Century and Millennium Finder
Century and millennium basics (and why 1800 is in the 18th century)
People often expect the year 1800 to be the start of the 19th century because it begins with “18.” Historically, that isn’t how centuries (or millennia) are counted. A century is a complete block of 100 years, and a millennium is a complete block of 1,000 years. By convention, counting begins at year 1, not year 0. That means:
- 1st century CE = years 1 through 100
- 2nd century CE = years 101 through 200
- …and so on
So the year 1800 is the last year of the 18th century (1701–1800). The year 1801 is the first year of the 19th century (1801–1900). The exact same idea applies to millennia: the 2nd millennium CE runs from 1001 through 2000, and the 3rd millennium begins in 2001.
Formulas used by the calculator
To compute a century number from a year, you divide by 100 and round up to the next whole number (the “ceiling” function). For millennia, divide by 1,000 and round up.
Century
Century number = ceil(|year| / 100)
Millennium
Millennium number = ceil(|year| / 1000)
The calculator uses absolute value (|year|) so that the same arithmetic works for BCE and CE years. After the number is found, the result is labeled as BCE when the input year is negative and CE when the input year is positive.
MathML version
How BCE inputs are handled
This tool uses a simple input convention: negative years represent BCE. For example, enter -44 for 44 BCE. Internally, the calculator computes the century and millennium from the magnitude of the year, then appends the BCE label.
Examples:
- -44 → 44 BCE → 1st century BCE, 1st millennium BCE
- -101 → 101 BCE → 2nd century BCE, 1st millennium BCE
Interpreting the results (including boundary years)
Because centuries and millennia are grouped into full blocks that start at 1, boundary years can feel surprising at first. Here are the key boundary rules the calculator follows:
- Years 1–100 are the 1st century; years 101–200 are the 2nd century.
- Years 1–1000 are the 1st millennium; years 1001–2000 are the 2nd millennium.
- 1800 is in the 18th century (1701–1800), while 1801 starts the 19th century.
- 2000 is the final year of the 2nd millennium; 2001 begins the 3rd millennium.
Worked example
Example: What century and millennium is 1905?
- Compute century: 1905 / 100 = 19.05 → ceil(19.05) = 20 → 20th century CE
- Compute millennium: 1905 / 1000 = 1.905 → ceil(1.905) = 2 → 2nd millennium CE
So 1905 is in the 20th century and the 2nd millennium.
Quick comparison table (common and boundary cases)
| Input year | Era | Century | Millennium | Why |
|---|---|---|---|---|
| 1 | CE | 1st | 1st | Counting starts at year 1 |
| 100 | CE | 1st | 1st | End of the first 100-year block |
| 101 | CE | 2nd | 1st | Begins the second century |
| 1000 | CE | 10th | 1st | End of the first millennium |
| 1001 | CE | 11th | 2nd | Begins the second millennium |
| 1800 | CE | 18th | 2nd | 1701–1800 is the 18th century |
| 2000 | CE | 20th | 2nd | End of the 2nd millennium (1001–2000) |
| -1 | BCE | 1st | 1st | 1 BCE falls in the first century BCE |
| -44 | BCE | 1st | 1st | 44 BCE is within years 1–100 BCE |
| -101 | BCE | 2nd | 1st | 101–200 BCE corresponds to the 2nd century BCE |
Ordinal labels (st/nd/rd/th)
The tool formats century and millennium numbers as ordinals so they read naturally (for example, “21st century” instead of “21 century”). Suffix rules include a special case for 11, 12, and 13 (which always use “th”).
Assumptions & limitations
- No year 0: Results follow the common historical BCE/CE convention where 1 BCE is immediately followed by 1 CE.
- Input convention: Enter BCE years as negative integers (e.g., -44). Enter CE years as positive integers (e.g., 1905).
- Year 0 is not valid historically: If you enter 0, it does not correspond to a BCE/CE year in this convention; you should use -1 for 1 BCE or 1 for 1 CE.
- Integer years only: Centuries and millennia are defined for whole years; fractional years are not meaningful in this context.
- Astronomical year numbering not used: Some scientific contexts include year 0 and different negative-year mapping; this calculator uses the common historical convention used in most classrooms and general history references.