How to use the julian date calculator
- Pick the direction: calendar date to Julian Date, Julian Date to calendar date, or year and day of year to calendar date.
- For a calendar date, enter the date and the time in UTC. Leave the time blank for midnight. Open More options to add seconds.
- For a Julian Date, enter the number and choose whether it is a JD or a Modified Julian Date.
- Read the results, including the day of the year (ordinal date) for the date you entered.
Formula
JDN = day + floor((153 m + 2) / 5) + 365 y + floor(y / 4) - floor(y / 100) + floor(y / 400) - 32045
where a = floor((14 - month) / 12), y = year + 4800 - a and m = month + 12 a - 3
JD = JDN + (hour - 12) / 24 + minute / 1440 + second / 86400
MJD = JD - 2400000.5
The Julian Date is a continuous count of days used by astronomers. A Julian day starts at noon UTC, which is why midnight ends in .5.
Worked examples
The J2000 epoch: noon UTC on January 1, 2000 has a Julian Day Number of 2451545, and the time part is (12 - 12) / 24 = 0, so JD = 2451545.0. The Modified Julian Date is 2451545.0 - 2400000.5 = 51544.5.
Midnight: 00:00 UTC on January 1, 2000 is half a day earlier, so JD = 2451544.5.
October 10, 2026 at 00:00 UTC: JD 2461323.5 and MJD 61323.0. It is day 283 of 365 in the ordinal sense.
Back to a date: MJD 60000 converts to February 25, 2023 at 00:00:00 UTC.
Two meanings of "Julian day"
Astronomers use the Julian Date, a running count of days and fractions of days since noon on January 1, 4713 BC in the Julian calendar. The Modified Julian Date subtracts 2400000.5, so it starts at midnight on November 17, 1858 and the numbers stay shorter.
In other settings, "Julian day" or "Julian date" simply means the day of the year, from 1 to 365 or 366, sometimes written as a two-digit year plus a three-digit day. This tool shows both so you can tell which one you need. They are unrelated calculations that happen to share a name.
Precision and range
Julian Dates are shown to six decimal places, which is about 0.09 seconds. Converting back rounds to the nearest second. Supported dates run from January 1, 1000 (JD 2086302.5) to the end of year 9999.
Dates are read as UTC in the Gregorian calendar, extended backward. Astronomical tables for dates before October 15, 1582 use the Julian calendar, so those entries will not match this tool day for day.
Assumptions and limits
- The input is a UTC date and time. Time zones and daylight saving time are not applied.
- The Gregorian calendar is extended backward before 1582.
- Results are rounded to six decimal places for JD and MJD, and to the nearest second for dates.
- Leap seconds and the difference between UTC and astronomical time scales (such as TT) are not modeled.
Frequently asked questions
What is the Julian Date for January 1, 2000 at noon?
It is 2451545.0, which is the J2000.0 reference epoch (that epoch is strictly defined in Terrestrial Time, a minute or so away from UTC). Midnight at the start of that day is 2451544.5.
What is the difference between JD and MJD?
MJD equals JD minus 2400000.5. It starts counting at midnight on November 17, 1858 instead of noon on an ancient date, so recent values have five digits instead of seven.
Is a Julian date the same as a Julian calendar date?
No. The Julian calendar is an old civil calendar from Julius Caesar. A Julian Date is a day count that scientists use, and it is the same no matter which calendar you use to write the date.
How do I find the day number within the year?
Enter the date and read "Day of the year (ordinal)". October 10, 2026 is day 283. You can also go the other way with the year and day of year option.