Roman to Arabic Converter

About Roman to Arabic Converter

Roman numeral conversion: place smaller value before larger for subtraction (IV=4, IX=9, XL=40, XC=90, CD=400, CM=900).

How to use this calculator

1. Type the Roman numeral exactly as it appears, for example \(MCMXCIX\).
2. Check the order of the letters, because Roman numerals depend on whether a smaller value comes before or after a larger one.
3. Click convert to get the Arabic number, which is the regular number system you use every day.
4. Read the result and compare it with the values of the Roman symbols to see how the number was built.

The formula explained

Roman numerals are converted by adding values when symbols go from larger to smaller, and subtracting when a smaller symbol appears before a larger one. For example, \(MCMXCIX\) becomes \(1000 + 900 + 90 + 9 = 1999\).

• I = the Roman numeral for \(1\)
• V = the Roman numeral for \(5\)
• X = the Roman numeral for \(10\)
• L = the Roman numeral for \(50\)
• C = the Roman numeral for \(100\)
• D = the Roman numeral for \(500\)
• M = the Roman numeral for \(1000\)

Step by step method

1. Identify each Roman symbol and its value, such as \(M = 1000\) and \(C = 100\).
2. Scan from left to right, if a symbol is smaller than the symbol after it, subtract it, otherwise add it.
3. Combine the values to get the Arabic number.

Worked example

Problem. Convert \(MCMXCIX\) to an Arabic number.

1. \(M = 1000\), \(CM = 900\), \(XC = 90\), and \(IX = 9\).
2. Add the parts, so \(1000 + 900 + 90 + 9\).
3. The total is \(1999\).

Tips and common mistakes

• Watch for subtractive pairs like \(IV\), \(IX\), \(XL\), \(XC\), \(CD\), and \(CM\), because they do not follow simple addition.
• Do not repeat a symbol too many times, since Roman numerals have rules for how many times each letter can appear in a row.

Frequently asked questions