Roman numerals

The seven letters

I 1 · V 5 · X 10 · L 50 · C 100 · D 500 · M 1000

Everything else is built from those, largest first, with one rule that does the real work.

The subtractive rule

A smaller numeral placed before a larger one is subtracted from it. So 4 is IV, not IIII, and 9 is IX. The same at each scale: 40 is XL, 90 is XC, 400 is CD, 900 is CM.

Only six such pairs are valid — IV, IX, XL, XC, CD, CM — because only I, X and C may be subtracted, and only from the next two values up. IL for 49 is wrong; it is XLIX.

Input here accepts the additive form as well, because clock faces use IIII for 4. Nobody is entirely sure why; the usual explanation is visual balance against the VIII opposite it.

Why it stops at 3999

This is a real limit, not a shortcut.

Classical Roman numerals have no character for 5000. To write 4000 you need either MMMM — which breaks the rule that no numeral repeats more than three times — or a vinculum, a bar drawn over a numeral to multiply it by a thousand. The bar is not a character you can type, and the Unicode combining overline renders inconsistently.

So 4000 and above are refused rather than approximated. Emitting MMMM would be inventing a form the system does not have.

There is no zero

Roman numerals have no zero and no way to express one. The concept arrived in Europe with Arabic numerals, centuries after this system was in daily use. Negative numbers and fractions are equally absent — the Romans had fractions, but in a separate duodecimal notation with its own symbols.

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