The French Republican calendar was adopted by a decree of La Convention Nationale on Gregorian date October 5, 1793 and went into effect the following November 24th, on which day Fabre d'Églantine proposed to the Convention the names for the months. It incarnates the revolutionary spirit of "Out with the old! In with the relentlessly rational!" which later gave rise in 1795 to the metric system of weights and measures which has proven more durable than the Republican calendar.

The calendar consists of 12 months of 30 days each, followed by a five- or six-day holiday period, the jours complémentaires or sans-culottides. Months are grouped into four seasons; the three months of each season end with the same letters and rhyme with one another. The calendar begins on Gregorian date September 22nd, 1792, the September equinox and date of the founding of the First Republic. This day is designated the first day of the month of Vendémiaire in year 1 of the Republic. Subsequent years begin on the day in which the September equinox occurs as reckoned at the Paris meridian. Days begin at true solar midnight. Whether the sans-culottides period contains five or six days depends on the actual date of the equinox. Consequently, there is no leap year rule per se: 366 day years do not recur in a regular pattern but instead follow the dictates of astronomy. The calendar therefore stays perfectly aligned with the seasons. No attempt is made to synchronise months with the phases of the Moon.

The Republican calendar is rare in that it has no concept of a seven day week. Each thirty day month is divided into three décades of ten days each, the last of which, décadi, was the day of rest. (The word "décade" may confuse English speakers; the French noun denoting ten years is "décennie".) The names of days in the décade are derived from their number in the ten day sequence. The five or six days of the sans-culottides do not bear the names of the décade. Instead, each of these holidays commemorates an aspect of the republican spirit. The last, jour de la Révolution, occurs only in years of 366 days.

Napoléon abolished the Republican calendar in favour of the Gregorian on January 1st, 1806. Thus France, one of the first countries to adopt the Gregorian calendar (in December 1582), became the only country to subsequently abandon and then re-adopt it. During the period of the Paris Commune uprising in 1871 the Republican calendar was again briefly used.

The original decree which established the Republican calendar contained a contradiction: it defined the year as starting on the day of the true autumnal equinox in Paris, but further prescribed a four year cycle called la Franciade, the fourth year of which would end with le jour de la Révolution and hence contain 366 days. These two specifications are incompatible, as 366 day years defined by the equinox do not recur on a regular four year schedule. This problem was recognised shortly after the calendar was proclaimed, but the calendar was abandoned five years before the first conflict would have occurred and the issue was never formally resolved. Here we assume the equinox rule prevails, as a rigid four year cycle would be no more accurate than the Julian calendar, which couldn't possibly be the intent of its enlightened Republican designers.

Adapted from Formilab's Calendar Converter.