Roman Numeral Converter
Convert between Roman numerals and Arabic numbers instantly. Supports numbers from 1 to 3,999 with step-by-step breakdown.
Roman Numeral Reference
How to Use This Tool
- Choose a direction: "Number → Roman" or "Roman → Number" using the tabs.
- For Number → Roman, enter a whole number between 1 and 3,999.
- For Roman → Number, type a Roman numeral (e.g. MMXXIV) using the letters I, V, X, L, C, D, M.
- View the converted result instantly, along with a symbol-by-symbol breakdown for number-to-Roman conversions.
- Use the Copy button to copy the result to your clipboard.
- Reference the Roman Numeral Reference table for the value of each base symbol and common subtractive pairs.
Formula & How It Works
Greedy Largest-Value Algorithm (Number → Roman)
while remaining ≥ symbolValue: append symbol, remaining -= symbolValueThe converter walks through symbols from largest to smallest (M=1000, CM=900, D=500, CD=400, C=100, XC=90, L=50, XL=40, X=10, IX=9, V=5, IV=4, I=1), repeatedly subtracting the largest symbol value that still fits until nothing remains.
Left-to-Right Summation (Roman → Number)
total = Σ symbolValue, but subtract a symbol if its value is less than the symbol immediately after itEach letter is scanned left to right. If a letter's value is smaller than the next letter's value (like I before V), it is subtracted instead of added — this handles subtractive pairs like IV and XC. The result is validated by converting it back to Roman and checking it matches the input.
Practical Examples & Common Use Cases
Converting the year 2024 to Roman numerals
2024 = 1000 + 1000 + 10 + 10 + 4 → M + M + X + X + IV = MMXXIV.
Converting 1994 to Roman numerals
1994 = 1000 + 900 + 90 + 4 → M + CM + XC + IV = MCMXCIV, a classic example combining three subtractive pairs.
Converting MMXXIV back to a number
M(1000) + M(1000) + X(10) + X(10) + I(1, before V so subtracted) + V(5) = 1000+1000+10+10-1+5 = 2024.
Frequently Asked Questions
Using standard notation, the largest number is 3,999, written as MMMCMXCIX. Numbers 4,000 and above require a vinculum (overline) notation which is not standard.
IV uses the subtractive principle — I (1) before V (5) means 5−1=4. This makes numerals shorter and clearer. Similarly IX=9, XL=40, XC=90, CD=400, CM=900.
Enter the year in the number input above and get the Roman numeral instantly. For example, 2024 = MMXXIV.
Yes! Roman numerals are used in clock faces, movie sequels, Super Bowl editions, book chapters, monarchs (King Charles III), and official documents.