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How to Calculate Percentages

Percentage problems generally fall into four distinct shapes, and mixing up which one applies is the most common source of errors. "X is what percent of Y?" divides the part by the whole and multiplies by 100: (X ÷ Y) × 100. If 30 out of 150 students passed with distinction, that's (30 ÷ 150) × 100 = 20%. "What is X% of Y?" reverses the question — you already know the rate and need the amount: Y × (X ÷ 100). 20% of a 150 bill is 150 × 0.20 = 30. "What is the percentage change from Y to X?" measures growth or decline relative to the starting point: ((X − Y) ÷ Y) × 100. A price moving from 80 to 60 is ((60 − 80) ÷ 80) × 100 = −25%, a 25% decrease. "What is Y after adding or subtracting X%?" applies the rate directly to the base and returns the new total in one step: Y × (1 ± X ÷ 100). Adding 18% tax to a 200 invoice gives 200 × 1.18 = 236.

A worked example ties the four together: a shop lists a product at 150 (Y) and marks it down to 120 (X). The discount is a change calculation: ((120 − 150) ÷ 150) × 100 = −20%. If the shop later restores the original price, that is a 25% increase from 120, not 20% — because the base changed. This asymmetry (a 20% drop needs a larger 25% rise to undo it) trips up a lot of mental math, and is exactly why picking the correct formula for the situation matters more than memorizing a single "percentage equation."

What to Watch Out For

• Percentage points and percent are not interchangeable. If an interest rate rises from 10% to 15%, that is a 5 percentage-point increase, but a 50% relative increase (5 ÷ 10 × 100) — a distinction that gets blurred constantly in financial and economic news, where "rates rose 5%" and "rates rose 5 points" describe very different moves.
• The base matters more than the number itself. A 50% loss followed by a 50% gain does not return you to the starting value, because the second 50% is calculated on a smaller base.
• Rounding compounds. When chaining several percentage operations (a discount, then tax, then a coupon), round only the final result rather than each intermediate step, so small errors don't accumulate.
• All four calculators on this page update live as you type and run entirely in your browser — no numbers are sent anywhere.