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Julian Date Calculator

Converts a Gregorian calendar date and time (in UTC or an IANA zone) to the astronomical Julian Day Number, Julian Date (JD), Modified Julian Date (MJD), Truncated Julian Date, days since the J2000.0 epoch and Julian centuries, plus day of year and ISO week.

When to use

You need JD/MJD values for astronomy, satellite or ephemeris work, or want to know the day count between dates via Julian Day Numbers.

Do not use when: You mean the 'Julian date' used in food packaging or the military (a day-of-year number such as 2026-266; see day-of-week for day of year) or Unix epoch seconds (use unix-timestamp).

Formula

a = ⌊(14 − month)/12⌋, y = year + 4800 − a, m = month + 12a − 3; JDN = day + ⌊(153m + 2)/5⌋ + 365y + ⌊y/4⌋ − ⌊y/100⌋ + ⌊y/400⌋ − 32045; JD = JDN − 0.5 + (hours_UT / 24); MJD = JD − 2400000.5

Proleptic Gregorian calendar; times are converted to UT via the tz database before the day fraction is added. Leap seconds and the ~69 s difference between UT and Terrestrial Time are ignored (relevant only for sub-minute ephemeris work).

Inputs

Parameter	Type	Required	Description
`date`	date	default today	Gregorian calendar date (YYYY-MM-DD); defaults to the current UTC date.
`time`	string	default 00:00	Time of day, 24-hour HH:MM (seconds optional), in time_zone.
`time_zone`	string	default UTC	IANA zone of the given date and time; JD is always expressed in Universal Time.

Outputs

Output	Type	Unit	Description
`julian_day_number`	integer		Integer day count of the UTC calendar date (the JD at 12:00 UT that day); JDN 0 = 1 January 4713 BC (Julian).
`julian_date`	number	days	Days since noon UT on 1 January 4713 BC, with the fraction of the day since noon.
`modified_julian_date`	number	days	JD − 2,400,000.5 (starts at midnight UT on 17 November 1858).
`truncated_julian_date`	integer		⌊JD − 2,440,000.5⌋, NASA convention counting from 24 May 1968.
`days_since_j2000`	number	days	JD − 2,451,545.0 (J2000.0 = 2000-01-01 12:00 TT, taken here as UT).
`julian_century`	number		(JD − 2,451,545) / 36,525, the T used in astronomical formulas.
`utc_datetime`	string		The instant in UTC (ISO 8601).
`day_of_week`	string		Day of the week of the UTC date.
`day_of_year`	integer		Ordinal day of the UTC date, 1 January = 1.
`iso_week_date`	string		UTC date in ISO 8601 week notation YYYY-Www-D.

Example

J2000.0 epoch: 2000-01-01 12:00 UTC: {"date":"2000-01-01","time":"12:00","time_zone":"UTC"} → {"julian_day_number":2451545,"julian_date":2451545,"modified_julian_date":51544.5,"truncated_julian_date":11544,"days_since_j2000":0,"julian_century":0,"day_of_week":"Saturday","day_of_year":1,"iso_week_date":"1999-W52-6"}

MJD epoch: 1858-11-17 00:00 UTC: {"date":"1858-11-17","time":"00:00"} → {"julian_date":2400000.5,"modified_julian_date":0,"julian_day_number":2400001,"day_of_week":"Wednesday"}

GET https://tttkmbb.com/api/v1/calculate/julian-date?date=2000-01-01&time=12%3A00&time_zone=UTC

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/julian-date (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/julian-date · Markdown: https://tttkmbb.com/time/julian-date.md · JSON definition: https://tttkmbb.com/time/julian-date.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="julian-date"
OpenAPI operationId: convert_julian_date
Freshness: daily. Authentication: none. Rate limit: fair use (see rate limits).

Sources

USNO Astronomical Applications – Julian Date Converter (government)
Julian day – JDN algorithms and epochs (Wikipedia) (reference)

FAQ

Why does the Julian Date have a .5 at midnight?

Julian days begin at noon UT, so midnight falls halfway through a Julian day: 2000-01-01 00:00 UT is JD 2451544.5 and 12:00 UT is JD 2451545.0. MJD shifts the origin to midnight to avoid this.

Is the Julian Date related to the Julian calendar?

Only historically; the count was proposed by Joseph Scaliger in 1583 and named after his father Julius. The calendar date entered here is Gregorian.

Related calculators

Unix Timestamp Converter — Unix epoch value of the same instant.
Day of the Week Calculator — Weekday and ordinal day of year of a date.
Date Difference Calculator — Days between two dates (equal to the JDN difference).