What are Roman numerals?
Roman numerals are a numeral system that originated in ancient Rome, using combinations of letters from the Latin alphabet to represent numbers. They were the standard numbering system in Europe until the 14th century, when they were gradually replaced by the Hindu-Arabic system (0–9) that we use today.
The seven basic symbols
The entire Roman numeral system is built on just seven symbols:
| Symbol | Value | Latin Name |
|---|---|---|
| I | 1 | unum |
| V | 5 | quinque |
| X | 10 | decem |
| L | 50 | quīnquāgintā |
| C | 100 | centum |
| D | 500 | quingenti |
| M | 1,000 | mille |
There is no symbol for zero — in the Roman mind, anything with zero value was not a number and was expressed by the Latin word nulla (nothing).
How to convert: the three rules
Rule 1: Write left to right in decreasing order
Start with the largest symbol and work down. For example, 1,666 = MDCLXVI (M + D + C + L + X + V + I).
Rule 2: No symbol repeated four or more times
Use subtractive notation instead. So 4 is IV (not IIII), and 40 is XL (not XXXX).
Rule 3: Subtractive notation
A smaller symbol placed before a larger one means subtraction:
- IV = 4 (5 − 1)
- IX = 9 (10 − 1)
- XL = 40 (50 − 10)
- XC = 90 (100 − 10)
- CD = 400 (500 − 100)
- CM = 900 (1,000 − 100)
Only I, X, and C can be used as subtractive prefixes.
Roman numerals: 1 to 10
| Roman | Value | Explanation |
|---|---|---|
| I | 1 | |
| II | 2 | 1 + 1 |
| III | 3 | 1 + 1 + 1 |
| IV | 4 | 5 − 1 |
| V | 5 | |
| VI | 6 | 5 + 1 |
| VII | 7 | 5 + 1 + 1 |
| VIII | 8 | 5 + 1 + 1 + 1 |
| IX | 9 | 10 − 1 |
| X | 10 |
Roman numerals: 10 to 20
| Roman | Value | Explanation |
|---|---|---|
| X | 10 | |
| XI | 11 | 10 + 1 |
| XII | 12 | 10 + 1 + 1 |
| XIII | 13 | 10 + 1 + 1 + 1 |
| XIV | 14 | 10 + (5 − 1) |
| XV | 15 | 10 + 5 |
| XVI | 16 | 10 + 5 + 1 |
| XVII | 17 | 10 + 5 + 1 + 1 |
| XVIII | 18 | 10 + 5 + 1 + 1 + 1 |
| XIX | 19 | 10 + (10 − 1) |
| XX | 20 | 10 + 10 |
Advanced subtractive rules
The subtractive notation has additional constraints:
- Only I, X, C can subtract — V, L, D, M cannot be used as subtractive prefixes
- Only one subtractive prefix — 27 is XXVII, not IIIXXX
- The subtracted value must be at least 1/10 of the larger value — X can subtract from L or C (making 40 or 90), but not from D or M
This means 1999 must be written MCMXCIX (M + CM + XC + IX), not MIM.
Example: converting MCMXXII
Let's convert MCMXXII to a number:
- M = 1,000
- CM = 900 (C before M = 1,000 − 100)
- XX = 20 (10 + 10)
- II = 2 (1 + 1)
- Total = 1,000 + 900 + 20 + 2 = 1,922
Recent years in Roman numerals
| Year | Roman | Year | Roman |
|---|---|---|---|
| 2026 | MMXXVI | 2025 | MMXXV |
| 2024 | MMXXIV | 2023 | MMXXIII |
| 2022 | MMXXII | 2021 | MMXXI |
| 2020 | MMXX | 2019 | MMXIX |
| 2018 | MMXVIII | 2017 | MMXVII |
| 2016 | MMXVI | 2015 | MMXV |
| 2014 | MMXIV | 2013 | MMXIII |
Large numbers beyond 3,999
The standard Roman system maxes out at 3,999 (MMMCMXCIX). For larger numbers, two systems were used:
Vinculum
A horizontal bar over a numeral multiplies it by 1,000:
- V̅ = 5,000
- X̅ = 10,000
- L̅ = 50,000
- C̅ = 100,000
- D̅ = 500,000
- M̅ = 1,000,000
Apostrophus
Uses bracket-like symbols: C|Ↄ = 1,000, |Ↄ = 500, with each extra set multiplying by 10.
Common uses of Roman numerals today
- Clock faces — many analog clocks use IIII for 4 and IX for 9
- Movie sequels — Star Wars Episode IV, Rocky III
- Sporting events — Super Bowl LVIII, Olympics
- Monuments and buildings — construction dates on buildings
- Book chapters and outlines — academic numbering
- Royal and papal names — Henry VIII, Pope Benedict XVI
Mnemonics to remember the symbols
- My Dear Cat Loves Xtra Vitamins Intensely — M, D, C, L, X, V, I
- I Value Xylophones Like Cows Dig Milk — I, V, X, L, C, D, M