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Julian date converter

The Julian Day Number is a continuous count of days since January 1, 4713 BCE used in astronomy to compare dates across calendar systems. Enter a Gregorian date or a JDN to.

About this calculator

Formula

Gregorian date → JDN (Meeus, “Astronomical Algorithms” Ch. 7)

a = floor((14 − month) / 12)
y = year + 4800 − a
m = month + 12·a − 3
JDN = day + floor((153·m + 2) / 5) + 365·y + floor(y/4) − floor(y/100) + floor(y/400) − 32045

Adding a time component

JD = JDN + (hour − 12)/24 + minute/1440 + second/86400

At noon UTC the fractional part is 0, so JD = JDN exactly.

Derived quantities

QuantityFormula
Modified Julian Date (MJD)JD − 2400000.5
J2000 offset (days)JD − 2451545.0

Worked example

Date: January 1, 2000 at 12:00:00 UTC (J2000 epoch)

  • JDN = 2451545
  • JD = 2451545.0 (noon)
  • MJD = 51544.5
  • J2000 = 0.0

Known reference points

DateJDN
Jan 1, 1970 (Unix epoch)2440588
Jan 1, 2000 (J2000 epoch)2451545
Jan 1, 20242460311

Notes

  • The algorithm handles proleptic Gregorian dates (dates before the Gregorian calendar was adopted).
  • Dates before October 15, 1582 were in the Julian calendar era; this converter uses the proleptic Gregorian formula for all dates.

Frequently asked

What is a Julian Day Number?
A Julian Day Number (JDN) is an integer count of days since the start of the Julian Period — January 1, 4713 BCE in the Julian calendar, noon UTC. JDN 0 is that starting day. January 1, 2000 is JDN 2451545. The system gives astronomers a single timeline that spans any historical date.
What is a Julian Date vs. a Julian Day Number?
A Julian Day Number is an integer (the whole-day count). A Julian Date (JD) adds a fractional part representing the time of day, anchored to noon UTC. At noon on January 1, 2000, JD = 2451545.0 exactly.
What is the Modified Julian Date?
The Modified Julian Date (MJD) = JD − 2400000.5. It resets the origin to midnight on November 17, 1858, producing smaller numbers convenient for modern calculations. MJD 0 = JD 2400000.5.
What is J2000?
J2000 is the standard astronomical epoch: January 1.5, 2000 UTC (noon on January 1, 2000) = JD 2451545.0. The J2000 offset shows how many days before or after that epoch a date falls.
Is this the same as the Julian calendar?
No. The Julian Day Number is a counting system invented by astronomers. The Julian calendar is a civil calendar that predates the Gregorian calendar. The names happen to share origin (both named after Julius Caesar), but the systems are different.

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