Roman Numeral Converter
Convert between decimals and Roman numerals in both directions.
Supports 1 to 3,999 using standard subtractive notation for I, V, X, L, C, D, and M.
Roman numeral conversion uses an additive and subtractive system based on seven fixed letter values. Understanding the rules allows you to convert any integer from 1 to 3,999 into Roman numerals and back.
Seven base symbols:
| Symbol | Value |
|---|---|
| I | 1 |
| V | 5 |
| X | 10 |
| L | 50 |
| C | 100 |
| D | 500 |
| M | 1,000 |
Addition rule: When a symbol of equal or lesser value follows a larger symbol, add the values.
- XI = 10 + 1 = 11
- VII = 5 + 1 + 1 = 7
Subtraction rule: When a symbol of lesser value precedes a larger symbol, subtract it.
- IV = 5 − 1 = 4
- IX = 10 − 1 = 9
- XL = 50 − 10 = 40
- XC = 90, CD = 400, CM = 900
Valid subtractive pairs (only these six are used):
- I before V or X (4, 9)
- X before L or C (40, 90)
- C before D or M (400, 900)
Conversion algorithm (Arabic → Roman): Work from largest to smallest value. For each step, subtract the largest applicable symbol value, write that symbol, and repeat.
What each variable means:
- Additive notation — the default; stack same or descending symbols
- Subtractive notation — the six special pairs that prevent four-in-a-row repetition (IIII is non-standard; IV is correct)
- Maximum repetition — no symbol except M repeats more than 3 times consecutively; M can repeat up to 3 times (MMM = 3,000)
Worked example — 2,024:
- 2,024 ÷ 1,000 = 2 → MM (remainder 24)
- 24 ÷ 10 = 2 → XX (remainder 4)
- 4 = IV → IV
- 2024 = MMXXIV
Worked example — 1,987:
- 1,000 → M (remainder 987)
- 900 = CM → CM (remainder 87)
- 50 → L (remainder 37)
- 10 × 3 → XXX (remainder 7)
- 5 → V (remainder 2)
- 1 × 2 → II
- 1987 = MCMLXXXVII
Roman numerals are still used today for clock faces, book chapter numbers, movie sequel names, Super Bowl numbering, and year of film production in credits.