Additive and Subtractive Notation
Roman numerals combine seven symbols using two rules. Additive notation places symbols largest-to-smallest and adds their values: VI is 5 + 1 = 6. Subtractive notation places a smaller symbol immediately before a larger one to subtract: IV is 5 − 1 = 4.
The Seven Symbols
L = 50, C = 100
D = 500, M = 1,000
Only six subtractive pairs are standard: IV (4), IX (9), XL (40), XC (90), CD (400), and CM (900) — each subtracting exactly one power-of-ten step, never more. MCMXCIV, the numeral for 1994, breaks down as M (1000) + CM (900) + XC (90) + IV (4), reading left to right as the largest remaining chunk at each step.
The Rules That Make a Numeral Valid
Not every combination of symbols is a valid Roman numeral. A handful of rules distinguish correct notation from an arbitrary string of letters.
No symbol repeats more than three times in a row
III is 3, but IIII is not standard notation for 4 — IV is used instead. The same applies to X, C, and M: XXX is 30, but 40 is XL, never XXXX.
V, L, and D never repeat
There is no valid numeral using VV, LL, or DD — each of these symbols appears at most once in any correct numeral, since two of them would always be replaceable by the next symbol up.
A subtractive pair only subtracts one step
IX is valid (10 − 1 = 9); IL is not valid notation for 49, even though 50 − 1 = 49 arithmetically — subtraction only applies across one power-of-ten gap, so 49 is written XLIX (40 + 9), not IL.
Where Roman Numerals Persist Today
Roman numerals survive in specific, largely ceremonial contexts rather than for everyday counting, where Arabic numerals replaced them centuries ago for practical arithmetic. Movie and book copyright years, monarch and pope regnal numbers (Elizabeth II, Louis XIV), Super Bowl numbering, and clock faces are the contexts most people still encounter them in.
The appeal in these contexts is largely aesthetic and traditional — Roman numerals are genuinely worse than Arabic numerals for arithmetic, since there is no simple written procedure for adding or multiplying them directly, which is part of why the positional Arabic system displaced them for practical mathematics starting in the medieval period.