How Roman Numerals Work
Roman numerals are a numeral system originating in ancient Rome. They remained the standard way of writing numbers throughout Europe well into the Late Middle Ages, and are still widely used today for clock faces, book chapters, film credits, and year inscriptions.
The Seven Symbols
The entire system is built from seven base symbols:
| Symbol | Value | Name |
|---|---|---|
| I | 1 | Unus |
| V | 5 | Quinque |
| X | 10 | Decem |
| L | 50 | Quinquaginta |
| C | 100 | Centum |
| D | 500 | Quingenti |
| M | 1000 | Mille |
Additive Notation
When a symbol is followed by one of equal or lesser value, you add them. For example: VIII = 5 + 1 + 1 + 1 = 8. LXXX = 50 + 10 + 10 + 10 = 80.
Subtractive Notation
When a smaller symbol appears before a larger one, it is subtracted. Only six subtractive combinations are standard:
- IV = 4 (5 − 1)
- IX = 9 (10 − 1)
- XL = 40 (50 − 10)
- XC = 90 (100 − 10)
- CD = 400 (500 − 100)
- CM = 900 (1000 − 100)
Rules
- I, X, C, and M can be repeated up to three times in succession.
- V, L, and D are never repeated.
- Only one small-value numeral may be subtracted from any given larger numeral.
- The largest possible numerals are written first (left to right).
Reading a Roman Numeral
To read MCMXCIV: work left to right. M = 1000. C before M = subtract 100, so CM = 900. X before C = subtract 10, so XC = 90. I before V = subtract 1, so IV = 4. Total: 1000 + 900 + 90 + 4 = 1994.
The Range 1–3999
The standard Roman numeral system covers 1 to 3,999 (MMMCMXCIX). Numbers above this require either a different notation or are simply written with extra Ms (though this becomes unwieldy). See the Extended Notation page for how the Romans handled larger numbers.