Roman numerals
Type a number or a Roman numeral: it converts as you type, in both directions, and automatically flags malformed numerals.
| Subtractive pair | Value | Rule |
|---|---|---|
| IV | 4 | I is subtracted only from V and X |
| IX | 9 | never IIII or VIIII |
| XL | 40 | X is subtracted only from L and C |
| XC | 90 | never LXXXX |
| CD | 400 | C is subtracted only from D and M |
| CM | 900 | never DCCCC |
How the Roman numeral system works
Seven letters cover everything: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1000. Values add up from left to right, with one exception: when a smaller symbol comes before a larger one, it's subtracted. A symbol repeats at most three times in a row, and V, L, and D never repeat at all, which is why IIII, VV, and XXXX aren't valid Roman numerals. This tool flags them right away instead of quietly giving you a wrong answer.
Why the limit is 3999
In standard notation the largest writable number is MMMCMXCIX, i.e. 3999: anything bigger would need four Ms in a row, which the three-repetition rule forbids. For huge numbers the Romans used the "vinculum," a bar drawn over a letter that multiplies its value by a thousand. That's also why Roman numerals today show up on clock faces, in Super Bowl editions (Super Bowl LVIII), movie sequels, kings and popes (Louis XIV), and book chapters, but never in actual arithmetic.