Roman Numeral and Decimal (Arabic) Converter

How does the Roman numeral converter work?

Our tool is a bidirectional converter, allowing conversion between Roman numerals and Arabic numbers. To perform a conversion, simply enter the Roman or decimal number in the corresponding text box, and the calculator will automatically make the conversion.

How to convert Roman numerals to decimals (or Arabic numerals)?

Converting Roman numerals to Arabic numbers involves following some key rules and principles. Here's a step-by-step guide to performing this conversion:

Step 1: Understand Roman symbols

In the Roman numeral system, seven main symbols are used:

• I represents 1.
• V represents 5.
• X represents 10.
• L represents 50.
• C represents 100.
• D represents 500.
• M represents 1,000.

Remember that Roman numerals are written from left to right and read from left to right.

Step 2: Identify Roman symbols

To convert a Roman numeral into an Arabic number, identify each Roman symbol in the numeral.

Step 3: Apply addition and subtraction rules

The key rules for conversion are:

• If a Roman numeral is followed by an equal or smaller numeral, add its value to the result. Example: "VII" becomes 5 (V) + 1 (I) + 1 (I) = 7.
• If a Roman numeral is followed by a larger numeral, subtract its value from the result. Example: "IV" becomes 5 (V) - 1 (I) = 4.
• Symbols cannot be repeated more than three times in a row. If a symbol repeats four times in a row, you need to use subtraction notation. Example: "CD" becomes 500 (D) - 100 (C) = 400.

Step 4: Sum the values

Once you have applied the addition and subtraction rules, sum all the values to obtain the equivalent Arabic number.

Step 5: Conversion examples

Here are some conversion examples:

• "XII" becomes 10 (X) + 1 (I) + 1 (I) = 12.
• "XXI" becomes 10 (X) + 10 (X) + 1 (I) = 21.
• "XLV" becomes 50 (L) - 10 (X) + 5 (V) = 45.

Step 6: Final verification

Ensure that you have correctly applied the rules and that the values add up to the desired Arabic number.

Roman Numerals Over 4,000 and Non-Integer Numbers

In the Roman numeral system, starting from 4,000, a rule is introduced that adds a horizontal line above the numbers to indicate that they should be multiplied by 1,000. For example, 5,000 is represented as V with a horizontal bar. Additionally, the system includes Roman fractions to represent non-integer numbers, such as ½ represented as "S" and ⅓ as "U". Roman numerals, with their history and versatility in representing both whole and fractional quantities, continue to be a valuable part of our cultural and linguistic heritage.

Roman Numerals Throughout History

Roman numerals, originating in ancient Rome, have a rich history and a lasting influence on modern society. Despite the prevalence of Arabic numerals, Roman numerals still play a crucial role in various areas:

• Watch Design: Roman numerals are a classic choice on watch faces for indicating hours, adding an element of elegance.
• Centuries and Eras: Centuries in history and literature are commonly expressed using Roman numerals, such as the 19th century or the Renaissance.
• Literature and Documents: Roman numerals are used to number chapters, sections, and volumes in books and documents, providing structure and organization.
• Royalty and Succession: In monarchy and nobility, Roman numerals identify successors and heirs to the throne.
• Religion and Hierarchy: Popes and emperors throughout history have been distinguished by Roman numerals, highlighting their importance.
• Academic and Legal Documentation: Today, Roman numerals are common in academic and legal documents, marking sections, chapters, and parts.