Roman numerals are a numeral system originating in ancient Rome that remain widely used today in clock faces, book chapters, movie sequels, Super Bowl numbering, and formal outlines. This tool converts between Roman numerals (I, V, X, L, C, D, M) and standard Arabic (decimal) numbers in both directions, with validation and step-by-step breakdowns.
Convert between Arabic numbers and Roman numerals. Supports values from 1 to 3999.
Breakdown
Roman Numeral Reference
Enter a Roman numeral (e.g., MCMXCIV) in the Roman input field to see its Arabic (decimal) equivalent, or enter an Arabic number (e.g., 1994) in the number field to see its Roman numeral representation. The tool validates your input in real time - invalid Roman numeral sequences are flagged with specific error messages explaining the issue. A step-by-step breakdown shows how each Roman numeral symbol maps to its value and how subtractive notation works (e.g., IV = 5 - 1 = 4). The tool supports standard Roman numerals from 1 to 3,999 and extended notation with vinculum (overline) for larger values.
Roman numeral conversion is commonly needed for formatting document outlines and legal references (Section IV, Clause IX), numbering book chapters, acts, and scenes in literary and theatrical works, interpreting dates on buildings, monuments, and historical documents (e.g., MCMXLV = 1945), displaying Super Bowl numbers and Olympic Games editions, creating clock face designs and watch interfaces, academic and educational exercises in number systems, and generating formal numbering schemes in contracts, bylaws, and constitutional documents.
Roman numerals use seven symbols: I (1), V (5), X (10), L (50), C (100), D (500), M (1000). The subtractive principle allows placing a smaller value before a larger one to indicate subtraction: IV = 4, IX = 9, XL = 40, XC = 90, CD = 400, CM = 900. The conversion algorithm processes the Arabic number by greedily subtracting the largest possible Roman value at each step. For Roman-to-Arabic, the parser scans left to right, adding each symbol's value unless the next symbol is larger (indicating subtraction). Validation ensures no symbol repeats more than three times and only valid subtractive combinations are used.
Roman numerals use seven symbols: I=1, V=5, X=10, L=50, C=100, D=500, M=1000. Numbers are formed by adding symbols left to right (XVII = 10+5+1+1 = 17). When a smaller symbol precedes a larger one, it is subtracted (IV = 5-1 = 4, IX = 9, XL = 40, XC = 90, CD = 400, CM = 900).
In standard notation, the largest number is 3,999 (MMMCMXCIX). This tool supports values from 1 to 3,999, which covers the full range of standard Roman numeral notation using the seven symbols I, V, X, L, C, D, and M.
The subtractive principle (IV instead of IIII) was standardized to keep Roman numerals concise and avoid four consecutive identical symbols. However, IIII is historically valid and is still used on many clock faces - a convention sometimes called the 'watchmaker's four' for aesthetic balance with VIII on the opposite side.
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