What this calculator does
Roman numerals combine seven letters, I, V, X, L, C, D and M, using addition and a limited form of subtraction. A smaller symbol before a larger one subtracts, so IV is four and IX is nine, while the same symbols in the other order add.
The system has no zero and no place value, which makes arithmetic with it awkward and is why it was displaced for calculation. It survives for numbering, dates on buildings, book chapters, monarchs and film credits, where its formality is the point.
The formula
Converting to Roman uses a greedy algorithm: repeatedly subtract the largest value that fits and append its symbol, including the six subtractive pairs. Converting back scans left to right, subtracting any symbol smaller than the one that follows it and adding the rest.
| Term | Meaning |
|---|---|
| I, V, X | 1, 5, 10. |
| L, C | 50, 100. |
| D, M | 500, 1000. |
| Subtractive pairs | IV, IX, XL, XC, CD, CM. |
The inputs explained
| Field | What to enter |
|---|---|
| Number or numeral | Either a number from 1 to 3999, or a Roman numeral. The calculator detects which you entered and converts in the appropriate direction. |
When to use it
Reading a date on a building
Cornerstones and monuments are frequently dated in Roman numerals. MCMXCIV resolves to 1994: M for 1000, CM for 900, XC for 90, IV for 4.
Numbering chapters or sections
Front matter, appendices and outline levels still commonly use Roman numerals, and lower-case forms are conventional for preliminary pages.
Understanding film and television credits
Copyright years in credits are routinely given in Roman numerals, a convention that dates from an era when it made the year less immediately obvious.
Checking a numeral is well formed
Not every string of these letters is valid. IIII is sometimes seen on clock faces but IV is the standard form, and this converter uses standard rules.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
Numbers as Roman numerals
A range of numbers converted into standard Roman form.
Roman numerals back to numbers
Numerals of the kind found on buildings and in credits, converted back.
Questions
Why is there no zero in Roman numerals?
The system counts quantities rather than using place value, so a symbol for nothing was not needed. Zero as a number arrived in Europe much later, via Indian and Arabic mathematics.
What is the largest Roman numeral?
In the standard system, 3999: MMMCMXCIX. Larger values require an overline above a letter to multiply it by a thousand, a notation that is rarely used today.
How does subtractive notation work?
A smaller symbol placed before a larger one is subtracted. Only six pairs are valid: IV, IX, XL, XC, CD and CM. Only powers of ten are ever subtracted, and only from the next two larger symbols.
Why do some clocks show IIII instead of IV?
A long-standing horological convention, with several competing explanations: visual balance against VIII on the opposite side is the most commonly offered. IV remains the standard mathematical form.
How do I write years in Roman numerals?
Break the year into thousands, hundreds, tens and units, and convert each. 2024 is MM for 2000, XX for 20, and IV for 4, giving MMXXIV.
For conversion between number bases, see the base converter.