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MasterMath

Roman Numeral Converter

Convert numbers to Roman numerals and back, and find out whether a numeral is written canonically — many that people write are not.

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How this was worked out

    The rule

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

    Why it works

    Roman numerals add symbol values from left to right, with one twist: a smaller symbol before a larger one is subtracted. That subtractive rule is what turns IIII into IV, and it is also where most mistakes come from.

    How to do it by hand

    1. Take the largest symbol value that fits and write it
    2. Subtract it and repeat with what is left
    3. Use the subtractive pairs where they apply: IV, IX, XL, XC, CD, CM
    4. Reading back, subtract any symbol smaller than the one after it

    What is worth knowing

    The subtractive rule has strict limits that casual use ignores: only I, X and C may be subtracted, and only from the next two values up. So 99 is XCIX, not IC, even though IC looks reasonable. The system also has no zero and no way to write anything above 3999 without extra notation, which is exactly why it was abandoned for arithmetic. Clock faces are the famous exception to canonical spelling: many still use IIII rather than IV, a tradition with no agreed explanation but several competing stories.

    Frequently asked questions

    How do Roman numerals work?

    Add the symbol values from left to right, except when a smaller symbol precedes a larger one, in which case it is subtracted.

    Why is 99 not IC?

    Because only I, X and C can be subtracted, and only from the next two values up. 99 is XCIX.

    Why do clocks use IIII instead of IV?

    Tradition, with several competing explanations and no settled one. It is not canonical, but it is very common.

    What is the largest Roman numeral?

    3999, written MMMCMXCIX. Beyond that the classical system needs overlines or other extensions.