Understanding Roman Numerals
Roman numerals originated in ancient Rome and were used throughout the Roman Empire. They remained the primary way to write numbers in Europe well into the Late Middle Ages. Today, they're still used in specific contexts such as clock faces, book chapters, movie sequels, and formal events.
Basic Roman Numerals
| Symbol |
Value |
Origin |
| I | 1 | One finger |
| V | 5 | Open hand |
| X | 10 | Two hands crossed |
| L | 50 | Half of C (centum) |
| C | 100 | Centum (hundred) |
| D | 500 | Half of M |
| M | 1,000 | Mille (thousand) |
Rules for Roman Numerals
1. Additive Principle
When a smaller numeral appears after a larger one, add them:
- VI = 5 + 1 = 6
- XII = 10 + 1 + 1 = 12
- LXVII = 50 + 10 + 5 + 1 + 1 = 67
2. Subtractive Principle
When a smaller numeral appears before a larger one, subtract it:
- IV = 5 - 1 = 4
- IX = 10 - 1 = 9
- XL = 50 - 10 = 40
- XC = 100 - 10 = 90
- CD = 500 - 100 = 400
- CM = 1000 - 100 = 900
3. Repetition Rule
A symbol can be repeated up to three times to add value:
- I = 1, II = 2, III = 3
- X = 10, XX = 20, XXX = 30
- C = 100, CC = 200, CCC = 300
- M = 1000, MM = 2000, MMM = 3000
Note: V, L, and D are never repeated (use IV instead of IIII, XL instead of XXXX)
4. Subtraction Rules
Only specific pairs can use subtraction:
- I can be subtracted from V and X only
- X can be subtracted from L and C only
- C can be subtracted from D and M only
Common Roman Numerals
| Roman |
Decimal |
Roman |
Decimal |
| I | 1 | XI | 11 |
| II | 2 | XII | 12 |
| III | 3 | XIII | 13 |
| IV | 4 | XIV | 14 |
| V | 5 | XV | 15 |
| VI | 6 | XX | 20 |
| VII | 7 | XXX | 30 |
| VIII | 8 | XL | 40 |
| IX | 9 | L | 50 |
| X | 10 | C | 100 |
Larger Numbers
| Roman |
Decimal |
Notes |
| C | 100 | Centum |
| CC | 200 | |
| CCC | 300 | |
| CD | 400 | 500 - 100 |
| D | 500 | |
| DC | 600 | 500 + 100 |
| DCC | 700 | |
| DCCC | 800 | |
| CM | 900 | 1000 - 100 |
| M | 1,000 | Mille |
| MM | 2,000 | |
| MMM | 3,000 | |
Real-World Uses of Roman Numerals
Clocks and Watches
Many traditional clocks use Roman numerals. Interestingly, most use IIII instead of IV for the number 4 for aesthetic balance.
Monarchs and Popes
- Queen Elizabeth II
- King Louis XIV (14th)
- Pope John Paul II
- King Henry VIII (8th)
Movies and Entertainment
- Movie sequels: Rocky IV, Star Wars Episode VI
- Super Bowl games: Super Bowl LVIII (58)
- Olympic Games: Paris XXXIII (33rd) Olympiad
Books and Documents
- Chapter numbers: Chapter XII
- Preface pages: i, ii, iii, iv, v
- Outlines: I. Introduction, II. Body, III. Conclusion
Architecture and Monuments
Cornerstones and plaques often use Roman numerals for dates: MCMXCIX (1999)
Converting Examples
Decimal to Roman
Example: 1994
- 1000 = M
- 900 = CM (1000-100)
- 90 = XC (100-10)
- 4 = IV (5-1)
- Result: MCMXCIV
Roman to Decimal
Example: XLII
- X before L: 50 - 10 = 40
- I + I after: 1 + 1 = 2
- Result: 40 + 2 = 42
Years in Roman Numerals
| Year |
Roman Numeral |
| 1900 | MCM |
| 1950 | MCML |
| 2000 | MM |
| 2024 | MMXXIV |
| 2025 | MMXXV |
| 2026 | MMXXVI |
Limitations
Roman Numeral Limitations:
- Standard system only goes up to 3,999 (MMMCMXCIX)
- No symbol for zero
- No decimal or fractional representation
- Difficult to perform arithmetic operations
- Longer representation for large numbers
Fun Facts
- The Romans had no symbol for zero, which was introduced by Indian mathematicians
- IIII is often used instead of IV on clocks for symmetry with VIII
- The longest year in standard notation is 3,888: MMMDCCCLXXXVIII
- Roman numerals are still the official numbering system for the Super Bowl
- In ancient Rome, larger numbers used different notation systems, including drawing bars over numerals