Julian Date Converter
Quick answer: A Julian Day Number (JDN) is a continuous day count used by astronomers, starting at noon on January 1, 4713 BC. October 13, 2026 (a Tuesday) is JDN 2,461,327, computed with the standard Fliegel–Van Flandern algorithm. The converter above translates both directions: Gregorian date to JDN and JDN back to Gregorian date.
Convert any Gregorian calendar date to its Julian Day Number (JDN) and back with this free Julian date converter. It uses the Fliegel–Van Flandern algorithm — the standard astronomical method — so the numbers match the values used in astronomy and software date math.
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Proleptic Gregorian calendar. Integer JDN counts whole days; the astronomical day starts at noon UTC.
How to use this calculator
Enter a year, month, and day to get its Julian Day Number, weekday, and day-of-year. To go the other way, type a Julian Day Number into the second field and the matching Gregorian date appears below. Everything recalculates instantly as you type.
How this is calculated
This page uses the Fliegel–Van Flandern algorithm, the standard astronomical method for Gregorian-to-JDN conversion:
- If month ≤ 2, subtract 1 from the year and add 12 to the month.
- A = ⌊year ÷ 100⌋; B = 2 − A + ⌊A ÷ 4⌋
- JDN = ⌊365.25 × (year + 4716)⌋ + ⌊30.6001 × (month + 1)⌋ + day + B − 1524
The reverse direction uses the inverse Fliegel–Van Flandern steps to recover year, month, and day from a JDN. Weekday follows from JDN mod 7, where a remainder of 0 is Monday through 6 is Sunday.
Assumptions and edge cases: dates are interpreted in the proleptic Gregorian calendar (the Gregorian rules extended backward before 1582), which is the convention astronomers use. The integer JDN counts days beginning at noon UTC; fractional times of day are not handled. Input years are limited to 1–9999.
Worked example
Convert October 13, 2026 (a Tuesday) to its Julian Day Number. Month (10) is greater than 2, so no year adjustment is needed:
- A = ⌊2026 ÷ 100⌋ = 20; B = 2 − 20 + ⌊20 ÷ 4⌋ = −13
- JDN = ⌊365.25 × 6742⌋ + ⌊30.6001 × 11⌋ + 13 − 13 − 1524 = 2,462,515 + 336 + 13 − 13 − 1524 = 2,461,327
Cross-check: the widely used epoch JDN 2,451,545 corresponds to January 1, 2000, and October 13, 2026 is 9,782 days later, giving 2,451,545 + 9,782 = 2,461,327 — the same result. Converting 2,461,327 back through the inverse algorithm returns 2026-10-13.
Reference data
This tool is pure math — no external data table is used. It names its method instead: the Fliegel–Van Flandern algorithm for the proleptic Gregorian calendar, with the astronomical epoch that JDN 2,451,545 = 2000-01-01 as its reference anchor.
Frequently asked questions
What is a Julian Day Number?
A Julian Day Number (JDN) is a continuous count of days since the start of January 1, 4713 BC in the proleptic Julian calendar. Astronomers use it because it makes calculating the number of days between any two dates simple subtraction, with no months or leap years to handle.
How do I convert a date to a Julian date?
Enter the year, month, and day in the converter above. It applies the Fliegel–Van Flandern algorithm, the standard astronomical formula, to compute the Julian Day Number instantly.
What is the difference between a Julian date and a Julian Day Number?
A Julian Day Number is the integer day count used in astronomy. Separately, some industries (like the military and manufacturers) use a Julian date format such as YYDDD, meaning the two-digit year followed by the day of the year. This converter computes the astronomical Julian Day Number.
Can I convert a Julian Day Number back to a calendar date?
Yes. Enter the Julian Day Number in the reverse converter section and it returns the matching Gregorian calendar date, using the inverse of the Fliegel–Van Flandern algorithm.