Maths
How do Roman numerals work?
Quick answer
Roman numerals write numbers with seven letters: I, V, X, L, C, D and M. Letters are added, and a smaller letter before a bigger one is subtracted, so IV is 4 and XI is 11.
In one sentence
Roman numerals are the number system of ancient Rome, where letters such as I, V, X and L stand for values that you add or subtract.
Explained
The Romans wrote numbers with just seven letters. Each one always means the same amount.
| Letter | I | V | X | L | C | D | M |
|---|---|---|---|---|---|---|---|
| Value | 1 | 5 | 10 | 50 | 100 | 500 | 1000 |
Two rules do almost all the work. First, add when letters go from big to small: VI is 5 + 1 = 6, and XXIII is 10 + 10 + 1 + 1 + 1 = 23. A letter can be repeated up to three times in a row. Second, subtract when a small letter sits in front of a bigger one: IV is 5 − 1 = 4. Only I, X and C are used this way, and only in front of the next two bigger letters (I before V or X, X before L or C, C before D or M).
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Roman numerals have no zero and no place value. The same letter keeps its value wherever it appears, which is why long numbers get long: 1888 is MDCCCLXXXVIII. Our own digits, with a zero and place value, are far quicker for sums. Try adding XLVII and XXVIII without converting them first. Most people convert to ordinary numbers, add, and convert back.
To read a Roman numeral, start at the left and look for a smaller letter before a bigger one. Work out those pairs first, then add everything up. To write one, split the number into thousands, hundreds, tens and ones: 2026 is 2000 + 20 + 6, so MM + XX + VI = MMXXVI.
Examples
| Number | Roman numeral | How it is built |
|---|---|---|
| 4 | IV | 5 − 1 |
| 9 | IX | 10 − 1 |
| 14 | XIV | 10 + 4 |
| 40 | XL | 50 − 10 |
| 90 | XC | 100 − 10 |
| 400 | CD | 500 − 100 |
| 1994 | MCMXCIV | 1000 + 900 + 90 + 4 |
| 2026 | MMXXVI | 2000 + 20 + 6 |
Common mistakes
- Writing 8 as IIX. Only one small letter may go in front of a bigger one, and 8 is VIII (5 + 3).
- Subtracting V, L or D. Writing VX for 5 is wrong; 5 is just V. Those three letters are never subtracted or repeated.
- Skipping a step for 99. It is not IC. Do tens and ones separately: XC + IX = XCIX.
- Four in a row. Most writers use IV for 4. Some clock faces use IIII, which is an old custom, not a mistake.
Quick quiz
Roman numerals
Check what you know with 4 quick questions.
Question 1 of 4
What number is XIV?
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