Julian Date Converter

A Julian date converter turns an ordinary calendar date into a running day count and back again. September 6, 2026 is Julian Day Number 2461290; at 14:30 Universal Time the full Julian Date is 2461290.10417, the Modified Julian Date is 61289.60417, and the ordinal code printed on packaging that day is 26249. This page converts all four forms in both directions.

Three sister tools cover the neighboring questions: the Week Number Calculator gives the ISO 8601 week for a date, the Date Calculator adds or subtracts days from a date, and the Business Days Calculator counts working days between two dates. Use this page when you need the day number itself, whether that is a seven-digit astronomical count or a five-digit factory code.

Two very different things are called a Julian date

Almost every Julian date problem starts here, so separate the two meanings before converting anything.

• The astronomical Julian Date. A continuous count of days that begins at noon on January 1, 4713 BC in the Julian calendar (November 24, 4713 BC in the proleptic Gregorian calendar). It never resets, so it is always a seven-digit number today, and the difference between two of them is simply a number of days.
• The ordinal or manufacturing Julian date. A short code of the form YYDDD, where the first two digits are the year and the last three are the day of the year. It resets every January 1 and only ever runs from 001 to 365, or 366 in a leap year. Food plants, pharmaceutical lots, airline maintenance records and government forms all use it.

Neither one has anything to do with the Julian calendar, the calendar system that the Gregorian calendar replaced. The shared name is a historical accident, and this converter reads and writes calendar dates in the Gregorian system throughout.

How the Julian Day Number is calculated

The standard conversion is the integer algorithm published by Fliegel and Van Flandern in 1968. It needs no lookup tables and no leap-year branching, which is why it has survived in astronomy libraries for decades. First compute a small correction term that pushes January and February into the previous year:

Then the Julian Day Number follows directly from the year y, month m and day d:

Every division there is integer division that discards the remainder. The three terms do recognizable work: the first counts the four-year leap cycle, the second turns the month into a running day offset, and the third removes the century days the Gregorian rule skips. For the full Julian Date with a time of day, add the fraction of a day measured from noon:

Worked example: September 6, 2026 at 14:30 UT

Take y = 2026, m = 9, d = 6. Because the month is later than February, the correction term is a = trunc((9 − 14) ÷ 12) = 0. Now the three main terms:

• (1461 × (2026 + 4800 + 0)) ÷ 4 = (1461 × 6826) ÷ 4 = 2,493,196
• (367 × (9 − 2 − 0)) ÷ 12 = 2,569 ÷ 12 = 214
• (3 × (6,926 ÷ 100)) ÷ 4 = (3 × 69) ÷ 4 = 207 ÷ 4 = 51

Put them together: 2,493,196 + 214 − 51 + 6 − 32,075 = 2,461,290. So JDN = 2461290, which by convention is written without commas. The time 14:30 UT is 2.5 hours after noon, which is 2.5 ÷ 24 = 0.10417 of a day, so the full Julian Date is JD 2461290.10417. Subtract the offset 2,400,000.5 and the Modified Julian Date is MJD 61289.60417. September 6 is day 249 of 2026, so the ordinal code that day is 26249, or 2026249 in the seven-digit form. The weekday falls out of the day number too: (2461290 + 1) mod 7 = 0, and 0 means Sunday.

Converting a Julian Day Number back to a calendar date

The reverse algorithm is the same paper's inverse, and it is just as mechanical. Starting from JDN = 2461290, each line uses integer division:

1. l = 2461290 + 68,569 = 2,529,859
2. n = (4 × l) ÷ 146,097 = 69 (this is the Gregorian 400-year cycle count)
3. l = l − (146,097n + 3) ÷ 4 = 9,685
4. i = (4,000 × (l + 1)) ÷ 1,461,001 = 26 (the year within the cycle)
5. l = l − (1461i) ÷ 4 + 31 = 220
6. j = (80 × l) ÷ 2,447 = 7, and the day is d = l − (2447j) ÷ 80 = 6
7. With k = j ÷ 11 = 0, the month is m = j + 2 − 12k = 9 and the year is y = 100 × (n − 49) + i + k = 2026

The result is September 6, 2026, which closes the loop. Starting from a Julian Date with decimals, take JDN = floor(JD + 0.5) first and keep the leftover fraction: multiply it by 24 to recover the hour, remembering that .5 means midnight because the Julian day begins at noon.

Modified Julian Date and the other shortened counts

Seven-digit numbers are awkward to store and easy to mistype, so several fields subtract a fixed offset. The most common is the Modified Julian Date, JD − 2,400,000.5. The half-day is deliberate: it moves the day boundary from noon back to midnight, so an MJD rolls over when the calendar date does. The epochs you are most likely to meet, all at Universal Time:

Two useful consequences: a Unix timestamp is (JD − 2440587.5) × 86,400 seconds, and the days since J2000.0 that appear in orbital formulas are simply JD − 2451545.0.

The ordinal Julian date used in manufacturing

In a warehouse, the "Julian date" on a carton is the ordinal code. It is compact, it sorts correctly as text within a year, and a line can stamp it without any month arithmetic. The rules are short: the day of the year runs from 001 on January 1 to 365 on December 31, or 366 in a leap year, and the year is usually abbreviated to two digits. So 26249 is day 249 of 2026 and 25365 is December 31, 2025.

The trap is the two-digit year: a code alone cannot say whether 26249 means 2026, 1926 or 2126, so the reading depends on context such as a product's shelf life. Where accuracy matters, plants print the seven-digit YYYYDDD form instead, sometimes with a shift or line letter after the digits. This converter accepts both lengths.

Ordinal Julian date reference table for 2026

2026 is a common year with 365 days. This table shows the day of the year, the ordinal code and the Julian Day Number for the first of each month, so you can read almost any 2026 code without a computer: find the row, then add the day of the month minus one.

The last column is the day of the year for the same month in a leap year such as 2028. Everything from March 1 onward shifts up by exactly one, which is the single rule you need to remember when reading old codes.

A second worked example: decoding the code 26249

A case of product is stamped 26249 and you want the pack date. Split the code: the year part is 26 and the day part is 249. Assume the current century, so the year is 2026, a common year with 365 days, which means 249 is a valid day number. Now walk the reference table above: September 1 is day 244, so day 249 is 244 + 5, which lands on September 6, 2026. Checking it the other way, the Julian Day Number for January 1, 2026 is 2461042, so day 249 is 2461042 + 248 = 2461290, and converting that number back gives September 6, 2026 as expected. If the code had instead read 25365, it would mean December 31, 2025.

Julian Day Numbers for landmark 2026 and 2027 dates

These are the values for 00:00 Universal Time on each date, which is why the Julian Date column ends in .5 rather than .0.

Notice how easy day arithmetic becomes: December 31, 2026 minus January 1, 2026 is 2461406 − 2461042 = 364 days, exactly one day short of the 365-day year because both endpoints are counted once.

How to use this Julian date converter

The tool has three modes, and the buttons at the top switch between them:

1. Date to Julian. Pick a calendar date and a time in Universal Time. The result card shows the Julian Date, the Julian Day Number, the Modified Julian Date and the ordinal code at once. Leave the time at 00:00 if you only care about the day.
2. Julian to date. Choose whether your number is a JD with decimals, a whole JDN, or an MJD, then type it in. You get back the calendar date, weekday, clock time in UT and day of the year.
3. Ordinal code. Type a five-digit YYDDD or seven-digit YYYYDDD code from a label. For the short form, use the century switch to place the two-digit year in the 1900s or the 2000s.

Below the result there is a reference table for whichever year is currently in view, listing the day of the year, ordinal code and Julian Day Number for the first of every month. That table is the fastest way to convert several codes from the same year by hand.

Who this converter is for

• Quality and warehouse staff decoding a lot code or a pack date on a carton or pallet label.
• Astronomers logging an observation or reading a variable-star epoch quoted in JD.
• Developers and analysts moving between Julian day counts, MJD and Unix timestamps in scientific data files, satellite telemetry or legacy records.
• Aviation and maintenance technicians reading work orders and part tags that carry ordinal dates.
• Anyone with a mystery five-digit number on a package who wants to know what day it was made.

Key terms explained

• Julian Day Number (JDN): the whole-number count of days since the start of the Julian Period. It names a full day, from noon UT to the next noon UT.
• Julian Date (JD): the same count carried to decimals so it names an instant. The fraction is the elapsed part of a day measured from noon.
• Modified Julian Date (MJD): JD − 2,400,000.5, a shorter number whose day starts at midnight.
• Ordinal date: a year plus a day-of-year number, written YYDDD or YYYYDDD. This is the "Julian date" of industry and the ordinal date format of ISO 8601.
• Proleptic Gregorian calendar: the Gregorian calendar rules extended backward before 1582, which is what date libraries and this converter use so that arithmetic stays consistent.
• Universal Time (UT): the time scale Julian Dates are quoted in. It is the basis of the civil clock at the Greenwich meridian, with no daylight saving shift.
• Epoch: a fixed reference instant, such as J2000.0 or the Unix epoch, that other counts are measured from.

What changes the result

Four things move the answer, and all four are worth checking before you trust a converted date:

• Which "Julian date" you have. A seven-digit number is astronomical, a five-digit number is almost certainly ordinal, and a five-digit number with decimals is probably MJD. Guessing wrong shifts the answer by thousands of years.
• The time of day. Because the astronomical day flips at noon, an evening event and the following morning share one Julian Day Number. Enter the time if the exact instant matters.
• The time zone. Julian Dates are quoted in Universal Time. A 9 p.m. Eastern Daylight Time observation is 01:00 UT the next day, so both the date and the day number change.
• Leap years. They add day 366 and push every ordinal number from March 1 onward up by one. 2026 is a common year; 2028, 2032 and 2036 are leap years.

Practical tips

• Use day numbers for date arithmetic. Subtracting two Julian Day Numbers gives an exact day count with no month-length or leap-year corrections.
• Write the seven-digit form on anything long-lived. YYYYDDD costs two characters and removes every century ambiguity from an archive.
• Sanity-check the magnitude. Any date in the 2020s has a JDN near 2.46 million and an MJD near 60,000. A result far from those means the wrong input type is selected.
• Convert local time first. Apply the UTC offset before converting, using the Time Zone Calculator if you are unsure of the offset for that date.

Limitations and assumptions

• Dates are read in the proleptic Gregorian calendar. Historical dates recorded before a country adopted that calendar were written in the Julian calendar and can differ by ten to thirteen days.
• The converter uses Universal Time and applies no time-zone or daylight-saving offset for you.
• It ignores leap seconds and does not distinguish UT1, UTC, TAI or Terrestrial Time. Precise astrometry needs the correct time scale.
• It does not compute Heliocentric or Barycentric Julian Dates, which add a light-travel correction of up to about 8.3 minutes.
• A two-digit ordinal year is resolved by the century switch, because the code itself carries no century.
• Results are for reference. For a regulated lot record, confirm against the issuing system's documentation.

How it compares to related calculators

This page answers "what day number is this date, and what date is this day number?" Other questions have better-fitting tools:

• For the ISO 8601 week number and the Monday-to-Sunday range of a date, use the Week Number Calculator.
• To add or subtract days from a date, use the Date Calculator, or the Date and Time Calculator when hours and minutes are involved.
• To count only working days between two dates, use the Business Days Calculator.
• To convert a clock time between cities first, use the Time Zone Calculator.
• For a birth date, use the Age Calculator; for a live count to a future date, the Countdown Calculator.

Sources

Julian date conversion is deterministic calendar arithmetic: the Julian Day Number, the noon-based Julian Date, the definition MJD = JD − 2,400,000.5 and the ordinal YYDDD form are exact definitions, so the results here need no estimated or surveyed data. The algorithm and the standards behind those definitions are:

• U.S. Naval Observatory, Astronomical Applications Department - Julian date definition and astronomical data services.
• National Institute of Standards and Technology (NIST) - Time and Frequency Division: Universal Time, UTC and time scales.
• Fliegel, H. F. and Van Flandern, T. C., "A Machine Algorithm for Processing Calendar Dates", Communications of the ACM, Vol. 11, No. 10 (1968) - the integer conversion used in both directions on this page.
• ISO 8601, "Date and time - Representations for information interchange" - the ordinal date format (year plus day of year) behind the YYDDD and YYYYDDD codes.