Roman numerals represent integers with repeated and combined symbols. Modern conventional notation uses a small set of subtraction pairs, but historical forms were less uniform.
The symbols
I, V, X, L, C, D, and M represent 1, 5, 10, 50, 100, 500, and 1,000. Symbols generally descend from left to right and are added. VIII is 5 + 1 + 1 + 1 = 8.
Subtraction pairs
Common subtractive forms include IV, IX, XL, XC, CD, and CM. They make 4, 9, 40, 90, 400, and 900 compact. Not every smaller-before-larger pairing is conventional.
Worked example: 2024
2024 decomposes as 2000 + 20 + 4, producing MMXXIV. Breaking the number into thousands, hundreds, tens, and ones makes conversion easier to audit.
Know the boundary
Standard classroom notation usually handles positive integers up to 3,999 without an overline convention. Zero has no standard classical Roman numeral; a converter should state how it displays zero rather than inventing a symbol.
Sources
The figures and rules in this guide are checked against:
- Roman Numerals — Wolfram MathWorld
- Roman numeral — Encyclopaedia Britannica
- Roman numerals — Khan Academy