Percentage formulas with worked examples
A percent means “per hundred.” This calculator has three modes because “find 15% of 200,” “what percent is 30 of 150,” and “how much did a value change?” are different questions with different denominators.
1. Find a percentage of a number
part = (percentage ÷ 100) × whole. Example: 15% of 200 is 0.15 × 200 = 30. For an $80 item discounted by 15%, the discount amount would be $12, before any taxes or other charges.
2. Find what percentage one number is of another
percentage = (part ÷ whole) × 100. Example: 30 out of 150 is 30 ÷ 150 × 100 = 20%. The whole cannot be zero because division by zero is undefined.
3. Find percentage change
change % = (new − original) ÷ |original| × 100. For example, moving from 80 to 100 is a 25% increase; moving from 100 to 80 is a 20% decrease. The calculator uses the absolute size of the original value as the denominator so that the sign follows the numeric direction of change. When the original value is zero, a percentage change is undefined.
Common mix-up
A 20% increase followed by a 20% decrease does not return to the original amount: $100 increased by 20% becomes $120, and a 20% decrease from $120 leaves $96. Each percentage is applied to its own current base.
Tips for accurate results
Pick the question you are actually asking: what is X percent of Y, what percent is X of Y, or what is the percentage change from X to Y. Each one uses a different formula, and choosing the wrong mode is the most common source of confusion.
Common mistakes and limits
Percent change from zero is undefined. A rise followed by an equal percentage fall does not return to the start, and percentage points differ from percent. Round only at the end to keep the answer accurate.
Learn more: Percentages in everyday life.