A Comprehensive Guide to Roman Numerals
Welcome to your complete guide to understanding Roman numerals. This page will walk you through the basic symbols, rules for forming numbers, and examples to help you master the system.
The Basic Symbols
The entire Roman numeral system is built upon seven basic symbols, each representing a different value:
- I = 1
- V = 5
- X = 10
- L = 50
- C = 100
- D = 500
- M = 1,000
Core Rules of Combination
To form numbers, these symbols are combined using two primary principles: the additive and subtractive rules.
1. The Additive Principle
When symbols are placed from left to right in order of greatest to least value, their values are added together.
- Example: VI = 5 + 1 = 6
- Example: LXI = 50 + 10 + 1 = 61
- Example: MMXIV = 1000 + 1000 + 10 + 4 = 2024 (This also includes a subtractive part, see below)
A symbol can be repeated up to three times in a row. For instance, III is 3, but IIII for 4 is incorrect under standard rules.
2. The Subtractive Principle
To avoid repeating a symbol four times, a smaller value symbol can be placed before a larger value symbol. When this happens, the smaller value is subtracted from the larger one.
- I can be placed before V (5) and X (10) to make 4 (IV) and 9 (IX).
- X can be placed before L (50) and C (100) to make 40 (XL) and 90 (XC).
- C can be placed before D (500) and M (1000) to make 400 (CD) and 900 (CM).
Key restrictions for the subtractive principle:
- Only one smaller-value symbol can be placed before a larger-value symbol. (e.g., 8 is VIII, not IIX).
- The subtracted symbol must be a power of ten (I, X, or C).
- The smaller symbol must be no less than one-tenth of the value of the larger symbol (e.g., 99 is XCIX, not IC).
Reading Roman Numerals: A Step-by-Step Example
Let's break down how to read the number MCMXCVIII.
- Start from the left: M is 1000.
- Next is CM. C (100) is smaller than M (1000), so we subtract: 1000 - 100 = 900.
- Next is XC. X (10) is smaller than C (100), so we subtract: 100 - 10 = 90.
- Next is VIII. V (5) is followed by smaller symbols, so we add: 5 + 1 + 1 + 1 = 8.
- Finally, add all the parts together: 1000 + 900 + 90 + 8 = 1998.
Ready to test your knowledge? Head back to our Roman numeral converter and try converting some numbers!