Roman numerals use seven symbols: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, and M = 1000. They remain common for centuries, chapters, monarchs, clock faces, and events. Unlike base-ten notation, the system is not positional and has no classical Roman symbol for zero.
When symbols are added or subtracted
Symbols in nonincreasing order are added: VIII = 5 + 1 + 1 + 1 = 8 and LXII = 50 + 10 + 1 + 1 = 62. When an allowed smaller symbol precedes a larger one, the pair is subtractive: IV = 4 and IX = 9.
| I | V | X | L | C | D | M |
|---|---|---|---|---|---|---|
| 1 | 5 | 10 | 50 | 100 | 500 | 1000 |
Convert integers and Roman numerals
Move the value and follow its decomposition into thousands, hundreds, tens, and ones.
Which subtractive pairs belong to standard notation?
I may precede V or X; X may precede L or C; C may precede D or M. Thus 49 is XLIX, not IL, and 99 is XCIX, not IC. V, L, and D do not repeat. I, X, C, and M may normally occur no more than three times in a row.
Historical inscriptions contain variations, but modern converters usually enforce this canonical form. State the convention whenever older variants are relevant.
Converting a Roman numeral to an integer
Scan the symbols from left to right. Subtract a value if it is smaller than the one immediately following it; otherwise add it. In MCMXLIV, the groups are M + CM + XL + IV = 1000 + 900 + 40 + 4 = 1944.
An arithmetic total alone does not validate the notation. IIX might be manipulated to give 10, but it is not canonical; 10 is X.
Writing an integer in Roman form
Decompose the value using the largest available symbols and subtractive pairs. For 2748, 2000 = MM, 700 = DCC, 40 = XL, and 8 = VIII, giving MMDCCXLVIII. Converting back provides a reliable check.
A compact reference pattern
The ones follow I, II, III, IV, V, VI, VII, VIII, IX. The same pattern reappears with X in the tens and C in the hundreds: 40 = XL, 90 = XC, 400 = CD, and 900 = CM. Learning these place-based blocks is more useful than memorizing a list to 1000.
| 1 | 4 | 5 | 9 |
|---|---|---|---|
| I | IV | V | IX |
| X | XL | L | XC |
| C | CD | D | CM |
The standard convention above covers 1 through 3999. Larger-number systems using overlines or parentheses exist, but they vary and must be defined before use.
