How to Convert Roman Numerals — Rules & Examples

The Foundation: Seven Symbols and Two Principles

The Roman numeral system is elegantly simple, built on just seven Latin letters, each representing a fixed value:

| Symbol | Value | |--------|-------| | I | 1 | | V | 5 | | X | 10 | | L | 50 | | C | 100 | | D | 500 | | M | 1,000 |

All numbers are formed by combining these symbols using two key principles:

1. The Additive Principle

When a symbol of equal or lesser value follows a larger one, add the values.

• II = 1 + 1 = 2
• VI = 5 + 1 = 6
• LX = 50 + 10 = 60
• MDC = 1,000 + 500 + 100 = 1,600

2. The Subtractive Principle

To avoid four identical symbols in a row, a smaller numeral precedes a larger one to indicate subtraction. Only six combinations are valid:

• IV = 5 – 1 = 4
• IX = 10 – 1 = 9
• XL = 50 – 10 = 40
• XC = 100 – 10 = 90
• CD = 500 – 100 = 400
• CM = 1,000 – 100 = 900

💡 Memory Aid: Notice the pattern: I before V/X, X before L/C, C before D/M.

Critical Rules to Remember

• No more than three repeats: III (3) is valid; IIII (4) is not (use IV).
• V, L, D are never repeated: VV (10) is invalid (use X).
• Only subtract from the next two higher values:
  • I can only precede V or X (not L, C, etc.)
  • X can only precede L or C
  • C can only precede D or M

⚠️ Common Mistake: IC for 99 is invalid. Correct form: XCIX (90 + 9).

Step-by-Step Conversion Methods

Converting Arabic Numbers → Roman Numerals

1. Break the number into place values (thousands, hundreds, tens, units).
2. Convert each part using the symbol table and subtractive rules.
3. Concatenate the results.

Example: 1984

• 1,000 = M
• 900 = CM
• 80 = LXXX (50 + 10 + 10 + 10)
• 4 = IV
• Result: MCMLXXXIV

Converting Roman Numerals → Arabic Numbers

1. Read left to right.
2. If a smaller numeral precedes a larger one, subtract it.
3. Otherwise, add all values.

Example: CDXLIV

• CD = 400 (500 – 100)
• XL = 40 (50 – 10)
• IV = 4 (5 – 1)
• Total: 400 + 40 + 4 = 444

Pro Tips & Common Mistakes

• Always use subtractive notation for 4, 9, 40, 90, etc. (IV, not IIII).
• Uppercase is standard for formal use (e.g., copyrights, monuments).
• Validate your work: Ensure no invalid repetitions (VV) or subtractive pairs (IL).
• For large numbers: The standard system maxes out at 3,999 (MMMCMXCIX). Historical extensions (e.g., bars over numerals) are non-standard and rarely used today.
• No zero or negatives: The system has no symbol for zero and cannot represent negative numbers.

Practical Applications

• Reading film copyrights: “© MMXXIV” = 2024
• Understanding event numbering: Super Bowl LVIII = 58
• Deciphering clock faces: Many use IIII for 4 (a stylistic exception), but formal writing uses IV.
• Historical research: Interpreting dates on monuments, documents, and regnal years (e.g., Elizabeth II).
• Formal outlines: Creating hierarchical structures in legal or academic documents (I., A., 1., a.).

Advanced: Why the Rules Exist

The subtractive principle isn’t arbitrary—it reflects Roman efficiency. Writing IV (2 characters) instead of IIII (4 characters) saved space on stone carvings and scrolls. The restriction to only six subtractive pairs ensured clarity and prevented ambiguous forms like IL (which could be misread as 49 or 51).