Seven symbols and two rules

The additive rule: symbols in descending order are added, so LXVII is 50 plus 10 plus 5 plus 1 plus 1, or 67. The subtractive rule: a smaller symbol placed before a larger one is subtracted, so IX is 9 and CD is 400.

The subtractive rule is tightly constrained, and this is where most hand-written numerals go wrong. Only I, X and C may be subtracted, and each only from the next two values up:

Two further constraints: I, X, C and M may repeat at most three times, and V, L and D never repeat at all. So 1999 is MCMXCIX, not MIM — a form that appears constantly and is not valid, because I cannot be subtracted from M.

How the conversion actually works

Every standard converter uses the same table of thirteen value-and-symbol pairs, taken largest first, subtracting as many times as each fits:

Including the four subtractive pairs in the table is what makes the greedy approach produce valid output automatically — there is no separate step that decides when to subtract.

Worked example, 2026. Take 1000 twice, leaving 26. Take 10 twice, leaving 6. Take 5, leaving 1. Take 1. Result MMXXVI, and checking backwards: 1000 plus 1000 plus 10 plus 10 plus 5 plus 1 is 2026.

Worked example, 1994. Take 1000, leaving 994. Nine hundred fits, so CM, leaving 94. Ninety fits, so XC, leaving 4. Four fits, so IV. Result MCMXCIV, which reads as 1000 plus 900 plus 90 plus 4.

Reading in the other direction is a single pass: add each symbol value, but subtract instead of adding whenever the current symbol is smaller than the one after it.

Why clock faces show IIII

Strict subtractive notation is a later standardisation, not classical practice. Roman inscriptions and manuscripts use IIII and XXXX freely alongside IV and XL, and the choice was often a matter of the space available or the mason preference. The tidy rule set above was settled long after Rome.

Clock dials preserve the older habit, and IIII rather than IV is still the overwhelming convention on traditional dials. Several explanations circulate — visual balance against the VIII opposite it, avoiding a resemblance to the initials of the Roman god Jupiter, easier casting of moulds when the numerals are struck rather than engraved — and none of them is documented well enough to state as fact. What is safe to say is that IIII on a clock is not an error, and that a converter which only ever emits IV is following a modern convention rather than a historical one.

What the system cannot represent

There is no zero. The seven symbols have no way to write nothing, which is not a gap in the notation so much as a difference in what it is for: it is a tally-derived system for recording quantities, not a positional system for calculating with them. Medieval computists working out Easter dates simply wrote the word for nothing, and the letter N stood in for zero in Bede calendrical tables in the eighth century.

There is no place value. Written arithmetic in Roman numerals is awkward, which is why Romans did not do it that way — calculation happened on a counting board or abacus and only the result was written down. The frequent claim that Roman numerals held back mathematics for centuries overstates it; the counting board handled the arithmetic perfectly well.

There are no fractions in the seven symbols. Romans used a separate duodecimal scheme for parts, with S for a half and dots for twelfths — unrelated to the letters and not supported by any modern converter.

There is a ceiling at 3999. With three M at most, the largest expressible number is MMMCMXCIX. Above that, historical practice used a vinculum — an overline multiplying a numeral by a thousand — or the older bracketing notation. Neither is well supported in plain text, so most tools, including this one, stop at 3999 rather than inventing a form.

Practical notes for people using them today

Roman numerals survive in clock dials, film and broadcast copyright lines, the front matter of printed books, regnal and papal numbers, chemical oxidation states, and chord analysis in music theory. The American football championship used them continuously until the fiftieth game in 2016, which was branded with an Arabic 50 because L on its own looked wrong, and then reverted to LI the following year — a good illustration of the system being a typographic choice rather than a numeric one.

Three things worth knowing if numerals end up in software:

• They do not sort. Alphabetically, IX comes before V, and XL comes before XLI but also before XV. Sorting a list of Roman numerals as text produces an order unrelated to their values, so store the number and render the numeral.
• Lenient parsers accept nonsense. A simple add-and-subtract reader happily returns 49 for IL and 4 for IIII, and something for IXIX. If input validity matters, validate against the constraints above rather than relying on the parser not to crash.
• Unicode has lookalike characters. There are precomposed Roman numeral code points that display as Ⅰ, Ⅱ and Ⅲ but are not the letters I and V. Text containing them will not match a search for the letter forms, and comparisons fail silently. Convert them to plain letters on input.

Two pieces of trivia that are actually verifiable: the longest year written in Roman numerals in the modern era was 1888, thirteen characters as MDCCCLXXXVIII, and the longest number below four thousand is 3888 at fifteen characters, MMMDCCCLXXXVIII.

Questions people actually ask

Is IIII wrong?

Not historically, and not on a clock. In modern prose and for anything a style guide governs, use IV.

Why does my numeral not match another converter?

Usually because one of them permits non-standard subtractive forms. MCMXCIX and MIM look like alternatives for 1999 but only the first is valid, and a lenient tool may produce or accept the second.

How do I write a number above 3999?

There is no plain-text standard. An overline multiplying by a thousand is the historical answer, but it needs typography rather than characters, which is why most converters stop.

Is anything I convert here recorded?

No. The conversion runs in your browser and nothing is sent to a server, logged or stored.