Convert decimal to Roman numerals
255 in decimal is CCLV in Roman numerals. Each digit is multiplied by its place value — the base raised to the digit's position, counting from zero on the right — and the products are added. The page prints every one of those products rather than only the total. The conversion is exact: bases are positional notation for the same number, so nothing is rounded and the result can be checked digit by digit.
Conversion rules checked · How we check
255 in decimal
CCLV
How it gets there
- Take the largest symbol that fits, repeatedly
- C = 100 C = 100 L = 50 V = 5
- Subtractive pairs
- IV, IX, XL, XC, CD and CM are the six pairs where a smaller symbol before a larger one means subtract. Only these six; IIX and VC are not numerals.
decimal to Roman numerals, at a glance
Roman numerals have no zero and no place value, so they are added and occasionally subtracted rather than positioned: IV is one before five. That is also why arithmetic in them is so awkward that the abacus outlived them.
| decimal | Roman numerals |
|---|---|
| 1 | I |
| 4 | IV |
| 5 | V |
| 9 | IX |
| 10 | X |
| 40 | XL |
| 50 | L |
| 90 | XC |
| 100 | C |
| 400 | CD |
| 500 | D |
| 900 | CM |
| 1000 | M |
| 2026 | MMXXVI |
Why is the working shown?
Every other converter of this kind prints the answer and stops. A base is a positional system, so the answer is a sum you can check: each digit is multiplied by the base raised to its position, and the results are added. Going the other way is repeated division, reading the remainders upwards. Neither is a black box, and this page refuses to be one.
Other conversions
For the rules themselves — why 99 is not IC, why IIII is on clock faces, and what the overline means above 3,999 — see the Roman numeral converter, which reads a numeral and names the rule when one is written the wrong way.