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Century Counting: Why the 1400s Are the 15th Century

One rule converts any year to its century, forwards or backwards. Here it is, where the off-by-one came from, and how to read sources that use both.

By Published 5 min read

Reign Creative LLC makes World History Timeline Sim, which this article links to, so we have a commercial interest in it. How we write and check articles.

Key takeaways

  • One rule covers every case: divide the year by 100 and round up. 1492 becomes 14.92, which rounds up to 15, so 1492 is in the fifteenth century.
  • The offset exists because the year count starts at 1 rather than 0, a convention fixed in the sixth century and never revised.
  • The same rule works for BCE dates using the year's magnitude: 44 BCE is in the first century BCE and 150 BCE is in the second, because BCE centuries count backwards from the boundary.
  • "The 1400s" and "the fifteenth century" are different sets of years, differing by one year at each end, and careful writing says which it means.
  • The argument about when the millennium started was an arithmetic question with a correct answer, and the US Naval Observatory's answer was 1 January 2001.

The 1400s are the fifteenth century because the count starts at year 1, not year 0. The first century covers the years 1 to 100, so every century number ends up one ahead of the digits at the front of the year. The US Naval Observatory states the pattern plainly: the first century comprises the years AD 1 through AD 100, and each subsequent century shifts forward by 100 years. That single missing slot at the start of the count is the whole explanation.

One rule, every year

Divide the year by 100 and round up to the next whole number.

  • 1492 ÷ 100 = 14.92 → 15th century
  • 1066 ÷ 100 = 10.66 → 11th century
  • 1900 ÷ 100 = 19 exactly → 19th century (its last year)
  • 2001 ÷ 100 = 20.01 → 21st century

Years ending in 00 are the only ones that behave differently, and they behave differently because they are the last year of their century rather than the first. That is the detail almost everyone gets wrong, and it is the reason the rule is "round up" rather than "add one".

Where the off-by-one actually came from

The convention is older than the arithmetic confusion it causes.

The era itself was devised in the sixth century by the monk Dionysius Exiguus, who was compiling a table of Easter dates. As the standard reference account in the Explanatory Supplement to the Astronomical Almanac describes it, an existing table covered a nineteen-year period labelled 228–247, counted from the start of the reign of the Roman emperor Diocletian. Dionysius continued the table for a further nineteen years, which he designated Anni Domini Nostri Jesu Christi 532–550 — so his AD 532 corresponds to Diocletian year 248. Recent scholarship dates the introduction of the system to 525 and notes that how Dionysius arrived at his starting year has still not been satisfactorily explained; the question is an active research problem rather than a settled one.

Two consequences follow. First, Dionysius did not establish an accurate date for the birth of Christ, and scholars generally hold that the birth occurred some years before AD 1. The epoch is a convention, not a measurement. Second, because he was numbering years forward from an epoch, there was no occasion to number anything before it. The backward count was added later, by the eighth-century English historian Bede, who began counting years backwards from AD 1 — producing the sequence 1 BC, AD 1, with no year in between.

The sixteenth century saw that "historical" system settle into general use; the alternative astronomical numbering, which does include a year zero, was not adopted until the eighteenth, when the astronomer Jacques Cassini introduced it. Our article on BCE and CE notation covers the arithmetic consequences of the missing year in more detail.

Counting backwards

BCE centuries run in the opposite direction, which trips people up far more often than the forward case.

The first century BCE is 100 BCE to 1 BCE. The second is 200 BCE to 101 BCE. The rule is the same — take the size of the year, divide by 100, round up — but the sequence increases as you go further back in time.

  • 44 BCE ÷ 100 = 0.44 → 1st century BCE
  • 150 BCE ÷ 100 = 1.5 → 2nd century BCE
  • 508 BCE ÷ 100 = 5.08 → 6th century BCE

Two practical warnings. A larger BCE year number is an earlier date, so 500 BCE precedes 400 BCE. And "early" and "late" invert: the early fifth century BCE means years closer to 500 BCE, while the late fifth century BCE means years closer to 401 BCE. Readers who convert the number correctly still frequently reverse the direction.

"The 1400s" and "the fifteenth century" are different sets

These two phrases are used interchangeably in ordinary writing, and they do not name the same years.

Phrase Years it covers
The 1400s 1400–1499
The fifteenth century 1401–1500

The overlap is 1401–1499, so for ninety-nine years out of a hundred the distinction does not matter. It matters at the edges, and it matters most in exactly the contexts where people reach for a century label — the "turn of the century", the "end of the fifteenth century", a claim about the first or last decade of a period.

When you are reading, assume a source using digit forms ("the 1400s", "the 1900s") means the hundred years sharing those leading digits, and assume a source using ordinals means the strict count — but check if the argument depends on a boundary year. When you are writing, an explicit range removes the ambiguity entirely.

The millennium argument had a correct answer

The public dispute about whether the new millennium began in 2000 or 2001 was not a matter of taste. The US Naval Observatory's position is unambiguous: the 21st century began on 1 January 2001 and runs through 31 December 2100, and the third millennium likewise began on 1 January 2001. The same page sets out the two competing year-numbering conventions — the historical one, in which AD 1 is preceded by 1 BC with no year zero, and the astronomical one, in which AD 1 is designated +1 and is preceded by year 0.

The celebration happened a year early because the visually satisfying rollover and the arithmetically correct boundary are not the same date. Both facts are true at once, which is a reasonable summary of this entire topic.

Making the rule stick

Century arithmetic is the sort of thing that stays learned only through use. Browsing a chronology by year and watching which century label each range carries does that work incidentally, which is part of why a timeline is a good place to practise. World History Timeline Sim, our own app built by Reign Creative, lets you jump to a specific year and move through the surrounding entries, and its Guess the Year mode asks you to estimate when an event happened rather than recall a period label. That is practice, not instruction; for the conventions themselves, the observatory pages cited here are the authority, and the app is not a substitute for a reference work.

For the wider machinery these numbers sit inside, how calendars and dating systems work covers the calendars themselves, and how historians date events covers where a date on a timeline comes from in the first place. More on chronology is collected in the world history timelines hub, alongside how to actually learn from a timeline app, and our other study tools are listed under education and brain games.

Good to know

Frequently asked questions

What is the quickest way to convert a year to its century?
Divide by 100 and round up to the next whole number. 1066 becomes 10.66, rounded up to 11, so it is the eleventh century. A year ending in exactly 00 needs no rounding: 1500 divided by 100 is 15, so 1500 is the last year of the fifteenth century, not the first year of the sixteenth.
Is 1900 in the nineteenth century or the twentieth?
By the counting rule it is the final year of the nineteenth century, because the nineteenth century runs from 1801 to 1900. In ordinary speech many people treat 1900 as the start of the twentieth, and "the 1900s" usually means 1900 to 1999. Both usages circulate, so when precision matters the safest form is the explicit year range.
How do centuries work for BCE dates?
The same rule applies to the year's size, but the sequence runs backwards. The first century BCE is 100 BCE to 1 BCE, the second is 200 BCE to 101 BCE, and so on. So 44 BCE sits in the first century BCE and 250 BCE sits in the third. A larger BCE year number means an earlier date and a higher century number.
Why is there no year zero to make this simpler?
The scheme was devised in the sixth century by Dionysius Exiguus for calculating Easter, and the backward count before it was established later by Bede. Neither was working in a tradition where zero functioned as an ordinary number in year counts. Astronomers later adopted a numbering that does include a year zero, which is why astronomical and historical year numbers for BCE dates differ by one.

Sources

  1. The 21st Century and the 3rd Millennium (opens in a new tab)Astronomical Applications Department, U.S. Naval Observatory — accessed
  2. Calendars and their History (opens in a new tab)NASA Goddard Space Flight Center (reprinted from the Explanatory Supplement to the Astronomical Almanac) — accessed
  3. Decoding the Christian Era of Dionysius Exiguus (opens in a new tab)Collectanea Theologica (Cardinal Stefan Wyszyński University in Warsaw) — accessed
  4. Introduction to Calendars (opens in a new tab)Astronomical Applications Department, U.S. Naval Observatory — accessed

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