Roman Numerals Converter
A free online Roman Numeral converter and Roman arithmetic calculator. Convert standard Arabic integers (1 to 3999) to Roman numerals, or decode Roman strings to decimal values with detailed step-by-step mathematical addition and subtraction breakdowns. Includes a Roman numerals arithmetic tab to add, subtract, multiply or divide numerals with detailed equations. Perfect for learning ancient numbering styles.
Arabic Integer to Roman
- M represents 1 × 1000 = 1000 (remaining: 994)
- CM represents 1 × 900 = 900 (remaining: 94)
- XC represents 1 × 90 = 90 (remaining: 4)
- IV represents 1 × 4 = 4 (remaining: 0)
Roman to Arabic Integer
- Standard symbol "M": value is 1000. Accumulator + 1000.
- Subtractive pair "CM": value is 1000 - 100 = 900. Accumulator + 900.
- Subtractive pair "XC": value is 100 - 10 = 90. Accumulator + 90.
- Subtractive pair "IV": value is 5 - 1 = 4. Accumulator + 4.
- Final sum: M + CM + XC + IV = 1994
Core Roman Numeral Rules
1. Basic Additive Rule
Symbols are written from largest to smallest value, left to right. Their values are summed.XVI = 10 + 5 + 1 = 16
2. Subtractive Pairs Rule
To avoid writing a symbol four times in succession, subtractive notation is used:
• I before V or X subtracts 1 (IV = 4, IX = 9)
• X before L or C subtracts 10 (XL = 40, XC = 90)
• C before D or M subtracts 100 (CD = 400, CM = 900)
3. Repetition Limits
Standard Roman numerals do not repeat a symbol more than three times. For example, 4 is represented as IV, not IIII. Also, V, L, and D are never repeated.
4. Range Limits
Standard systems cannot represent zero (nulla), negative values, decimals, or integers larger than 3999 (which would require MMMM or overline symbols like Vinculum).