About this tool
This page collects the five percentage questions people actually ask, each as its own live calculator: what is X% of Y (tips, discounts, tax), X is what percent of Y (test scores, market share), the percent change from one value to another (price rises, growth rates), a value increased or decreased by a percentage (markup, sale price), and the reverse problem, Y is X% of what number (finding the original price after a discount). Every result shows the formula with your numbers substituted so you can check it or reproduce it in a spreadsheet. It also explains the difference between percentage points and percent difference, a distinction that matters when interest rates or poll numbers move.
How it works
The calculators use the elementary definitions. X% of Y is X / 100 x Y. X as a percent of Y is X / Y x 100. Percent change from X to Y is (Y - X) / X x 100, so a rise is positive and a fall is negative, and the base is always the starting value; that is why 50 to 75 is +50% but 75 to 50 is -33.3%. Increasing Y by X% is Y x (1 + X / 100) and decreasing is Y x (1 - X / 100). The reverse problem, Y is X% of what, divides: Y / (X / 100). A percentage-point difference is simply the arithmetic difference between two percentages, while the percent difference between them is the relative change, (new - old) / old x 100.
Frequently asked questions
How do I calculate a percentage of a number?
Divide the percentage by 100 and multiply by the number: 15% of 80 is 0.15 x 80 = 12. A quick mental method is to find 10% by moving the decimal point one place left (8), then scale: 5% is half of that (4), so 15% is 8 + 4 = 12. For 20% tips, double the 10% figure.
Why is the percent change from 50 to 75 different from 75 to 50?
Percent change is always measured against the starting value. Going from 50 to 75 is a change of 25 on a base of 50, which is +50%. Going from 75 to 50 is a change of -25 on a base of 75, which is -33.3%. This asymmetry is why a 50% loss needs a 100% gain to recover, and why you cannot undo a 20% discount by adding 20% back.
What is the difference between percentage points and percent?
Percentage points measure the simple difference between two percentages; percent measures the relative change. If an interest rate rises from 4% to 5%, that is an increase of 1 percentage point but a 25% increase in the rate itself, because (5 - 4) / 4 = 0.25. News reports often mix these up; this page shows both figures side by side.
How do I find the original price before a discount?
Use the reverse calculator. If a jacket costs $60 after a 25% discount, you paid 75% of the original, so the original is 60 / 0.75 = $80. In general, if Y is X% of some number, that number is Y / (X / 100). Adding 25% back to $60 would give $75, which is wrong, because the discount was taken off the larger original figure.