What is a Julian Day Number?

The Julian Day Number (JDN) is a continuous count of whole days since noon UTC on 1 January 4713 BC in the proleptic Julian calendar. It is widely used in astronomy and software because it turns dates into a single running integer that is easy to subtract.

What is the difference between JD and MJD?

The Julian Date (JD) adds the fractional day measured from noon UTC, so JD increments at midday. The Modified Julian Date (MJD) is JD minus 2,400,000.5, which shifts the day boundary to midnight and gives smaller, more convenient numbers for modern dates.

Does this work for historical dates?

The calculation uses the proleptic Gregorian calendar for the input date, so it is consistent for any year you enter, but dates before the Gregorian reform of 1582 will differ from contemporary Julian-calendar records.

Julian Day Number Calculator

Julian Day Number, JD and MJD

Astronomers and software use the Julian Day count to turn calendar dates into a single running number, so the days between any two events is just a subtraction. This tool converts a Gregorian calendar date (and an optional UTC time) into its Julian Day Number (JDN), the full Julian Date (JD) with a fractional day, and the Modified Julian Date (MJD).

How it works

The JDN is computed with the standard integer algorithm. For a date with month m and year y:

a = ⌊(14 − m) / 12⌋
JDN = day + ⌊(153·(m + 12a − 3) + 2) / 5⌋
        + 365y' + ⌊y'/4⌋ − ⌊y'/100⌋ + ⌊y'/400⌋ − 32045

where y' = y + 4800 − a. This counts whole days from noon UTC on 1 January 4713 BC in the proleptic Julian calendar. The fractional day is measured from noon — (hour − 12)/24 + minute/1440 — so JD increments at midday. The Modified Julian Date shifts the boundary to midnight: MJD = JD − 2,400,000.5.

Quantity	Definition
JDN	whole days since noon 1 Jan 4713 BC
JD	JDN plus the fraction of a day since noon UTC
MJD	JD − 2,400,000.5 (day starts at midnight)

Example

For 2000-01-01 at 12:00 UTC, the JDN is 2451545, the JD is 2451545.0 (noon means zero fraction), and the MJD is 2451545.0 − 2400000.5 = 51544.5. Subtract two JDNs — say this date and 2000-01-31 — to get exactly 30 days.

All of it is computed in your browser.