🏛 Roman Numeral Converter
Convert a number into Roman numerals or a numeral back into a number, anywhere from 1 to 3,999, with a breakdown showing which symbol contributes what.
How Roman numerals work, and where they still appear
Roman numerals use seven letters, combined by addition, with one rule for subtraction. There is no zero and no place value, which is exactly why the system was eventually abandoned for arithmetic and why it survives only where numbers are read rather than calculated with.
The seven symbols
| Symbol | Value | Origin |
|---|---|---|
| I | 1 | A single tally mark |
| V | 5 | Possibly an open hand |
| X | 10 | Two hands, or a crossed tally |
| L | 50 | From an older symbol for 50 |
| C | 100 | From centum |
| D | 500 | Half of an archaic symbol for 1,000 |
| M | 1,000 | From mille |
The subtractive rule
A smaller symbol placed before a larger one is subtracted rather than added. IV is 4, not 6; IX is 9; XL is 40; CM is 900. Only six such pairs are valid in standard notation:
| Pair | Value | Pair | Value |
|---|---|---|---|
| IV | 4 | XL | 40 |
| IX | 9 | XC | 90 |
| CD | 400 | CM | 900 |
The constraints are that only I, X and C can be subtracted, and each only from the next two higher symbols. That rules out IL for 49, which must be written XLIX, and it rules out VX, LC and DM entirely.
Reading and writing them
To read, work left to right adding each value, except where a symbol is smaller than the one after it, in which case subtract. To write, work from the largest value down, taking as many of each as will fit. For 1994: one thousand (M), nine hundred (CM), ninety (XC), four (IV), giving MCMXCIV.
Clock faces often show IIII rather than IV for four. This is a long-standing convention, usually explained by visual balance against the VIII opposite, and it is not an error. The converter flags it as non-standard because it is, while recognising the value correctly.
The limits
Standard numerals run from 1 to 3,999. There is no symbol for zero, because Roman arithmetic had no use for one, and nothing above M, so 4,000 cannot be written without extending the system. The classical extension is a vinculum, an overline multiplying a symbol by a thousand, so V with a bar is 5,000. It is rarely used outside scholarly work and this converter does not implement it.
The absence of zero and of place value is also why Roman numerals are useless for calculation. Multiplying MCMXCIV by XVII is not a thing anyone did; Romans used an abacus and wrote the result down in numerals afterwards.
Where they still turn up
- Clock and watch faces, where they are decorative rather than functional.
- Film and television copyright dates, originally to make the year less obvious to audiences.
- Monarchs and popes: Elizabeth II, Louis XIV, Benedict XVI.
- Book front matter, where prefaces are numbered i, ii, iii before the main pagination starts.
- Super Bowls, with the odd exception of Super Bowl 50, which the NFL judged looked wrong as L.
- Chemistry and medicine, for oxidation states and clotting factors.
A worked example
Write 2,026. Two thousands gives MM, leaving 26. Twenty is XX, leaving 6. Five is V, leaving 1, which is I. The result is MMXXVI. Reading it back: 1000 + 1000 + 10 + 10 + 5 + 1 = 2,026, with no subtractive pairs involved.
Frequently Asked Questions (FAQs)
Why is 4 written IV and not IIII?
Standard notation uses the subtractive form, where a smaller symbol before a larger one is subtracted. IIII is the older additive form and still appears on clock faces by convention, where it balances the VIII opposite it. Both are understood; only IV is standard.
What is the largest number in Roman numerals?
3,999, written MMMCMXCIX, using only the standard seven symbols. Larger numbers need a vinculum, an overline that multiplies a symbol by a thousand, which is rare outside academic contexts.
Is there a Roman numeral for zero?
No. The system had no need for one, since it is not positional and nothing has to hold an empty column. Latin writers occasionally used the word nulla when a zero was needed in a table, but there was never a symbol.
How do I write the current year in Roman numerals?
Break it into thousands, hundreds, tens and units and convert each. 2026 is MM + XX + VI = MMXXVI. 2024 was MMXXIV, using the subtractive IV for the four.
Why do films use Roman numerals for the year?
The practice began in early Hollywood, partly from a convention of formality and partly, it is often said, to make the release year less immediately legible to audiences watching a re-release. It stuck as a stylistic habit long after the reason faded.
Can Roman numerals be used for arithmetic?
Not practically. Without place value or a zero, there is no column-based method for addition or multiplication. Romans calculated on an abacus and recorded the results in numerals, which is the division of labour the system was actually designed for.