Conversion
Convert between decimal numbers and Roman numerals instantly. Supports 1–3999.
Converted Value
MMXXIV
Roman numerals use the symbols: I (1), V (5), X (10), L (50), C (100), D (500), M (1000). Valid range is 1–3999.
A Roman numeral converter is a bidirectional translation tool that converts standard decimal numbers (1–3999) into Roman numeral notation and back. Roman numerals use seven symbols—I (1), V (5), X (10), L (50), C (100), D (500), and M (1000)—combined with subtractive notation rules (e.g., IV for 4, IX for 9) to represent values without a zero.
The converter works in two modes: Number to Roman uses place-value decomposition, starting with the largest Roman values (M, CM, D, CD, C, etc.) and subtracting from the input until zero; Roman to Number sums symbol values right-to-left, subtracting when a smaller value precedes a larger one (subtractive rule), then validates the result by converting back to confirm accuracy. Both modes enforce the valid range of 1–3999.
Number to Roman: Decompose n into multiples of {1000, 900, 500, 400, 100, 90, 50, 40, 10, 9, 5, 4, 1}, appending the corresponding Roman symbols. Roman to Number: Sum values right-to-left; subtract if current value < next value (to the right).Roman numeral conversion relies on place-value decomposition for forward conversion and the subtractive principle for reverse. The subtractive rule allows smaller values to precede larger ones to reduce repetition (e.g., IV instead of IIII for 4), which is key to compact Roman notation.
| Input | Result | Notes |
|---|---|---|
| 2024 | MMXXIV | 2000 (MM) + 20 (XX) + 4 (IV) = 2024. The IV is subtractive notation for 4. |
| 1994 | MCMXCIV | 1000 (M) + 900 (CM) + 90 (XC) + 4 (IV) = 1994. Multiple subtractive pairs show the power of the notation. |
| CDXLII | 442 | 400 (CD) + 40 (XL) + 2 (II) = 442. Reading right-to-left and applying subtractive rules yields the sum. |
The converter supports 1–3999. For 5000 and beyond, Roman numerals require an overline (vinculum) above the symbol, which this standard tool does not implement.
Roman numerals were developed by the Romans before the concept of zero as a number was fully established. The system is additive/subtractive and doesn't need a placeholder; zero was introduced to mathematics later by Indian mathematicians.
While IIII was used historically (particularly on ancient inscriptions and clock faces), modern standard Roman numeral notation uses IV. This converter validates against the subtractive rule (IV, not IIII).
Invalid subtractive pairs (e.g., IL for 49, or IC for 99) are not allowed in standard notation. Only I, X, and C can be subtractive prefixes: I before V or X; X before L or C; C before D or M.
Convert it to a number, then convert that number back to Roman. If it matches, the original was valid. This tool does exactly that internally.
No. This converter runs entirely in your browser. All conversion happens locally; no data is transmitted to a server.