How Roman Numeral Subtractive Notation Works
Roman numerals combine seven symbols (I=1, V=5, X=10, L=50, C=100, D=500, M=1000) by addition when a smaller symbol follows a larger or equal one (VI = 5+1 = 6), and by subtraction when a smaller symbol precedes a larger one (IV = 5−1 = 4) — modern convention only allows subtracting a power of ten from the next two higher symbols (I before V or X, X before L or C, C before D or M), and no symbol repeats more than three times in a row.
This subtractive convention is what most people find confusing about Roman numerals, but it follows a small, consistent set of rules once broken down.
The additive rule
When a symbol is followed by an equal or smaller one, their values simply add together — XII is 10 + 1 + 1 = 12, and VIII is 5 + 1 + 1 + 1 = 8. This is the more intuitive half of the system and covers most numbers that don't sit just below a round value like 9, 40, or 900.
The subtractive rule and its specific limits
When a smaller symbol precedes a larger one, its value is subtracted rather than added — IX is 10 − 1 = 9, and XL is 50 − 10 = 40. Modern usage restricts this subtraction to specific pairs only (I from V/X, X from L/C, C from D/M), which is why 99 is written XCIX (XC=90, IX=9), not a chain of subtractions across unrelated symbols.