The Rules of Roman Numerals

Rule 1 — order from largest to smallest

Outside of subtraction pairs, letters are written in descending order of value and their values are added. DCLXVI reads 500 + 100 + 50 + 10 + 5 + 1 = 666, each symbol smaller than the last. A larger letter never sits to the right of a smaller one unless the smaller one is part of a subtraction pair, which Rule 3 covers.

Rule 2 — repetition is limited

Only the "powers of ten" letters may repeat, and only up to three times in a row: I, X, C and M. So 3 is III and 30 is XXX, but 4 is never IIII — a fourth repeat is replaced by a subtraction pair. The "five" letters V, L and D never repeat at all, because two of them would simply equal the next larger letter (two Vs would be an X).

Rule 3 — only I, X and C subtract

Subtraction is tightly restricted. Only I, X and C can be placed before a larger letter, and each can only be subtracted from the next two larger symbols:

This is why IL, IC, VX and LM are all invalid — they break the "next two larger" limit. And V, L and D are never subtracted at all.

Rule 4 — one subtraction per place value

You subtract at most once within each decimal place. To write 8 you add (VIII), you never subtract twice like IIX. Likewise 1999 is MCMXCIX — a separate subtraction in the hundreds (CM), tens (XC) and ones (IX) place — not a single sweeping shortcut such as MIM.

Rule 5 — no zero, no fractions

The system is whole-number only and starts at 1; there is no symbol for zero and no place-holder. That is also why there is a hard ceiling at 3999 for standard numerals: to go higher you need the vinculum (an overline that multiplies by 1000), which our converter supports up to 3,999,999.

Invalid vs valid, at a glance

• IIII ✗ → IV ✓
• VV ✗ → X ✓
• IL ✗ → XLIX ✓ (for 49)
• MIM ✗ → MCMXCIX ✓ (for 1999)
• XXXX ✗ → XL ✓ (for 40)

Turn on strict validation in the converter and it flags any of these the moment you type them, suggesting the canonical form instead.