Free astronomical day-count converter
Julian Date Calculator
Convert a calendar date and universal time to Julian Date, Julian Day Number and Modified Julian Date. Reverse any supported JD into Gregorian, Julian or historical calendar form.
Last Updated: July 25, 2026
Convert Calendar Dates and Julian Dates
Choose a direction, calendar rule and display precision. Times use a universal-time-style 24-hour clock.
A Julian Date calculator turns a calendar date and time into one continuous astronomical day count. It also reverses that count into a readable date. This page reports Julian Date (JD), Modified Julian Date (MJD), the noon-based Julian Day Number, a civil-date day index, the offset from J2000, weekday, calendar position, and matching Gregorian and Julian calendar dates.
The tool is designed for astronomy, scientific records, software checks and historical calendar comparison. It does not silently treat a local clock reading as universal time. Enter the instant after converting it to the universal-time basis required by your source.
How to Use the Julian Date Calculator
- Select Calendar date to Julian Date for a forward conversion, or Julian Date to calendar date for a reverse conversion.
- Choose the historical switch, proleptic Gregorian or proleptic Julian calendar rule.
- For a calendar input, enter the year, era, month, day, hour, minute and second.
- For a JD input, enter a decimal value from 0 through 5373484.499999.
- Select the number of decimal places to display.
- Select the conversion button and review JD, MJD, the two day-number conventions and both calendar equivalents.
- Check the audit table before using the result in software or a scientific record.
- Use Copy Result to save the complete plain-text conversion.
What Is a Julian Date?
The astronomical Julian Date is a continuous count of days and fractions of a day. The U.S. Naval Observatory Julian Date service defines the origin as noon on January 1, 4713 BC in the Julian calendar. Astronomical year numbering writes that year as -4712 because it includes a year zero.
Unlike a civil date, a Julian day starts at noon. This convention places midnight at a fractional value ending in .5. Noon has an integer JD. Six hours after noon ends in .25, while six hours before noon ends in .75 on the preceding integer.
JD is useful because subtraction gives an elapsed-day difference without separately counting months or leap years. A gap of 2.25 JD units represents 2 days and 6 hours under the uniform-day model used by the calculation.
Julian Date Conversion Formula
The calendar algorithm first assigns an integer day index to the entered civil date. The Gregorian and Julian versions differ in their leap-year corrections. The time component then shifts the midnight-based date into the noon-based JD system.
The value called civil-date JDN on this page is floor(JD + 0.5). It stays attached to the civil date from midnight through the following midnight. The noon-based Julian Day Number follows the U.S. Naval Observatory glossary convention and uses floor(JD). The two integers differ between midnight and noon.
Worked Example: J2000
Use January 1, 2000 CE at 12:00:00 under the Gregorian calendar.
- The Gregorian calendar algorithm assigns the civil date the integer 2451545.
- Subtract 0.5 to move from the civil-date boundary at midnight to JD 2451544.5.
- Twelve hours equal 43,200 seconds.
- 43,200 divided by 86,400 equals 0.5 day.
- Add the time fraction: 2451544.5 + 0.5 = JD 2451545.0.
- Subtract 2400000.5 to get MJD 51544.5.
- Subtract the J2000 reference value, 2451545.0. The offset is zero days.
The matching Julian calendar date is December 19, 1999 CE. Both calendar labels identify the same instant. They differ because the calendars apply different leap-year rules across their histories.
Julian Date, Julian Day Number and MJD
| Term | Calculation | Boundary | J2000 example |
|---|---|---|---|
| Julian Date | Full continuous day count | Integer changes at noon | 2451545.000000 |
| Julian Day Number | floor(JD) | Noon-based whole day | 2451545 |
| Civil-date JDN | floor(JD + 0.5) | Midnight-based date index | 2451545 |
| Modified Julian Date | JD minus 2400000.5 | Integer changes at midnight | 51544.500000 |
| J2000 offset | JD minus 2451545.0 | Relative to J2000 | 0.000000 |
Terminology varies across books and software. A system may use "Julian day" for the decimal JD, the whole JDN, or a day-of-year code. Record the formula or label with the number so another person can reproduce the same meaning.
Why Julian Dates Begin at Noon
The noon boundary is the source of the most common half-day error. A civil date begins at 00:00. JD begins twelve hours later. Therefore, a modern date at midnight usually has a JD ending in .5. The same date at noon usually has an integer JD.
| Universal time on January 1, 2000 | Julian Date | JD fractional part |
|---|---|---|
| 00:00:00 | 2451544.500000 | .500000 |
| 06:00:00 | 2451544.750000 | .750000 |
| 12:00:00 | 2451545.000000 | .000000 |
| 18:00:00 | 2451545.250000 | .250000 |
If another source differs by exactly 0.5 day, compare its boundary and time-zone assumptions first. The source may use MJD, a midnight-based day count or a local date without a universal-time conversion.
Gregorian, Julian and Historical Calendar Rules
The calendar name and the Julian Date are separate ideas. Julian Date is a continuous number. The Julian calendar and Gregorian calendar are two ways to label an instant with a year, month and day.
- Proleptic Gregorian applies today's Gregorian leap-year rule backward and forward across the full supported range.
- Proleptic Julian applies a leap year every fourth astronomical year across the range.
- Historical switch mode follows the convention used by the U.S. Naval Observatory converter. It uses the Julian calendar through October 4, 1582 and the Gregorian calendar from October 15, 1582.
Historical mode rejects October 5 through October 14, 1582 because those labels were omitted in the specified reform. Julian October 4 begins at JD 2299159.5. The next civil date under this convention is Gregorian October 15, beginning at JD 2299160.5. The JD count remains continuous even though ten date labels disappear.
Countries adopted the Gregorian calendar at different times. The October 1582 switch is a calculation convention, not a complete local-history database. Choose a proleptic calendar or verify the jurisdiction's actual adoption date when studying a historical document.
Leap-Year Rules in Both Calendars
The Julian calendar treats every fourth year as a leap year. The Gregorian calendar normally does the same, but a century year must also be divisible by 400. This makes 2000 a leap year and 2100 a common year under Gregorian rules. Both are leap years under Julian rules.
| Year | Gregorian | Julian | Effect |
|---|---|---|---|
| 1900 | Common year | Leap year | Calendar labels diverge by another day after February. |
| 2000 | Leap year | Leap year | Both calendars include February 29. |
| 2024 | Leap year | Leap year | Both include February 29, under different date labels. |
| 2100 | Common year | Leap year | Gregorian February has 28 days, Julian February has 29. |
Converting a Julian Date Back to a Calendar Date
Reverse conversion first restores the midnight-based civil-date index. The tool adds 0.5 to JD and takes the floor. The remaining fraction becomes the time since midnight.
The selected calendar algorithm converts the integer day index into year, month and day. The same integer is also converted with the proleptic Gregorian and proleptic Julian algorithms, so the result panel shows both labels for comparison.
Decimal rounding can move the displayed time by a fraction of a second. Six JD decimals represent steps of about 0.0864 second. Three decimals represent steps of 86.4 seconds. Keep more decimals when you need closer time reconstruction, but do not claim accuracy beyond the source time scale and original data.
BCE Dates and the Missing Year Zero
Civil era notation moves directly from 1 BCE to 1 CE. There is no civil year zero. Astronomical formulas often use year zero to simplify arithmetic. In astronomical numbering, 1 BCE is year 0, 2 BCE is year -1, and 4713 BCE is year -4712.
The calculator accepts a positive year number plus a separate CE or BCE selector. It performs the astronomical-year conversion internally, then returns civil-era wording. This prevents an input such as "year 0 CE" from receiving an unclear interpretation.
Astronomical JD vs Ordinal "Julian Date" Codes
Manufacturing, logistics, food packaging and military records sometimes call a year-plus-day-of-year code a "Julian date." A value such as 2026-206 means the 206th day of 2026. It is not astronomical JD 2026206.
This calculator places the ordinal code in a separate result card. The code uses the selected calendar's actual year position. In historical-switch mode, 1582 contains 355 civil dates because ten labels are omitted. Verify a company's lot-code format before interpreting a short code such as 6206, since it might mean YYDDD, YDDD or another private convention.
Time Scales, UTC, UT1 and Leap Seconds
A JD number is incomplete in high-accuracy work unless its time scale is known. The NASA NAIF time-system guide distinguishes Julian Date UTC from ephemeris forms such as JED. The U.S. Naval Observatory converter uses UT1.
This browser calculator treats the entered clock as a universal-time-style value and assumes every day has exactly 86,400 seconds. It does not retrieve the observed UT1 minus UTC correction. It also does not accept 23:59:60 or model a positive or negative leap second.
For calendar planning, education and ordinary software checks, this model is clear and reproducible. For telescope pointing, spacecraft navigation, precise Earth orientation or sub-second event timing, use a time-scale-aware astronomy library with current leap-second and Earth-orientation data.
Reference Julian Date Examples
| Instant | Calendar rule | JD | MJD |
|---|---|---|---|
| January 1, 4713 BCE, 12:00 | Julian | 0.000000 | -2400000.500000 |
| October 4, 1582, 00:00 | Julian | 2299159.500000 | -100841.000000 |
| October 15, 1582, 00:00 | Gregorian | 2299160.500000 | -100840.000000 |
| January 1, 1970, 00:00 | Gregorian | 2440587.500000 | 40587.000000 |
| January 1, 2000, 12:00 | Gregorian | 2451545.000000 | 51544.500000 |
| February 29, 2024, 00:00 | Gregorian | 2460369.500000 | 60369.000000 |
Common Julian Date Mistakes
- Forgetting the noon boundary and producing a 0.5-day error.
- Entering local time without converting it to the required universal time.
- Confusing astronomical Julian Date with the Julian calendar.
- Confusing JD with a day-of-year lot code.
- Using Gregorian leap-year rules for a Julian calendar input.
- Entering a historical-switch date from October 5 through 14, 1582.
- Using civil year zero instead of 1 BCE or 1 CE.
- Dropping decimal digits before completing a time difference.
- Assuming UTC, UT1, TT and TDB share the same JD at sub-second precision.
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Frequently Asked Questions
What is a Julian Date?
A Julian Date is a continuous count of days and day fractions from noon on January 1, 4713 BCE in the proleptic Julian calendar. Its integer boundary occurs at noon, not midnight.
What Julian Date is January 1, 2000 at noon?
January 1, 2000 at 12:00 universal time is JD 2451545.0. This instant is the J2000 reference epoch used in many astronomical calculations.
Why does a Julian Date at midnight end in .5?
A Julian day begins at noon. Midnight occurs halfway through the noon-to-noon Julian day, so a modern midnight JD normally has a fractional part of .5.
What is Modified Julian Date?
Modified Julian Date equals JD minus 2400000.5. The subtraction shortens modern values and shifts integer boundaries from noon to midnight.
Is Julian Date the same as the Julian calendar?
No. Julian Date is a continuous astronomical day count. The Julian calendar is a civil calendar with a leap year every fourth year. One instant can have both Julian and Gregorian calendar labels but only one JD under a stated time scale.
How does the calculator handle October 1582?
Historical-switch mode uses the Julian calendar through October 4, 1582 and the Gregorian calendar from October 15. It rejects the ten omitted labels from October 5 through October 14.
Can I convert BCE dates?
Yes. Enter a positive year number and choose BCE. The calculator converts civil era notation to astronomical year numbering internally, where 1 BCE is year zero.
Is a YYYY-DDD code an astronomical Julian Date?
No. YYYY-DDD is an ordinal date made from a year and day-of-year number. Manufacturing and logistics systems sometimes call it a Julian date, but it is different from astronomical JD.
Does this calculator account for leap seconds and UT1?
No. It treats the entered clock as a universal-time-style value with 86400 seconds per day. Precise astronomy should use current leap-second and Earth-orientation data with an explicitly stated time scale.
Method and Sources
The day-count definitions, supported epoch and October 1582 convention follow the U.S. Naval Observatory Julian Date Converter. The forward and reverse calendar formulas are consistent with the USNO conversion guidance. MJD uses JD minus 2400000.5. Time-scale cautions follow the NASA NAIF SPICE time documentation.
This calculator provides educational and technical reference results. Verify the calendar convention, time scale, time-zone conversion, leap-second treatment and required precision before using a value for scientific operations, legal records, historical conclusions or safety-critical software.