Roman Numeral Converter
Convert between Roman numerals and Arabic numbers with step-by-step arithmetic breakdown.
Input Parameters
Live Result
Details
Steps
Add symbol: M (1000)
Add symbol: M (1000)
Add symbol: X (10)
Add symbol: X (10)
Add symbol: V (5)
Add symbol: I (1)
Quick Answer & Understanding Your Result
A Roman Numeral Converter translates ancient Roman numeral symbols (I, V, X, L, C, D, M) into standard Arabic decimal integers (and vice versa) utilizing classical additive and subtractive arithmetic rules.
Primary Roman Numeral Symbols & Values
- I = 1 | V = 5 | X = 10 | L = 50
- C = 100 | D = 500 | M = 1,000
Classical Subtractive Notation Rules
- IV (4) = 5 - 1 | IX (9) = 10 - 1
- XL (40) = 50 - 10 | XC (90) = 100 - 10
- CD (400) = 500 - 100 | CM (900) = 1,000 - 100
- Repetition Rule: Symbols I, X, C, M cannot repeat more than 3 consecutive times; V, L, D cannot repeat.
Enter any Roman numeral (e.g. MMXXVI) or decimal number (1 to 3999) above to convert instantly with complete step breakdown.
Formula & Calculation Logic
Mathematical FormulaProcesses Roman characters from left to right: if a symbol is followed by one of greater value, the smaller value is subtracted from the larger; otherwise, symbol values are summed additively.
Step-by-Step Guide
Enter Roman Numeral or Decimal Integer
Type an Arabic number (e.g. 2026, 1994) or Roman numeral (e.g. MMXXVI, XLII, MCMXCIV).
Select Conversion Mode (Optional)
Keep 'Auto-Detect' or specify 'Number to Roman' or 'Roman to Number'.
View Converted Result & Syntax Status
Inspect the converted value and verify syntax linter checks for subtractive validity.
Examine Step-by-Step Arithmetic Breakdown
Review the decomposed summation steps (e.g. M (1000) + CM (900) + XC (90) + IV (4) = 1994).
Worked Examples Table
| Example | Input Values | Calculated Result | Explanation |
|---|---|---|---|
| Year 2026 to Roman Numeral | 2026 decomposes into 1000 (M) + 1000 (M) + 10 (X) + 10 (X) + 5 (V) + 1 (I) = MMXXVI. | ||
| Year 1994 (MCMXCIV to Integer) | M (1000) + CM (900) + XC (90) + IV (4) = 1994. |
Frequently Asked Questions
Evidence-Based Methodology & Authoritative References
Encyclopaedia Britannica - Roman Numerals History and System
MathWorld Wolfram - Roman Numerals Mathematics
NIST - Numbers and Unit Representation Standards
Standard: ISO / W3C / IETF Authoritative Domain Standard
Formula: Roman to Integer: Total = Sum(Additive Values) + Sum(Next Symbol - Current Symbol for Subtractive Pairs)
Last Reviewed: August 21, 2026
Primary Source: Encyclopaedia Britannica - Roman Numerals History and System
Reference Document: MathWorld Wolfram - Roman Numerals Mathematics
Computation Privacy: 100% client-side 0ms computation, zero data retention
Calculated results are modeled based on standard scientific and mathematical formulas. Please verify with domain-specific technical documentation for specialized applications.
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Calculated results are modeled based on standard scientific and mathematical formulas. Please verify with domain-specific technical documentation for specialized applications.