Roman Number Converter

What are Roman Numerals?

Roman numerals are a numeral system that originated in ancient Rome, using a set of letters to represent numbers. This system was widely used during the Roman Empire and continues to be seen in many contexts today, such as to indicate years, chapter numbers, clock faces, and more. The Roman numeral system uses the letters I, V, X, L, C, D, M to represent different values.

Basic Rules of Roman Numerals

Roman numerals are made up of seven basic symbols:

• I = 1
• V = 5
• X = 10
• L = 50
• C = 100
• D = 500
• M = 1000

By combining these symbols, Roman numerals can represent various numbers.

Rules for Forming Roman Numerals

1. Addition Rule: When a smaller numeral is placed to the right of a larger numeral, their values are added together. However, a numeral should not be repeated more than three times. For example: VI = V + I = 5 + 1 = 6, XV = X + V = 10 + 5 = 15, VIII = 5 + 3 = 8 (valid), IIII = 4 (invalid, the correct form is IV)
2. Subtraction Rule: When a smaller numeral is placed to the left of a larger numeral, it is subtracted from the larger one. For example: IV = V - I = 5 - 1 = 4, IX = X - I = 10 - 1 = 9. Other rules for subtraction:
   • Limitations on Left Subtraction: Only I, X, and C can be used for subtraction. For example, IV (4) and IX (9) are valid, but VL is incorrect.
   • Subtraction Cannot Span Multiple Place Values: When subtracting, the smaller numeral must be adjacent to only one place value. Specifically, I can only be placed before V or X, X can only be placed before L or C, and C can only be placed before D or M. For example, IC (100 - 1 = 99) is incorrect, and the correct form is XCIX.
3. Repetition Rule: A numeral can only be repeated three times in a row. For example: III = 3, XXX = 30, CCC = 300.

How to Convert Arabic Numerals to Roman Numerals?

To convert Arabic numerals into Roman numerals, break down the number into its corresponding Roman numeral symbols, following the rules above. For example:

• 99to Roman Numerals: XCIX
  • 99 can be split into 90 + 9
  • 90 = 100 - 10 → XC
  • 9 = 10 - 1 → IX
  • 99 → XCIX
  • We do not use IC (100 - 1) for 99 because I cannot span to the place value of C.
• 2023 to Roman Numerals: MMXXIII
  • 2023 = 2000 + 20 + 3
  • 2000 = 1000 + 1000 → MM
  • 20 = 10 + 10 → XX
  • 3 = 1 + 1 + 1 → III
  • 2023 → MMXXIII
• 3999 to Roman Numerals: MMMCMXCIX
  • 3999 = 3000 + 900 + 90 + 9
  • 3000 = 1000 + 1000 + 1000 → MMM
  • 900 = 1000 - 100 → CM
  • 90 = 100 - 10 → XC
  • 9 = 10 - 1 → IX
  • 3999 → MMMCMXCIX

How to Convert Roman Numerals to Arabic Numerals?

To convert Roman numerals back into Arabic numerals, analyze each symbol and its position, then add or subtract their values accordingly. For example:

• XCIX to Arabic Numerals: 99
  • XC → 100 - 10 = 90
  • IX → 10 - 1 = 9
  • XCIX → 90 + 9 = 99
  • We do not use IC (100 - 1) for 99 because I cannot span to the place value of C.
• MMXXIII to Arabic Numerals: 2023
  • MM → 1000 + 1000 = 2000
  • XX → 10 + 10 = 20
  • III → 3
  • MMXXIII → 2000 + 20 + 3 = 2023
• MMMCMXCIX to Arabic Numerals: 3999
  • MMM → 1000 + 1000 + 1000 = 3000
  • CM → 1000 - 100 = 900
  • XC → 100 - 10 = 90
  • IX → 10 - 1 = 9
  • MMMCMXCIX → 3000 + 900 + 90 + 9 = 3999

Rules for Representing Large Numbers in Roman Numerals

Roman numerals combine letters to represent larger numbers. The largest value that can be represented using traditional Roman numerals is 3999 (MMMCMXCIX). For numbers beyond this, traditional Roman numerals are insufficient, but extended methods (such as placing a bar or subscript on the letters, like adding a line above M to indicate multiplication by 1000) can be used to represent larger values.