NumbersRoman numerals: the rules, with examples
Roman numerals write numbers with seven capital letters. They came from ancient Rome and are still used on clock faces, for chapters and volumes of books, for the names of kings and popes, in outlines and lists, and for the class numbers in many Indian schools (Class VI, Class X).
The seven symbols
| Symbol | I | V | X | L | C | D | M |
|---|---|---|---|---|---|---|---|
| Value | 1 | 5 | 10 | 50 | 100 | 500 | 1000 |
There is no symbol for zero, and no place value. The value of a numeral comes from adding and subtracting the symbols.
The rules
- Repeating a symbol adds its value. II is 2, XXX is 30, CC is 200.
- A symbol is never repeated more than three times in a row. 4 is not IIII but IV. (Some clock faces do show IIII, by an old custom.)
- V, L and D are never repeated, because VV would be X, LL would be C and DD would be M.
- A smaller symbol to the right is added. VI is 5 + 1 = 6. LX is 60. MC is 1100.
- A smaller symbol to the left is subtracted. IV is 5 − 1 = 4. XL is 40. CM is 900.
- Only I, X and C can be subtracted, and only from the next two larger symbols: I from V and X, X from L and C, C from D and M. So 49 is XLIX, not IL, and 99 is XCIX, not IC.
- V, L and D are never subtracted. 45 is XLV, not VL.
- Only one smaller symbol is subtracted at a time. 8 is VIII, not IIX.
The six subtractive pairs
Rules 5 to 8 leave exactly six pairs. Learn them and the rest is addition.
| IV | IX | XL | XC | CD | CM |
|---|---|---|---|---|---|
| 4 | 9 | 40 | 90 | 400 | 900 |
Writing a number in Roman numerals
Break the number into thousands, hundreds, tens and ones, write each part, and join them.
- 38 = 30 + 8 = XXX + VIII = XXXVIII
- 94 = 90 + 4 = XC + IV = XCIV
- 149 = 100 + 40 + 9 = C + XL + IX = CXLIX
- 444 = 400 + 40 + 4 = CD + XL + IV = CDXLIV
- 1947 = 1000 + 900 + 40 + 7 = M + CM + XL + VII = MCMXLVII
- 2026 = 2000 + 20 + 6 = MM + XX + VI = MMXXVI
- 3999 = 3000 + 900 + 90 + 9 = MMM + CM + XC + IX = MMMCMXCIX
Reading a Roman numeral
Go from left to right. If a symbol is smaller than the one after it, subtract it. Otherwise add it. For MCMXLVII: M is 1000. C before M is 900. X before L is 40. Then V, I, I add 7. Total 1947.
How far can you go?
With these rules the largest number is 3999, MMMCMXCIX, since 4000 would need four Ms. For larger numbers, a bar drawn over a symbol multiplies it by 1000, so V with a bar is 5000. School work stays within 3999, and most questions within 100.
Common mistakes
- IIII for 4, VIIII for 9, XXXX for 40: use IV, IX, XL.
- IC for 99 and IL for 49: I can be subtracted only from V and X.
- VX for 5: V is never subtracted.
- Small letters in formal writing: Roman numerals are normally capitals, though small letters (i, ii, iii) are used to number preface pages and list items.
Why we do not calculate with them
Try adding XLVIII and XXVII without changing them to 48 and 27. With no place value and no zero, sums are slow, which is why the Hindu-Arabic numerals we use today, which began in India, replaced Roman numerals for arithmetic across the world.
Use the Roman numeral converter to change any number from 1 to 3999 either way, or see the chart of Roman numerals 1 to 100. For practice sheets, see Roman numeral worksheets.