Roman Numerals Converter (number ↔ Roman, I–MMMCMXCIX)

Switch between “Number to Roman” and “Roman to number” and type the value. The Roman direction takes any whole number from 1 to 3999; the reverse accepts any properly-formed Roman numeral in the same range.

How the math works

For number → Roman the algorithm is a simple greedy decomposition: walk through the value table in descending order — [1000=M, 900=CM, 500=D, …, 4=IV, 1=I] — and emit the symbol as many times as it fits.

For Roman → number the algorithm reads left to right: a smaller letter followed by a larger one is subtracted; otherwise it’s added. So MCMXCIV is M (1000) + CM (900) + XC (90) + IV (4) = 1994.

What counts as valid

Valid input follows these rules:

• Only the seven letters: I, V, X, L, C, D, M (or lowercase — the calculator normalizes case).
• Each repeating letter (I, X, C, M) appears at most three times in a row. Four-in-a-row (IIII, XXXX, CCCC, MMMM) is rejected.
• V, L, D never repeat — they appear at most once.
• The only subtractive pairs are IV, IX, XL, XC, CD, CM. Pairs like IL, IC, VX, LC, DM are invalid.

The calculator enforces these implicitly by converting your input back to Roman with the canonical greedy algorithm and rejecting anything that doesn’t round-trip.

What was 0 for the Romans?

Nothing — Roman mathematics had no symbol for zero. (The Latin word nulla, “none”, was used in late-medieval calendars when a column needed to read “no entry”, but it wasn’t an arithmetic numeral.) The modern zero digit arrived in Europe via Arabic translations of Indian mathematics in the 12th century. That’s why every “valid Roman numeral” the calculator accepts is positive: there is no Roman zero to be tolerant of.

Why not 4000+?

To express 4000+ you need the vinculum: a horizontal overline that multiplies the underlying letter by 1000 (so V̄ = 5,000, M̄ = 1,000,000). This calculator doesn’t support it, because the rendering is medium-specific (an overline doesn’t survive plain text well) and the practical demand is nearly nil — every movie credit, every clock face, every Super Bowl number fits comfortably under 3999.