Why the 20th Century Is XX (and Starts in 1901)

The 20th century is written XX because it is the twentieth block of a hundred years since AD 1. It runs from 1901 to 2000, not from 1900 to 1999, because the calendar has no year zero. The years that start with "19" are the 1900s; the 20th century is shifted by one year.

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On this page
  1. Counting centuries like you count anything else
  2. Why there is no year zero
  3. The one-line rule
  4. Writing it in Roman numerals
  5. Don't confuse the century with the year
  6. Sources

Counting centuries like you count anything else

Think of how you count a list. The first item is number 1, not number 0. Centuries work the same way. The 1st century is the first hundred years, AD 1 to 100. The 2nd century is 101 to 200. Keep going and the 20th century lands on 1901 to 2000:

CenturyRomanFirst yearLast year
17XVII16011700
18XVIII17011800
19XIX18011900
20XX19012000
21XXI20012100

That's why the number of the century is "one more" than the first two digits of most of its years. 1789 starts with 17, but it sits in the 18th century, XVIII. 1969 starts with 19 and sits in the 20th, XX.

Why there is no year zero

The step that makes it all work is that year 1 BC is followed directly by AD 1. NRICH, the mathematics project of the University of Cambridge, puts it plainly: because "there is no such thing as year zero", the first century was complete only at the end of AD 100, and the 21st century began on 1 January 2001 (NRICH).

If there had been a year zero, centuries would line up with the digits and 1900 would open the 20th century. There wasn't, so 1900 is the last year of the 19th century, XIX.

The one-line rule

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

  • 1900 ÷ 100 = 19 → 19th century → XIX
  • 1901 ÷ 100 = 19.01 → 20th century → XX
  • 1999 ÷ 100 = 19.99 → 20th century → XX
  • 2000 ÷ 100 = 20 → 20th century → XX

The only years where "rounding up" doesn't change anything are those ending in 00, and they belong to the century of their first two digits.

Writing it in Roman numerals

Converting the century number is the easy part. 20 is two tens: XX. The neighbours follow the same pattern:

  • 18th century: XVIII (X + VIII)
  • 19th century: XIX (X + IX, not XVIIII)
  • 20th century: XX
  • 21st century: XXI

In English you will usually see "20th century" in digits. The Roman form is standard in other languages: Spanish siglo XX, French XXe siècle, Italian XX secolo. The guide to centuries in Roman numerals lists each convention with its source.

Don't confuse the century with the year

Two numerals get swapped often:

  • XX is the 20th century.
  • MCM is the year 1900, and MM is the year 2000.

So "XX century" and "the year MCM" point to different things, even though 1900 feels like the start of the 1900s.

The 20th century in Roman numeralsSee its first and last year, every decade from 1901 in Roman numerals, and how to write it.

Sources

  1. When does the new millennium start?. NRICH, University of Cambridge