Convert Roman numerals to decimal
MCMXCIV in Roman numerals is 1,994 in decimal. 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
MCMXCIV in Roman numerals
1,994
How it gets there
- Read left to right, subtracting where a smaller symbol comes first
- M → +1000 C before M → −100 M → +1000 X before C → −10 C → +100 I before V → −1 V → +5
- Total
- 1,994
Roman numerals to decimal, 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.
| Roman numerals | decimal |
|---|---|
| I | 1 |
| IV | 4 |
| V | 5 |
| IX | 9 |
| X | 10 |
| XL | 40 |
| L | 50 |
| XC | 90 |
| C | 100 |
| CD | 400 |
| D | 500 |
| CM | 900 |
| M | 1000 |
| MMXXVI | 2026 |
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.