Julian Date Calculator
The Julian Day Number is a continuous count of solar days used by astronomers, historians, and software engineers to simplify date arithmetic across different calendar systems. Rather than working with months of varying lengths, leap years, and calendar reform boundaries, a Julian Day Number reduces any date to a single integer, making it trivial to calculate the exact number of days between two events separated by centuries. The system was introduced in 1583 by Joseph Scaliger and is anchored to noon on January 1, 4713 BC in the proleptic Julian calendar. This calculator implements the algorithm from Jean Meeus's Astronomical Algorithms (Willmann-Bell), the definitive modern reference for calendar conversions. It supports two conversion modes: Gregorian to Julian Day Number (with Modified Julian Date as a secondary output), and Julian Day Number back to Gregorian date. The Modified Julian Date equals JDN minus 2,400,000.5 and is widely used in modern applications such as satellite tracking and geodesy because it fits in smaller numeric fields and starts at midnight rather than noon.
Julian Day Number formula (Jean Meeus, Chapter 7)
The algorithm below converts a Gregorian calendar date to a Julian Day Number. It accounts for the Gregorian calendar reform by applying the correction factor B only for dates on or after October 15, 1582. The inverse algorithm converts a JDN back to a Gregorian date.
If M <= 2: Y = Y - 1; M = M + 12
A = Math.floor(Y / 100)
B = 2 - A + Math.floor(A / 4)
JDN = Math.floor(365.25 * (Y + 4716)) + Math.floor(30.6001 * (M + 1)) + D + B - 1524.5
MJD = JDN - 2400000.5
JDN to Gregorian:
Z = JDN + 0.5; A = Math.floor(Z)
If A >= 2299161: alpha = Math.floor((A - 1867216.25) / 36524.25)
A = A + 1 + alpha - Math.floor(alpha / 4)
B = A + 1524; C = Math.floor((B - 122.1) / 365.25)
D = Math.floor(365.25 * C); E = Math.floor((B - D) / 30.6001)
day = B - D - Math.floor(30.6001 * E)
month = (E < 14) ? E - 1 : E - 13
year = (month > 2) ? C - 4716 : C - 4715
Worked example
For January 1, 2000 (Gregorian):
- Y = 1999, M = 13, D = 1 (January adjusted)
- A = 19, B = 2 - 19 + 4 = -13
- JDN = 2451544 + 1 + (-13) + 1 = 2,451,545
- MJD = 2,451,545 - 2,400,001 = 51,544
Julian date calculator: frequently asked questions
What is a Julian Day Number?
A Julian Day Number (JDN) is a continuous count of days since the beginning of the Julian Period on January 1, 4713 BC (in the proleptic Julian calendar), at noon Universal Time. It is widely used in astronomy and chronology because it eliminates the complexity of months, leap years, and calendar system changes, making it easy to calculate the number of days between any two historical dates.
Is Julian Day Number the same as the Julian calendar?
No. The Julian Day Number is an astronomical counting system invented by Joseph Scaliger in 1583. The Julian calendar is the predecessor to the Gregorian calendar, introduced by Julius Caesar in 46 BC. The naming similarity is coincidental: Julian Day Numbers are named after Scaliger's father, Julius Caesar Scaliger, not after Julius Caesar or the Julian calendar.
What is the Modified Julian Date?
The Modified Julian Date (MJD) equals the Julian Day Number minus 2,400,000.5. This offset shifts the epoch to midnight on November 17, 1858, and reduces the number of digits needed to express modern dates. MJD is commonly used in satellite tracking, geodesy, and modern astronomical software.
What is today's Julian Day Number?
The Julian Day Number changes at noon Universal Time each day. In mid-2026 the JDN is approximately 2,461,000. Enter today's date in the calculator above to find the exact current JDN.
Who created Julian Day Numbers?
Joseph Justus Scaliger introduced the Julian Day system in 1583, in his work Opus de emendatione temporum. He named the period after his father, the Renaissance scholar Julius Caesar Scaliger, not after Julius Caesar the Roman general or the Julian calendar.
Official sources
- Jean Meeus, Astronomical Algorithms (Willmann-Bell, 2nd ed. 1998) - Chapter 7: Julian Day.
- Astronomical applications and calendar resources: US Naval Observatory.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.