Roman Numeral Converter

How do Roman numerals work?

Seven letters carry fixed values and a numeral is read left to right, adding as you go, except where a smaller value sits before a larger one. That single exception is the subtractive rule, and it is the whole of the difficulty.

In XVI every symbol is smaller than or equal to the one before, so the values add: 10 plus 5 plus 1 is 16. In XIV the I sits before the V, so that pair subtracts: 10 plus 4 is 14. The breakdown table under the result shows which rule applied to each part of your input, which is the difference between getting an answer and understanding it.

Which subtractive pairs are allowed?

Six pairs, and no others. The rule is not that any smaller symbol may precede any larger one; only I before V or X, X before L or C, and C before D or M are valid.

• IV is 4 and IX is 9. I subtracts only from V and X.
• XL is 40 and XC is 90. X subtracts only from L and C.
• CD is 400 and CM is 900. C subtracts only from D and M.
• V, L and D never subtract. There is no such numeral as VX or LC.

This is why IC for 99 is wrong and XCIX is right, and why the tool rejects the first rather than guessing at it. Silently accepting an invalid numeral is how a wrong date ends up engraved on something permanent.

Why do Roman numerals stop at 3999?

Because M is the largest symbol and no more than three of any symbol may repeat, so MMMCMXCIX, or 3999, is the ceiling in the standard system. The tool says so rather than inventing notation beyond it.

Larger numbers were written with an overline, called a vinculum, which multiplies the symbol beneath it by a thousand. That convention is real but it is not plain text: it needs a combining overline or an image, it renders inconsistently across devices, and it is almost never what someone converting a birthday or a chapter number actually wants.

If you are converting a year, a date, an anniversary or a chapter, you are inside 1 to 3999 and the limit will never appear.

What are the four mistakes people make?

Four errors account for nearly every invalid numeral, and the tool names which one you hit rather than returning a blank.

1. Four of a symbol in a row. IIII is not 4. The subtractive form IV is, and the same applies to XXXX and CCCC.
2. An invalid subtraction. IC, IL and VX look reasonable and are not allowed. Only the six pairs above subtract.
3. Two subtractions in a row. IXIX is not 18. Each place value is written once, so 18 is XVIII.
4. Out of order symbols. Larger values come first except in a valid subtractive pair, so VIX means nothing.

Where are Roman numerals still used?

They survive in six places, and each one explains part of the search demand for a converter.

Clock and watch faces, where IIII rather than IV is a long-standing horological convention and one of the few sanctioned exceptions to the rule above. Book front matter and chapter numbers. Film and television copyright dates in end credits. Monarchs, popes and family suffixes such as Henry VIII or John Smith III. Numbered events, most visibly the Super Bowl and the Olympiads. And engraving: rings, tattoos and plaques, where a date in numerals is the point and a mistake is expensive.

That last case is why the breakdown table exists. Before something is engraved, seeing that MCMXCIV decomposes into M plus CM plus XC plus IV is worth more than the answer on its own.

What are the Roman numerals from 1 to 20?

The first twenty are worth reading as a set, because every rule in the system appears inside them. Four and nine are subtractive, ten to thirteen are additive, fourteen subtracts inside a larger numeral, and nineteen stacks both behaviours in one string.

Nineteen is the one people write wrongly most often. It is XIX, being ten followed by the subtractive nine, and not IXX, which would be a subtraction applied to a subtraction.

How do you convert a date to Roman numerals?

Convert each part separately and join them with a separator, because there is no Roman numeral for a date. The system has no zero and no notion of a date format, so 4 July 1776 becomes IV, VII and MDCCLXXVI, usually written IV.VII.MDCCLXXVI.

Two consequences follow. A day or month below 10 has no leading zero, since there is nothing to write it with. And the order is entirely yours: a date rendered as day, month, year in one country reads as month, day, year in another, and the numerals themselves carry no clue which you meant.

Paste each part into the box above in turn, and the breakdown table confirms each one before you commit it to metal.