How this works
Roman numerals are an additive-subtractive numeral system used across the Roman empire and still seen today on clock faces, book chapter numbers, movie copyright dates and pope / monarch regnal names. Seven letters form the system: I (1), V (5), X (10), L (50), C (100), D (500) and M (1,000). Numbers are written from largest to smallest, left to right, with a subtractive twist: when a smaller value sits immediately before a larger one (IV, IX, XL, XC, CD, CM) you subtract instead of add. The calculator runs both ways and rejects malformed input — "IIII" parses to 4 by the additive rule, but the canonical form is "IV", so it's flagged invalid.
The practical range is 1 – 3,999. Beyond that, Romans used the vinculum — an overline that multiplied the underlying value by 1,000 — but the convention isn't supported in modern web text. If you need years like 2026 (MMXXVI) or a copyright string, you're well within the safe range.
The formula
A letter can repeat at most three times in a row (III is fine, IIII isn't — write IV). Subtractive pairs only use powers of ten before the next two values up: I before V or X, X before L or C, C before D or M. V, L and D never subtract — you won't see VL or LD.
Example calculation
- Convert 2026 to a Roman numeral.
- 2026 = 2000 + 20 + 6 → MM + XX + VI = MMXXVI.
- Reverse: parse XLIX → 40 + 9 (XL is the 40 pair, IX is the 9 pair) = 49.
Frequently asked questions
Why is 4 written as IV and not IIII?
By the standard rule, no character may repeat more than three times in a row, so the next form for 4 is the subtractive IV (5 − 1). IIII does occasionally appear in the wild — most famously on clock faces, where it visually balances the VIII on the opposite side — but in normal text and arithmetic the canonical form is IV. This calculator round-trips through the canonical form, so it accepts IV → 4 → IV but flags IIII as invalid.
How do I write a year like 1999?
1999 is MCMXCIX, not MIM. The subtractive rule only allows I, X and C to precede the next two power-of-ten values up — so you can write IV and IX, but not IM (1,000 − 1) or IL (50 − 1). 1999 decomposes as 1000 + 900 + 90 + 9 → M + CM + XC + IX = MCMXCIX. Long, but canonical.
Did Romans have a zero?
No symbolic zero. The medieval scholar Bede used the word nulla (Latin for "none") when the calculation produced no value, and N as a placeholder, but neither was part of the standard numeric system used by Roman accountants and engineers. Practical zero as a digit arrived in Europe via the Hindu-Arabic numerals through Fibonacci's Liber Abaci (1202) and didn't catch on widely until the printing press. The lack of zero is one reason Roman numerals never developed positional arithmetic.