Roman numerals are a tally system with shortcuts, not a positional number system. Understanding that explains every rule and every limitation.
The symbols
| Symbol | Value |
|---|---|
| I | 1 |
| V | 5 |
| X | 10 |
| L | 50 |
| C | 100 |
| D | 500 |
| M | 1000 |
Read left to right, adding as you go. MMXXVI is 1000 + 1000 + 10 + 10 + 5 + 1 = 2026.
Free toolRoman Numeral ConverterConvert numbers to roman numerals and roman numerals back to numbers, with validation that rejects malformed numerals like IIII.Subtractive notation
Where a smaller symbol sits directly before a larger one, subtract it. IV is 4, IX is 9, XL is 40.
Only six pairs are legal, and the rule behind them is that you may only subtract a power of ten from the next two values up:
- I before V or X: IV, IX
- X before L or C: XL, XC
- C before D or M: CD, CM
This is why IL is not 49 and IC is not 99. Forty-nine is XLIX - forty written as XL, nine written as IX. You cannot subtract V, L or D from anything, and you cannot stack subtractions.
Why IIII appears on clocks
Clock faces almost universally use IIII rather than IV for four, and it is deliberate rather than an error.
The usual explanations are visual balance - IIII sits opposite VIII and the two heavy blocks mirror each other - and manufacturing, since a face using IIII needs exactly twenty I, four V and four X, which divides neatly across casting moulds. The convention also predates the hardening of subtractive notation into a rule.
Big Ben is the well-known exception, using IV.
The 3999 ceiling
MMMCMXCIX is 3999, and classical notation has no way past it. There is no symbol above M, and repeating M four times breaks the convention that no symbol appears more than three times consecutively.
Medieval scribes solved this with the vinculum: a bar drawn over a numeral multiplied it by a thousand, so a barred V meant 5,000. There is no standard plain-text way to write it, which is why software - including this site's converter - stops at 3999.
No zero, no fractions of the kind you expect
The system has no zero. It never needed one, because it is not positional: there is no empty column to mark. When Roman writers needed to express nothing, they wrote nulla.
They did have fractions, in twelfths, using a duodecimal set of symbols - S for a half, dots for twelfths. These have vanished from every modern use.
Reading a long numeral
Work left to right and check each symbol against the next. If it is smaller than the one following, subtract it; otherwise add.
MCMXCIV: M is 1000. CM is 900. XC is 90. IV is 4. Total 1994.
The most common misreading is treating CM as C + M, which gives 1100 rather than 900.
Where you still meet them
Monarch and pope regnal numbers, Super Bowl numbering, book preface pagination, film copyright dates, clock faces and outline numbering. In each case they are decorative or traditional rather than functional, which is why the 3999 limit has never been a practical problem.
Convert in either direction with the Roman numeral converter.