# Julian date converter

> The Julian Day Number is a continuous count of days since January 1, 4713 BCE used in astronomy to compare dates across calendar systems. Enter a Gregorian date or a JDN to.

Convert between Gregorian calendar dates and Julian Day Numbers (JDN). Also computes the Julian Date, Modified Julian Date, and J2000 epoch offset used in astronomy.

**Interactive version:** https://onlinecalculator.me/date-time/julian-date/
**Category:** Date & Time

## Formula

### Gregorian date → JDN (Meeus, "Astronomical Algorithms" Ch. 7)

```
a = floor((14 − month) / 12)
y = year + 4800 − a
m = month + 12·a − 3
JDN = day + floor((153·m + 2) / 5) + 365·y + floor(y/4) − floor(y/100) + floor(y/400) − 32045
```

### Adding a time component

```
JD = JDN + (hour − 12)/24 + minute/1440 + second/86400
```

At noon UTC the fractional part is 0, so JD = JDN exactly.

### Derived quantities

| Quantity | Formula |
|----------|---------|
| Modified Julian Date (MJD) | JD − 2400000.5 |
| J2000 offset (days) | JD − 2451545.0 |

## Worked example

**Date:** January 1, 2000 at 12:00:00 UTC (J2000 epoch)

- JDN = 2451545
- JD = 2451545.0 (noon)
- MJD = 51544.5
- J2000 = 0.0

## Known reference points

| Date | JDN |
|------|-----|
| Jan 1, 1970 (Unix epoch) | 2440588 |
| Jan 1, 2000 (J2000 epoch) | 2451545 |
| Jan 1, 2024 | 2460311 |

## Notes

- The algorithm handles proleptic Gregorian dates (dates before the Gregorian calendar was adopted).
- Dates before October 15, 1582 were in the Julian calendar era; this converter uses the proleptic Gregorian formula for all dates.

## Frequently asked questions

### What is a Julian Day Number?

A Julian Day Number (JDN) is an integer count of days since the start of the Julian Period — January 1, 4713 BCE in the Julian calendar, noon UTC. JDN 0 is that starting day. January 1, 2000 is JDN 2451545. The system gives astronomers a single timeline that spans any historical date.

### What is a Julian Date vs. a Julian Day Number?

A Julian Day Number is an integer (the whole-day count). A Julian Date (JD) adds a fractional part representing the time of day, anchored to noon UTC. At noon on January 1, 2000, JD = 2451545.0 exactly.

### What is the Modified Julian Date?

The Modified Julian Date (MJD) = JD − 2400000.5. It resets the origin to midnight on November 17, 1858, producing smaller numbers convenient for modern calculations. MJD 0 = JD 2400000.5.

### What is J2000?

J2000 is the standard astronomical epoch: January 1.5, 2000 UTC (noon on January 1, 2000) = JD 2451545.0. The J2000 offset shows how many days before or after that epoch a date falls.

### Is this the same as the Julian calendar?

No. The Julian Day Number is a counting system invented by astronomers. The Julian calendar is a civil calendar that predates the Gregorian calendar. The names happen to share origin (both named after Julius Caesar), but the systems are different.

## Sources

- [Julian day](https://en.wikipedia.org/wiki/Julian_day) — Wikipedia
- [Julian Date Converter](https://aa.usno.navy.mil/data/JulianDate) — U.S. Naval Observatory

## Related calculators

- [Unix timestamp converter](https://onlinecalculator.me/date-time/unix-timestamp/) — Convert between Unix timestamps and human-readable dates.
- [Date difference calculator](https://onlinecalculator.me/date-time/date-difference/) — Find the exact number of days between two dates.
- [Add or subtract days](https://onlinecalculator.me/date-time/add-subtract-days/) — Find a date a set number of days in the future or past.
- [Week number calculator](https://onlinecalculator.me/date-time/week-number/) — ISO 8601 and US week numbers for any date.
- [Moon phase calculator](https://onlinecalculator.me/date-time/moon-phase/) — Find the moon phase for any date using Julian Day arithmetic.

---

Part of [onlinecalculator.me](https://onlinecalculator.me/) — free calculators that run entirely in your browser.
Machine-readable index: https://onlinecalculator.me/llms.txt