Julian Day Calculator
Easily convert between everyday calendar dates, Julian Day Numbers (JDN), Modified Julian Dates (MJD), and the Day of the Year. Perfect for astronomy, satellite tracking, historical research, and students.
How Julian Days Are Calculated (Simple Formulas)
Julian Day counting turns complicated months, leap years, and leap centuries into a simple, continuous number of days. Here is how scientists and computers calculate it:
Converting Calendar Dates to Julian Days
Following standard algorithms from the U.S. Naval Observatory (USNO)open_in_new, the Fliegel–Van Flandern formula finds the integer Julian Day Number (JDN) for any calendar date:
+ (367 × (Month - 2 - 12 × ((Month - 14)/12)))/12
- (3 × ((Year + 4900 + (Month - 14)/12)/100))/4
+ Day - 32075
Adding the Time of Day as a Decimal Fraction
Because Julian Days start at 12:00 Noon, 12 hours is subtracted from morning or evening times to find the fraction of the day:
+ Minute / 1440
+ Second / 86400
JD = JDN + Day Fraction
Modified Julian Date (MJD)
As defined in satellite tracking standards by NASA JPL Solar System Dynamicsopen_in_new, subtracting 2,400,000.5 gives a shorter number that starts at civil midnight:
RJD = JD - 2400000.0 (Starts at 12:00 Noon)
TJD = JD - 2440000.5 (NASA Apollo 1968 count)
Unix Epoch = (JD - 2440587.5) × 86,400 s
Comparing Different Astronomical Time Systems
Here is how Julian Days compare to other common scientific and computer time counting formats:
| Time System | Starting Point / Origin | Day Starts At | Formula / Offset | Common Everyday & Science Uses |
|---|---|---|---|---|
| Julian Date (JD) | Jan 1, 4713 BCE at 12:00 Noon | 12:00 (Noon) | Base (0.0) | Astronomy, star charts, tracking variable stars |
| Modified Julian Date (MJD) | Nov 17, 1858 at Midnight | 00:00 (Midnight) | JD − 2,400,000.5 | Spacecraft orbits, satellite telemetry, GPS data |
| Reduced Julian Date (RJD) | Nov 16, 1858 at 12:00 Noon | 12:00 (Noon) | JD − 2,400,000.0 | Radio astronomy and pulsar timing |
| Truncated Julian Date (TJD) | May 24, 1968 at Midnight | 00:00 (Midnight) | JD − 2,440,000.5 | NASA Apollo & Space Shuttle flight logs |
| Unix Computer Time | Jan 1, 1970 at Midnight UTC | 00:00 (Midnight) | JD − 2,440,587.5 | Computers, smartphones, internet timestamps, servers |
| Day of the Year (DOY) | Jan 1 of the current year | 00:00 (Midnight) | Day 1 to 365 / 366 | Weather tracking, satellite data, school schedules |
The Story Behind the 7,980-Year Julian Calendar Period
In 1583, French classical scholar Joseph Justus Scaliger wanted to solve a major problem: different kingdoms and cultures counted years completely differently, making it very hard to compare historical dates. He cleverly combined three ancient calendar repeating cycles:
The number of years it takes for calendar days of the week to repeat on the exact same dates.
The number of years it takes for moon phases to recur on the exact same days of the year.
A 15-year imperial tax assessment cycle established in ancient Rome under Constantine.
By multiplying 28 × 19 × 15 = 7,980 years, he created a grand timeline where every single year has its own unique fingerprint. By counting backward to the last time all three cycles lined up at year 1, he arrived at January 1, 4713 BCE. Because this date was before all known recorded human history, historians and scientists could count forward with positive numbers.
Unlike standard civil days that roll over at midnight while astronomers are looking through telescopes, Julian days change at noon so an entire night of skywatching stays on one single date without splitting into two separate days.
The Missing 10 Days in October 1582
To realign the calendar with the Earth's seasons, Pope Gregory XIII skipped 10 days on the calendar: Thursday, October 4, 1582 was immediately followed the next morning by Friday, October 15, 1582. While the regular calendar jumped forward, the Julian Day count ticked steadily: JD 2,299,160 was followed directly by JD 2,299,161 without missing a single second.
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Frequently Asked Questions
Quick, friendly answers to common questions about Julian Days, stargazing time, and calendar history.