Roman Numeral Converter
Valid range: 1–3999
How Roman Numerals Work
Roman numerals are a numeral system originating in ancient Rome, using combinations of letters from the Latin alphabet to represent numbers. The seven basic symbols are I (1), V (5), X (10), L (50), C (100), D (500), and M (1,000). Unlike the Arabic decimal system we use today, Roman numerals are additive and subtractive — symbols are combined rather than placed in positional columns.
The core rules are straightforward. When a smaller value appears after a larger one, add them: VI = 5 + 1 = 6, and XI = 10 + 1 = 11. When a smaller value appears before a larger one, subtract it: IV = 5 − 1 = 4, and IX = 10 − 1 = 9. Only I, X, and C can be used as subtractive prefixes, and they can only precede symbols exactly five or ten times their value: I before V or X, X before L or C, C before D or M. Subtractive pairs include IV (4), IX (9), XL (40), XC (90), CD (400), and CM (900).
Numbers are built by combining symbols from left to right, generally largest to smallest. 1999 is MCMXCIX: M (1000) + CM (900) + XC (90) + IX (9). Each symbol can only be repeated up to three times consecutively — III is 3, but 4 must be written as IV, not IIII (though IIII historically appeared on clock faces). The standard range for classical Roman numerals is 1 to 3,999 (I to MMMCMXCIX); larger numbers use vinculum notation (overlines) in extended systems.
Roman numerals persist in modern use despite Arabic numerals dominating mathematics. They appear on clock faces, book chapter numbers, movie sequel titles (Rocky IV, Star Wars Episode VI), Super Bowl designations (Super Bowl LVIII), monarch names (Elizabeth II), and copyright dates on films and television. Olympic Games and outline headings also frequently use this system.
Converting from Arabic to Roman involves greedy decomposition: start with the largest symbol that fits, subtract its value, and repeat. Converting from Roman to Arabic reads left to right, adding each symbol unless a subtractive pair is detected (a smaller symbol immediately before a larger one). This calculator handles both directions for integers from 1 to 3,999, validating input to reject invalid sequences like IL (which should be XLIX for 49 in some contexts, but IL is non-standard) or repeated symbols beyond three.
Examples
| Example | Result |
|---|---|
| 1999 → Roman | MCMXCIX |
| 2024 → Roman | MMXXIV |
| 49 → Roman | XLIX |
| 4 → Roman | IV |
| 9 → Roman | IX |
| 500 → Roman | D |
| DCCCLXXXVIII → Arabic | 888 |
Frequently asked questions
IV. The subtractive rule places I before V to mean 5 − 1 = 4. IIII appears on some clock faces but IV is standard.
3,999 (MMMCMXCIX). Larger numbers traditionally use an overline (vinculum) to multiply a symbol by 1,000.
M (1000) + CM (900) + XC (90) + IX (9) = 1999. Read left to right, applying subtractive pairs where a smaller symbol precedes a larger one.