Percentage Calculator
Work out X% of a number, what percent one number is of another, or the percentage change between two numbers.
Percentage calculations
X% of Y = (X / 100) × Y
X is (X / Y × 100)% of Y
Change = (Y − X) / X × 100%
Pick the mode that matches your question. "X% of a number" finds a portion (e.g. a discount or tip); "X is what percent of Y" expresses one number as a percentage of another; "percentage change" gives the increase or decrease from a starting value to a new one (a positive result is an increase, a negative one a decrease).
Worked examples
A portion. 15% of 200 is (15 / 100) × 200 = 30 — a £30 discount on a £200 item, leaving £170 to pay.
One number as a percent of another. If 45 out of 60 questions are correct, that's (45 / 60) × 100 = 75%.
A change between two values. A price rising from £80 to £100 is (100 − 80) / 80 × 100 = +25%; falling back from £100 to £80 is (80 − 100) / 100 × 100 = −20%.
The mistake nearly everyone makes
A percentage rise and the matching fall are not equal, because each is measured against a different starting number. Going up 25% then down 25% does not return you to where you started — the 25% drop is taken from the larger amount, so you end up lower. That's also why a stock that loses 50% must then gain 100%, not 50%, just to break even. Whenever you compare two percentages, check they share the same base.
Everyday uses
The three modes cover almost every day-to-day percentage question: sale discounts and VAT, tips and service charges, test scores, and tracking how much a price, salary, or measurement has moved. For interest that compounds over time rather than a one-off percentage, see thecompound interest calculator.
Per cent and percentage point are different things
The commonest error with percentages is not arithmetic but language. If a rate moves from 4% to 6%, that is a rise of two percentage points and a rise of fifty per cent — both true, wildly different in impression, and routinely used interchangeably. The other trap is that percentage changes do not commute: a 20% rise followed by a 20% fall does not return you to the start, because the second percentage applies to a larger base.