Roman Numeral Converter

How Roman numerals work, and why IIII is not four

Roman numerals are seven letters and two rules: add when values descend, subtract when a smaller value precedes a larger one. What trips people up is that the subtractive rule is far narrower than it looks — only six subtractive pairs are legal, which is why IC is not 99 and IIII is not 4 in standard notation.

How it works

• Converts a number from 1 to 3,999 into standard Roman notation, and reads a numeral back into a number.
• Rejects non-canonical forms rather than guessing at them, so you can tell a valid numeral from a plausible-looking one.
• Lists the seven symbols and the values people most often look up, each one clickable.

the seven symbols
  I 1    V 5    X 10    L 50    C 100    D 500    M 1000

the only six legal subtractive pairs
  IV 4    IX 9    XL 40    XC 90    CD 400    CM 900

I subtracts only from V and X
X subtracts only from L and C
C subtracts only from D and M
V, L and D never subtract at all

Worked example

Writing 1987 in Roman numerals, largest value first.

1. 1987 - 1000 = 987 M
2. 987 - 900 = 87 CM (the subtractive pair, not DCCCC)
3. 87 - 50 = 37 L
4. 37 - 10 = 27 X
5. 27 - 10 = 17 X
6. 17 - 10 = 7 X
7. 7 - 5 = 2 V
8. 2 - 1 = 1 I
9. 1 - 1 = 0 I
10. result MCMLXXXVII

Greedy subtraction of the largest available value always produces the canonical form, which is why the encoding is unambiguous even though the notation looks loose. Reading is the reverse: add each symbol, but subtract any symbol smaller than the one after it.

Reading the result

• There is no zero and no negative number. The Romans had no symbol for nothing, and the system was built for counting and tallying rather than for arithmetic — try long division in numerals once and the reason positional notation won becomes obvious.
• Clock faces are the famous exception. Many use IIII for four rather than IV, for balance against the VIII opposite and, by one account, to avoid the first two letters of IVPITER. It is a genuine convention, but it is not standard notation, so this tool rejects it.
• The ceiling of 3,999 is a limit of the letters, not of the idea. Larger numbers needed a vinculum — a bar over a numeral multiplying it by a thousand — or the apostrophus. Neither is standardised in plain text, so calculators almost universally stop at MMMCMXCIX.
• This tool validates by re-encoding: it reads the value, writes it back out, and requires the result to match what you typed. That single rule catches IIII, VV, IC, XM and MMMM without enumerating them, and it is why a numeral that parses to the right number can still be rejected as non-canonical.

Common questions

Why is 99 XCIX and not IC?

Because I may only be subtracted from V and X. IC would require subtracting one from a hundred, which the notation does not allow. 99 is built as XC (90) followed by IX (9). The same rule makes 999 CMXCIX rather than IM.

What about years after 3999?

They need notation that plain text cannot carry — usually a vinculum, a bar drawn over a numeral to multiply it by a thousand, so V with a bar is five thousand. Since there is no agreed way to type that, this converter stops at 3,999 rather than inventing a format.

Is there a Roman numeral for zero?

No. Medieval scholars writing in Latin sometimes used N, for nulla, but it was never part of the numeral system itself. The absence is not an oversight — a tally system does not need a symbol for nothing until you start doing positional arithmetic with it.