Exact math and number tool

Roman Numeral Converter

Convert an Arabic integer to a conventional Roman numeral or convert a canonical Roman numeral back to an integer. One bidirectional tool owns both directions.

Enter values and select Calculate.

How to use this calculator

  1. Choose the conversion direction.
  2. Enter an integer from 1 through 3,999 or a Roman numeral.
  3. Lowercase Roman input is normalized to uppercase.
  4. Review both the canonical numeral and integer result.

Formula and method

Values are assembled from conventional symbols and subtractive pairs: IV, IX, XL, XC, CD, and CM. Reverse conversion must reproduce the same canonical numeral.

Worked example

2026 becomes MMXXVI. MCMXCIX converts back to 1999, while malformed forms such as IC and IIII are rejected.

Assumptions and limits

  • The supported system is conventional modern Roman notation.
  • Zero and negative values have no output in this traditional range.
  • Extended overline notation beyond 3,999 is not implemented.
  • The later medieval N convention for zero is not used.

Understanding the result

The result follows the displayed deterministic method. Exact-integer operations use BigInt where appropriate, and any controlled precision limit is stated before the related output can be interpreted.

Common mistakes

  • Repeating I four times instead of using IV
  • Subtracting I from C as IC
  • Assuming every sequence of Roman letters is valid
  • Expecting zero or values beyond 3,999

Methodology note

The calculator uses the arithmetic definitions shown on this page. It does not call an external calculator service, evaluate expressions, or infer unselected mathematical conventions.

This deterministic utility is a calculation aid. Confirm required notation, precision, and course or professional conventions separately.