Roman Numeral Converter

Encoding is straightforward. Decoding is where most converters fail, because a naive left-to-right scan happily accepts things that are not numerals at all. `IIII`, `VV`, `IC` and `XXXX` all produce a number under that approach — 4, 10, 99 and 40 respectively — and every one of them is invalid. Returning 99 for `IC` is worse than refusing it, because the reader has no reason to doubt the answer.

Rather than checking a list of rules, which is how these implementations get long and still miss cases, this decodes the input and then re-encodes the result. If the canonical spelling of that number is not what was typed, the input was not a valid numeral. There is exactly one correct way to write any number, so a single comparison catches every malformed case at once.

The subtractive rule is narrower than people assume. Only I, X and C are ever subtracted, and only from the next two values up — I from V and X, X from L and C, C from D and M. That is why 99 is XCIX, ninety plus nine, and never IC. V, L and D are never subtracted from anything.

There is no zero and no way to write beyond 3999 in plain text. Larger numbers used an overbar meaning multiply by a thousand, which has no plain-character equivalent — so 3999, MMMCMXCIX, is the practical ceiling.

One genuine exception to the rules: clock faces have used IIII for 4 rather than IV for centuries. The reasons offered are aesthetic — balance against the VIII opposite — and it is a convention rather than arithmetic. This tool follows the arithmetic.