Julian Date Converter

Julian Date (JD) is a continuous count of days from noon on January 1, 4713 BC (Julian Calendar). It provides a universal timescale for astronomy, eliminating confusion from calendar systems, time zones, and leap years.

Key epoch values:

• J2000.0 = JD 2451545.0 = January 1.5, 2000 (noon on Jan 1, 2000 UTC)
• J1950.0 = JD 2433282.5
• Unix epoch = JD 2440587.5 (January 1, 1970 00:00 UTC)

Modified Julian Date (MJD):

MJD = JD - 2400000.5

MJD starts at midnight rather than noon and is used for modern satellite tracking and space missions. MJD = 0 corresponds to November 17, 1858 (0h UTC).

The algorithm: For a date (Y, M, D) in the Gregorian calendar:

A = floor(Y / 100)
B = 2 - A + floor(A / 4)
JD = floor(365.25 × (Y + 4716)) + floor(30.6001 × (M + 1)) + D + B - 1524.5

For months January and February, use Y−1 and M+12.

Why noon? Julian Dates change at noon (12:00 UTC) rather than midnight. This was historically convenient for astronomers observing throughout the night — the date never changed during a single night’s observations.

J2000 epoch offset: Tells you how many days have elapsed since the J2000.0 epoch. Many orbital mechanics calculations use this as a reference.

Why the day starts at noon. The odd half-day offset is not an accident. Joseph Scaliger set the epoch in 1583, and astronomers work at night, so starting the count at noon keeps a single night’s observations inside one Julian Day instead of splitting them across a midnight rollover. That convenience is also why Modified Julian Date exists: MJD strips off the leading 2400000.5, which both shrinks the number and moves the start back to midnight, which suits satellite tracking and other daytime work better.

A caution on dates before 1582. The conversion here is purely Gregorian in both directions, so a date before the Gregorian reform of October 1582 is treated as proleptic Gregorian rather than as the Julian calendar that was actually in use. The two directions remain exact inverses of each other, but a historical date from, say, 1500 will not match what a contemporary would have written.