Scaliger had no computer. However, by convention Julian period 1 began on 1 January 4713 bce and will end on 23 January 3268 ce.

In the 19th century, astronomers adopted the Julian
Day
numbers at the suggestion of Sir John
Herschel.^{3}

Today astronomers define the Julian Day number as the number of days since Greenwich mean noon of 1 January 4713 bce. Julian Day 2,450,000 began at 12:00 Universal Time (8 am Eastern Daylight Time) on 9 October 1995. The Julian Day begins at noon, which was long the custom of astronomers.

The Julian Day number is not a measure of time; it is actually a unit of count, a count of days. However, it may be used to calculate durations as time, provided an uncertainty of as much as 88.7 minutes is acceptable (for dates within the first Julian Period).

1.
Joseph Justus Scaliger.*
De emendatione temporum*.

Paris, 1583.

2. It is often said that Scaliger named the Julian period after
his father, but at the end of the introductory section to Book V of *De
Emendatione Temporum* he explicitly states that he named his period after the
Julian year. We are grateful to Nachum Dershowitz and Edward Reingold for saving
us from the named-after-Dad error; see their *Calendrical Calculations*, page 12, footnote
7.

3. John Herschel.

*Outlines of Astronomy.*

London: Longman, Brown, Green and Longmans, 1849.

Pages 633-637.

Try converting today's date and then your birthday. Subtract to find out how many days old you are.

The modified Julian Day number (MJD) is the Julian Day number described above, less 2,400,000.5, which resets the count to begin at 0h on 17 November 1858, and makes the day begin at midnight instead of noon. Using the modified Julian Day number for contemporary records saves having to record two digits that will always be the same. Space programs and timekeeping laboratories use modified Julian Day numbers.

In 1970 the Jet Propulsion Laboratory held an informal “Great Julian Day Contest,” looking for the best computer algorithm for computing Julian Days.

Computer programmers are now the most extensive users of the Julian Day. The modified Julian Day figures in the calculation of monthly bank statements, mortgage payments, and so forth. Unfortunately, some of the algorithms that have been published for computing Julian Days are not accurate.

In Barycentric Coordinate Time (TCB), used by astronomers, the
Julian date was 2 443 144**.**500 372 5 at the earth's center on January 1,
1977, 0 hours 0 minutes 0 seconds, and has increased by 1 for each 86 400
seconds of TCB since.

International Astronomical Union 2006 Resolution B3.

In the late twentieth century–present = day of the year. An example of such use is dating provided on tags on nursery plants. This is an unfortunate development.

Gernot M. R. Winkler.

Modified Julian Date.

http://tycho.usno.navy.mil/mjd.html

CCIR Recommendation 457-1, Use of the Modified Julian Date by the standard frequency and time-signal services.

Copyright © 2000 Sizes, Inc. All rights reserved.

Last revised: 14 May 2008.