Julian Day Number Calculator
A Julian Day is a continuous day count starting at noon UTC on 1 January 4713 BC — the standard reference astronomers, satellite operators and historians use to put any date on a single linear scale. Enter a Gregorian date and the calculator instantly returns the Julian Day Number (JDN), Modified Julian Day (MJD), JD at 00:00 UTC, weekday, and day of year.
Please enter a valid Gregorian calendar date.
Julian Day Number (JDN)
2,461,176
The astronomical integer JDN at noon UTC of the date.
Modified Julian Day (MJD)
61,175
MJD at 00:00 UTC of the date (= JD − 2 400 000.5).
JD at 00:00 UTC
2,461,175.5
Weekday
Friday
Day of year
Day 135
Heads up: this date precedes 1582-10-15, when the Julian calendar was actually in use. The calculator uses the proleptic Gregorian calendar — historical use should account for the discrepancy.
Formula
a = ⌊(14 − M)/12⌋, y = Y + 4800 − a, m = M + 12a − 3, JDN = D + ⌊(153 m + 2)/5⌋ + 365 y + ⌊y/4⌋ − ⌊y/100⌋ + ⌊y/400⌋ − 32 045 | MJD = JD − 2 400 000.5
- · JDN is an integer representing noon UTC of the date; JD at 00:00 UTC is JDN − 0.5.
- · MJD was defined by the IAU in 1957 as JD − 2 400 000.5, with MJD 0 at 1858-11-17 00:00 UTC. Smaller magnitudes make it the standard for modern satellite, GPS and space-mission logs.
- · Astronomical anchors: 2000-01-01 has JDN 2 451 545 (the J2000.0 reference); 1970-01-01 (Unix epoch) is JD 2 440 587.5; 1858-11-17 is MJD 0.
- · The calculator uses the proleptic Gregorian calendar — Gregorian rules extended backwards before 1582-10-15. For pre-reform historical work, dates issued under the Julian calendar will differ (10–13 days, depending on the century); a warning shows for dates before the reform.
- · Forward conversion follows Fliegel & Van Flandern (1968), CACM. The inverse uses the Richards (2013) algorithm from the Explanatory Supplement to the Astronomical Almanac, 3rd ed.
- · Weekday: JDN mod 7, where 0 = Monday, 5 = Saturday, 6 = Sunday.
Frequently asked
What is the difference between JDN, JD and MJD?
JD (Julian Date) is the continuous real-valued day count starting at noon UTC on 1 January 4713 BC; the fractional part encodes the time of day (e.g. .25 = 18:00 UTC). JDN (Julian Day Number) is the integer part, used when you just want to identify a day. MJD (Modified Julian Day) = JD − 2 400 000.5, anchored at 1858-11-17 00:00 UTC — defined by the IAU in 1957 and now standard in satellite, GPS and space-mission timestamps because the numbers are much smaller.
Why does the Julian Day epoch start in 4713 BC?
The system was proposed by the French scholar Joseph Justus Scaliger in 1583. He picked 1 January 4713 BC (Julian calendar) because three astronomical/calendrical cycles — the 28-year solar cycle, the 19-year Metonic cycle and the 15-year Roman indiction — all reset on that day, giving a combined period of 7,980 years. Anchoring the count there meant every historical date had a single positive integer with no negatives.
I got a different JDN for a date in 1500 than my history textbook — why?
Before 1582-10-15 the Gregorian calendar was not in use; everyday European dates were Julian. This calculator uses the proleptic Gregorian calendar — Gregorian rules extended backwards — which is what astronomers prefer for arithmetic. If your textbook quotes the Julian-calendar date, the JDN will differ by roughly 10 days at 1582, and more in earlier centuries. The widget shows a warning for any date before the reform.
How does this relate to Unix time?
Closely. Unix time counts seconds since 1970-01-01 00:00 UTC, which is JD 2 440 587.5. So any Unix timestamp t corresponds to JD = 2 440 587.5 + t / 86 400 and MJD = 40 587 + t / 86 400. The two systems are just different origins and units for the same linear time-line.
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