Decade Century Calculator

Grouping years into decades, centuries, and millennia looks trivial until the absence of a year zero is accounted for. The Gregorian era numbering runs 1 BCE directly into 1 CE with nothing between, so ordinal periods are counted from year 1: the first century covers 1 to 100, the twentieth covers 1901 to 2000, and the twenty-first covers 2001 to 2100, and the third millennium runs from 2001 to 3000. Centuries and millennia therefore use a ceiling function, ceil(year / 100) and ceil(year / 1000), while decades in ordinary usage do not. Nobody says the 203rd decade; decades are named by the tens digit, so the 1980s means 1980 through 1989, obtained by floor(year / 10) multiplied by 10. This calculator follows both conventions as they are actually used, so a year such as 2000 sits in the 2000s decade but the twentieth century. Spans that cross the BCE-CE boundary cannot be computed by adding the two year numbers - 3 BCE to 3 CE is five years, not six - because there is no year zero to absorb the gap; astronomers avoid this by using a separate numbering in which year 0 equals 1 BCE and year -1 equals 2 BCE, the convention ISO 8601 adopts. The historical era labels attached to a year here, such as Medieval Period or Early Modern Period, are conventional shorthand rather than defined standards; the boundaries commonly cited at roughly 500 and 1500 are drawn from European historiography. Leap-year status is independent of all this and follows the divisible-by-4 rule with the century exception at 100 and 400.

The era being counted was fixed by a single administrative decision. The monk Dionysius Exiguus, working in Rome around 525 CE, was preparing tables for calculating the date of Easter and chose to number years from what he took to be the incarnation rather than from the reign of Diocletian, whose persecution of Christians made his era unwelcome. Dionysius simply began his table at year 1; he had no reason to include a zero, because Roman numerals had no symbol for it. The system spread slowly and owes much of its adoption to the Northumbrian scholar Bede, who used it throughout his Ecclesiastical History of the English People, completed in 731. The missing zero created a durable inconsistency that astronomers eventually routed around. Jacques Cassini, in tables published in 1740, introduced the astronomical year numbering that inserts a year 0 in place of 1 BCE and continues negatively, restoring ordinary arithmetic across the boundary. The consequence for centuries surfaced at every turn of a hundred years, and loudly in 1999, when observatories including the US Naval Observatory and the Royal Observatory at Greenwich pointed out that the third millennium began on January 1, 2001 while nearly all public celebrations were held a year earlier. Decade naming has its own cultural history, from the Roaring Twenties to the failure of English to settle on a name for the 2000 to 2009 decade, variously called the aughts or the noughties.