[h]Computing a French Revolutionary Calendar Date from a given JD[/h]
The Revolutionary calendar was in use in France from 1793 until 31 December 1805 and can be treated similarly to the Gregorian or Julian calendar. We can use the fact, that in the period the calendar was used officially, every fourth year was a leap year. In addition, getting the number of month and day from the number of the day within the year is much easier than in the Gregorian or Julian calendar, because of the constant lengths of months and the leap day being added at the end of the year.

We let the first 4-year cycle begin on 22 September 1791, which corresponds to 1 Vendmiaire 0 in theory. With this, the 3rd, 7th, and 11th year of the Republic become leap years. Clearly then

? = - 2375475

which is the negative JD of 21 September 1791. As above, ? is added to the given JD to get Nd. After that, the number of elapsed 4 year cycles b[/b] and years of the current 4 year cycle b[/b] are calculated.

The following formulas may serve to convert a given JD into its corresponding date of the French Revolutionary calendar. Y is the number of the year of the Republic, M the number of the month, and D the day of the French Revolutionary calendar date. Note, that the month Vendmiaire bears number 1, Brumaire is number 2, until Fructidor (12). The jours complmentaires are treated as a defective 13th month.

Nd = JD - 2375475
N4 = (Nd / 1461)
R4 = Nd mod 1461
N1 = min(3, (R4 / 365))
R1 = R4 - 365 * N1
D = (R1 mod 30) + 1
M = (R1 / 30) + 1
Y = 4N4 + N1 // -> what does 4N4 mean? 4*N4?

The formulas can only be applied to dates from 22 September 1792 until 22 September 1806.