The seven symbols
- I = 1
- V = 5
- X = 10
- L = 50
- C = 100
- D = 500
- M = 1000
A useful mnemonic for the order: I Value Xylophones Like Cows Dig Milk.
Values are generally written largest to smallest and added: MMXXVI is 1000 + 1000 + 10 + 10 + 5 + 1 = 2026.
Subtractive notation
The exception to the additive rule is that a smaller value placed before a larger one is subtracted. This exists to avoid four identical symbols in a row.
- IV = 4 (not IIII)
- IX = 9
- XL = 40
- XC = 90
- CD = 400
- CM = 900
Only six subtractive pairs are valid in the standard system. I may precede only V and X, X only L and C, and C only D and M. V, L, and D are never used subtractively.
So 99 is XCIX (90 + 9), not IC. And 1999 is MCMXCIX, not MIM — the subtraction applies within each place value separately.
Why the system stops at 3999
With only symbols up to M for 1000, the largest representable value using no more than three consecutive identical symbols is MMMCMXCIX = 3999.
Romans extended the system with a vinculum — a bar over a numeral multiplying it by 1000, so V̄ is 5,000 and X̄ is 10,000. A double bar multiplied by a million. This notation is difficult to render in plain text and is rarely used today, which is why most converters cap at 3999.
The system's fundamental limitation
Roman numerals have no zero and no positional value, which makes arithmetic genuinely difficult. Multiplying MCMXLVII by XXIII is not something anyone attempts by manipulating the symbols — Romans used a counting board or abacus and recorded results in numerals.
The absence of zero is the deeper problem. Without a placeholder there is no positional notation, and without positional notation there is no efficient algorithm for multiplication, long division, or written arithmetic of any complexity.
The Hindu-Arabic system reached Europe through Fibonacci's Liber Abaci in 1202 and displaced Roman numerals over the following centuries precisely because it made calculation tractable. This is a genuine case where notation, not intelligence, was the constraint.
Where they survive
Roman numerals persist in contexts where they signal formality or avoid confusion with ordinary numbers: clock faces, book chapter and preface numbering, monarch and pope regnal numbers, film copyright dates, building cornerstones, Super Bowl numbering, and outline hierarchies.
Clock faces have a curious convention: many use IIII rather than IV for four. Explanations vary — visual balance against the VIII opposite, avoiding the first two letters of IVPITER, or simply tradition from early clockmaking. There is no single agreed reason, and both forms appear on historical clocks.
Film credits traditionally used Roman numerals for the copyright year, which is sometimes attributed to making the date less immediately obvious to audiences judging a film's age.
Frequently asked questions
Why is 4 written IV and not IIII?
Subtractive notation avoids four identical symbols in a row. A smaller value before a larger one is subtracted, so IV is 5 minus 1. Clock faces are a notable exception and often use IIII.
What is the largest Roman numeral?
MMMCMXCIX, or 3999, using standard notation. Larger values required a bar over a numeral to multiply it by a thousand, which is difficult to render in plain text.
Why is 99 written XCIX and not IC?
Subtraction applies within each place value separately. 99 is ninety plus nine, giving XC plus IX. Only six subtractive pairs are valid: IV, IX, XL, XC, CD, and CM.
Did Romans do arithmetic with Roman numerals?
Not directly. They used a counting board or abacus and recorded the results in numerals. Without zero or positional value, written arithmetic is impractical, which is why Hindu-Arabic numerals eventually displaced them.