Roman Numerals Converter

How It Works

Roman numerals use seven symbols: I (1), V (5), X (10), L (50), C (100), D (500), and M (1000). Standard modern Roman numerals use a subtractive notation where a smaller symbol placed before a larger one means subtraction.

The six subtractive pairs are:
- IV = 4 (5 − 1)
- IX = 9 (10 − 1)
- XL = 40 (50 − 10)
- XC = 90 (100 − 10)
- CD = 400 (500 − 100)
- CM = 900 (1000 − 100)

Arabic to Roman algorithm:
The algorithm works by greedily subtracting the largest possible value at each step. A lookup table of value/symbol pairs (including the subtractive pairs) is sorted from largest to smallest: 1000/M, 900/CM, 500/D, 400/CD, 100/C, 90/XC, 50/L, 40/XL, 10/X, 9/IX, 5/V, 4/IV, 1/I. For each pair, the symbol is appended and the value subtracted as many times as possible before moving to the next pair.

Example: 2024
2024 − 1000 = 1024 → M
1024 − 1000 = 24 → MM
24 − 10 = 14 → MMX
14 − 10 = 4 → MMXX
4 − 4 = 0 → MMXXIV
Result: MMXXIV ✓

Roman to Arabic algorithm:
Each symbol has a base value. Reading left to right, if a symbol is smaller than the symbol that follows it, it is subtracted; otherwise it is added. This is the standard additive-with-subtraction parsing rule.

Example: MMXXIV
M(1000) + M(1000) + X(10) + X(10) + I(1) + V(5)
At I: next symbol V(5) > I(1), so subtract: −1
At V: no next symbol or next is smaller, so add: +5
Total: 1000 + 1000 + 10 + 10 − 1 + 5 = 2024 ✓

The range is 1–3999. Roman numerals do not have a symbol for zero, and the standard notation does not extend beyond 3999 without special extensions (like a bar over a letter to multiply by 1000).