Julian Date Calculator
Free Julian date calculator. Convert any Gregorian date to the astronomical Julian Day (JD), Modified Julian Date, and the YYDDD ordinal date instantly.
Updated 2026-06-14 · Free · No sign-up · Runs privately in your browser
Show the formula & steps
"Julian Date" can mean the astronomical Julian Day (a continuous day count) or the YYDDD ordinal date used in IT and aviation — both are shown.
How the Julian Date Calculator Works
This calculator converts an ordinary Gregorian calendar date (and optional time) into the values that astronomers, programmers, and analysts use to track time as a single running number. It returns the Julian Date (JD), the integer Julian Day Number, the Modified Julian Date (MJD), and the ordinal date (year plus day-of-year, including the YYDDD form).
The Formula
The integer Julian Day Number for a Gregorian date is computed with the Fliegel–Van Flandern algorithm. With a = floor((14 − month) ÷ 12), y’ = year + 4800 − a, and m’ = month + 12a − 3:
JDN = day + ⌊(153·m’ + 2) ÷ 5⌋ + 365·y’ + ⌊y’ ÷ 4⌋ − ⌊y’ ÷ 100⌋ + ⌊y’ ÷ 400⌋ − 32045
This JDN is valid at 12:00 noon Universal Time. To get the full Julian Date at any time of day, add the time fraction:
JD = JDN + (UT_hours − 12) ÷ 24 MJD = JD − 2,400,000.5
Worked Example
Convert 20 June 2024 at 00:00 UT:
- Julian Day Number (at noon) = 2,460,482
- JD at 00:00 = 2,460,482 + (0 − 12) ÷ 24 = 2,460,481.5
- MJD = 2,460,481.5 − 2,400,000.5 = 60,481.0
- Ordinal date = the 172nd day of 2024 → 2024-172, or YYDDD form 24172
| Date / time (UT) | Julian Date (JD) | MJD |
|---|---|---|
| 2000-01-01 12:00 | 2,451,545.0 | 51,544.5 |
| 2000-01-01 00:00 | 2,451,544.5 | 51,544.0 |
| 2024-06-20 00:00 | 2,460,481.5 | 60,481.0 |
Two Meanings of “Julian Date”
It is worth knowing which “Julian date” you need. The astronomical Julian Day is a continuous count starting in 4713 BC and is ideal for calculating the number of days between two events. The ordinal date (YYDDD) is a compact label — the year followed by the day number from 1 to 365 or 366 — widely used on manufacturing lot codes, food packaging, and mainframe systems. This calculator shows both so you are covered either way.
Why Use Julian Dates?
Because the Julian Date is a single increasing number, subtracting one JD from another instantly gives the exact number of days (and fractions of a day) between two moments, with no need to worry about month lengths or leap years. That makes it the standard time scale for astronomy, satellite tracking, and any software that needs unambiguous, calendar-free date arithmetic.
Frequently asked questions
What is a Julian date?+
The term has two meanings. In astronomy, the Julian Date (JD) is a continuous count of days since noon on 1 January 4713 BC, used to make time intervals easy to compute. In IT and aviation, the Julian date often means the ordinal date — the year plus the day-of-year, like 24172 for the 172nd day of 2024.
How do you calculate the Julian Day Number?+
Use the formula JDN = day + floor((153m'+2)/5) + 365y' + floor(y'/4) − floor(y'/100) + floor(y'/400) − 32045, where for January and February you treat them as months 13 and 14 of the previous year. The result is the integer day count valid at 12:00 noon Universal Time.
What is the Modified Julian Date (MJD)?+
The Modified Julian Date is the Julian Date minus 2,400,000.5. It was introduced to use smaller numbers and to start the day at midnight instead of noon. MJD day zero is the night of 17 November 1858.
Why does the Julian Day start at noon?+
Astronomers chose noon so that a single night of observation falls within one Julian Day rather than being split across a midnight date change. As a result, the Julian Date is a whole number at 12:00 UT and ends in .5 at midnight UT.
What is the Julian Date of January 1, 2000?+
At 12:00 UT on 1 January 2000 (the J2000.0 epoch), the Julian Date is exactly 2,451,545.0. At midnight (00:00 UT) the same day it is 2,451,544.5, because the Julian Day begins at noon.