Master Roman Numeral Conversion: Quick Rules and Examples
Basic symbols and values
- I = 1
- V = 5
- X = 10
- L = 50
- C = 100
- D = 500
- M = 1000
Core rules
- Additive rule: Place symbols from largest to smallest left-to-right and add their values.
- Example: XVI = 10 + 5 + 1 = 16
- Subtractive rule: Place a smaller-value symbol before a larger one to subtract. Only specific pairs are allowed:
- I before V or X (IV = 4, IX = 9)
- X before L or C (XL = 40, XC = 90)
- C before D or M (CD = 400, CM = 900)
- Repetition limits: I, X, C, M can repeat up to three times in a row (III = 3, XXX = 30). V, L, D are never repeated.
- No other subtractive combinations: You should not use multiple smaller symbols to subtract (e.g., IIX is invalid). Subtraction only uses one smaller symbol before one larger symbol.
- Largest-first convention: Represent numbers by using the largest possible symbols first (greedy method).
Step-by-step conversion (Arabic → Roman)
- Start with the largest Roman value ≤ number.
- Append its symbol and subtract that value.
- Repeat until the number is zero.
- Apply subtractive pairs where appropriate (e.g., prefer IV over IIII).
Example: 1987
- 1000 → M (remaining 987)
- 900 → CM (remaining 87)
- 50 → L (remaining 37)
- 30 → XXX (remaining 7)
- 5 → V (remaining 2)
- 2 → II
Result: MCMLXXXVII
Step-by-step conversion (Roman → Arabic)
- Read left-to-right, add values of symbols.
- If a symbol is followed by a larger one, subtract its value instead of adding.
- Sum all values.
Example: XLIV
- X (10) before L (50) → subtract: -10 + 50 = 40
- I (1) before V (5) → subtract: -1 + 5 = 4
Total: 44
Edge cases and tips
- Zero has no Roman numeral; use 0 or N (rare medieval usage).
- Standard modern usage covers 1–3999 (I–MMMCMXCIX). For numbers ≥4000, use bars/overlines to indicate multiplication by 1,000.
- Validate strings by ensuring allowed subtractive pairs and repetition limits.
Quick reference table
- 1 = I, 4
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