Julian Day Number Converter

1. What is a Julian Day Number?

A Julian Day Number (JDN) is a single integer assigned to each day, counting continuously from noon on 1 January 4713 BC in the Julian calendar. Today, 27 October 2026, is JDN 2,461,341. Yesterday was 2,461,340 and tomorrow will be 2,461,342. There are no months, no leap years and no eras in the count itself — the number is the date, and the interval between any two dates is a subtraction.

The day starts at noon, not midnight, and that is deliberate. Astronomers observe at night, and a midnight boundary would split a single night’s observations across two days. Starting the day at noon keeps the whole night on one number. A Julian Day Number is therefore the number of the day that begins at noon UTC on the date shown.

2. Where the count comes from

The count was proposed by Joseph Scaliger in 1583 and named after his father, Julius — it has nothing to do with Julius Caesar’s calendar except through the name. Scaliger chose his epoch by combining three cycles: the 28-year solar cycle, the 19-year Metonic lunar cycle and the 15-year indiction cycle. Their least common multiple is 28 × 19 × 15 = 7,980 years, the Julian period, and Scaliger placed its start far enough back that every recorded astronomical event would have a positive number: noon on 1 January 4713 BC.

The system caught on because it solves a real problem. Historical chronology before the count meant juggling Roman consuls, regnal years, Olympiads and competing calendars. A single running number made it possible to say, unambiguously, how many days passed between two events recorded in different systems. Astronomy adopted it for the same reason, and computing followed: day numbers are the easiest dates to store, sort and subtract.

3. How a date becomes a number

The conversion used here is the Fliegel–Van Flandern algorithm for the Gregorian calendar. In outline: months January and February are treated as months 13 and 14 of the previous year (so the leap day falls at the end of the “year” being counted), then the day number is built from the day of the month, the accumulated months, the years, and the Gregorian century corrections — the rule that century years are leap years only when divisible by 400.

Traced for 1 January 2000: January counts as month 13 of 1999, giving the intermediate values 6,799 (adjusted year) and 10 (adjusted month). The parts are 1 (day) + 306 (months) + 2,481,635 (years) + 1,699 (leap days) − 67 (century correction) + 16 (400-year correction) − 32,045 (epoch offset) = 2,451,545, which is the J2000 epoch — a useful check, because J2000 is independently defined as JD 2,451,545.0.

Traced for today, 27 October 2026: the adjusted year is 6,826 and the adjusted month is 7, giving 27 + 214 + 2,491,490 + 1,706 − 68 + 17 − 32,045 = 2,461,341. The inverse conversion runs the same arithmetic backwards and is checked by round-tripping: every day number in the supported range converts back to the date it came from.

4. JDN, Julian Date and Modified Julian Date

Three related numbers are easy to confuse. The Julian Day Number (JDN) is the integer for the day starting at noon. The Julian Date (JD) is the continuous count including fractions of a day: JD at noon on a date equals its JDN exactly (written with “.0”), and JD at midnight at the start of that date is JDN − 0.5. If you need the time as well as the day, you want the Julian Date; if you need the day alone, you want the JDN.

The Modified Julian Date (MJD) is a smaller, midnight-based variant created for space tracking, where seven-digit numbers and noon starts were both inconvenient: MJD = JD − 2,400,000.5. At midnight at the start of a date, MJD = JDN − 2,400,001; at noon it is JDN − 2,400,000.5. This converter shows the midnight MJD, which is the value most tables quote: 17 November 1858 is MJD 0, 1 January 2000 is MJD 51,544, and today is MJD 61,340.

5. Famous dates as day numbers

Some dates are easier to remember as day numbers than as calendar dates, and several famous ones double as checks on this converter. The Gregorian reform’s first day, 15 October 1582, is JDN 2,299,161. The Modified Julian Date epoch, 17 November 1858, is JDN 2,400,001. The Unix epoch, 1 January 1970, is JDN 2,440,588 — which is why Unix time and Julian dates convert into each other with one line of arithmetic.

Apollo 11 launched on 16 July 1969 (JDN 2,440,419, a Wednesday) and landed on 20 July 1969 (JDN 2,440,423, a Sunday) — four days apart by subtraction, as they should be. The Berlin Wall fell on 9 November 1989 (JDN 2,447,840, a Thursday). The J2000 epoch, 1 January 2000, is JDN 2,451,545, a Saturday. And the leap day 29 February 2024 is JDN 2,460,370.

6. What day numbers are used for

Astronomers use Julian Dates for everything from variable-star observations to spacecraft navigation, because the interval between two observations must be exact to the second and calendar arithmetic is a minefield of leap years and reforms. Ephemeris tables, eclipse predictions and satellite passes are all published against Julian Dates.

Outside astronomy, day numbers are the quiet workhorse of date arithmetic. Any program that needs “how many days between these two dates” converts both to day numbers and subtracts — including, in spirit, the date tools on this site. Unix time is the same idea with seconds instead of days: Unix seconds = (JD − 2,440,587.5) × 86,400, because the Unix epoch is JD 2,440,587.5 at midnight on 1 January 1970.

7. Gregorian dates, Julian dates — read this before 1582

This converter uses the proleptic Gregorian calendar for every year from 1 to 9999: it applies the Gregorian leap rule backwards before 1582, as if the Gregorian calendar had always existed. That is the standard convention for day-number conversion, but it is not how dates were written at the time. Before the reform, Europe used the Julian calendar, and the two calendars label the same day differently.

The concrete case: entering 4 October 1582 gives JDN 2,299,150, the proleptic Gregorian reading of that label — a Monday. But the day people at the time called 4 October 1582, the last day of the Julian calendar, is JDN 2,299,160, a Thursday, the day before the reform’s first Gregorian day (15 October 1582, JDN 2,299,161). Ten calendar labels were skipped, but only one day of time passed. If you are converting a historical date recorded before the reform, convert its Julian-calendar label with a Julian-calendar converter, not this one — or remember that the two readings differ by the accumulated drift, which was 10 days in 1582 and shrinks by about 3 days every 400 years going back.

8. Limits of this converter

The supported range is years 1 to 9999, JDN 1,721,426 to 5,373,484. The count itself extends back to 4713 BC, but this tool does not convert BC dates: year numbering before year 1 (no year zero in the BC/AD system, astronomical year numbering differs) is a separate source of errors, and the tool declines to guess rather than risk a wrong number.

Times are not converted. A Julian Day Number is a day, not a moment; for moments you need the fractional Julian Date, which this tool shows only at noon and midnight. The difference between Terrestrial Time (the astronomers’ uniform scale) and UTC (the civil scale, with leap seconds) is about 69 seconds in 2026 — immaterial for a day number except within about a minute of noon, where the two scales can disagree about which day it is.

9. Related Calculators

If this tool is not quite the question you are asking, a neighbouring calculator probably is:

11. Methodology & Data Integrity

Method: the engine uses the Fliegel–Van Flandern algorithm for the Gregorian calendar (January and February counted as months 13 and 14 of the previous year, with the Gregorian century corrections), and the standard inverse algorithm for JDN-to-date. Weekday is (JDN + 1) mod 7 with 0 = Sunday. MJD at midnight is JDN − 2,400,001; days since J2000 is JDN − 2,451,545. All arithmetic is integer arithmetic — no Date objects, so years 1–99 convert correctly.

Verification: the engine was checked against hand-verified values (J2000 2,451,545; Unix epoch 2,440,588; MJD epoch 2,400,001; Gregorian reform 2,299,161; range ends 1,721,426 and 5,373,484), against Python’s proleptic Gregorian ordinal plus 1,721,425 on 14 dates including year 42 and leap days, and by full round-trip sweeps (every 37th JDN across the whole range and every month-end in years 1–120) — all matched exactly.

Worked examples in this page were computed by the same engine: 27 October 2026 is JDN 2,461,341 (Tuesday, MJD 61,340); Apollo 11 launched 16 July 1969 (2,440,419) and landed 20 July 1969 (2,440,423); the Berlin Wall fell 9 November 1989 (2,447,840); 29 February 2024 is JDN 2,460,370.

Limits: Gregorian calendar only, proleptic before 1582; years 1–9999 only, no BC dates; day numbers only, no fractional times beyond noon/midnight; Terrestrial Time vs UTC differs by about 69 seconds, immaterial except within about a minute of noon.