Roman Numeral Converter

The seven symbols

I is 1, V is 5, X is 10, L is 50, C is 100, D is 500 and M is 1000. Everything is built from these by addition, reading left to right, with one exception that causes all the difficulty.

The subtractive rule and its limits

A smaller symbol before a larger one is subtracted: IV is 4, IX is 9, XL is 40, XC is 90, CD is 400, CM is 900. Only those six combinations are valid. I may precede only V and X, X only L and C, and C only D and M. V, L and D are never subtracted from anything. This means 99 is XCIX — ninety plus nine — and not IC, which is a common but incorrect construction, and 1999 is MCMXCIX rather than MIM.

Repetition rules

I, X, C and M may be repeated up to three times consecutively. V, L and D never repeat, because two of any of them equals the next symbol up. So 30 is XXX and 40 is XL, not XXXX. Roman clock faces famously use IIII for four, which is a deliberate typographic convention for visual balance against the VIII opposite, not a different numbering system.

There is no zero and no fractions

The system has no symbol for zero and no place value, which is why arithmetic in Roman numerals is impractical and why the adoption of Hindu-Arabic numerals in Europe was transformative rather than cosmetic. It also cannot represent negative numbers or decimals.

The upper limit

Standard notation reaches 3,999 as MMMCMXCIX, since M cannot repeat more than three times. Larger values used a vinculum, an overline multiplying a symbol by a thousand, so V with a bar is 5,000. This is rarely supported outside specialist typography, which is why most converters stop at 3,999.

Where they are still used

Regnal and papal names, film copyright dates, book preface pagination, clock faces, Super Bowl numbering, and outline numbering in formal documents. Reading a copyright date such as MMXXVI is the most common practical need, and the trick is simply to break it into place values: MM is 2000, XX is 20, VI is 6.