This equation gives you the fractional Julian Day when you input a Gregorian (standard modern calendar date) including hours/minutes/seconds.

The algorithm is valid at least for all positive Julian Day Numbers. The meaning of the variables are explained by the Computer Science Department of the University of Texas at San Antonio.

"It is worth noting that this algorithm does not follow the NASA or the US Naval Observatory - the convention in these systems being that the Gregorian calendar did not exist before the date October 15, 1582 (Gregorian). This algorithm effectively back-dates the Gregorian calendar onto the Julian calendar for dates before the introduction of the Gregorian calendar. Thus any calculations made with this formula before October 15, 1582, will not agree with these previous ephemerides."¹ 

Example

If you input January 1, 2000, this equation will return the Julian Day:  2451545.0

See Also

• Gregorian Calendar to Julian Day Number (JDN)
• Modified Julian Day (MJD)
• Truncated Julian Day

1. ^ https://en.wikipedia.org/wiki/Julian_day#Calculation