How is percent change calculated?

Percent change = ((new - old) / old) * 100. A negative result means a decrease. From 80 to 100 is +25%; from 100 to 80 is -20% (the percentages aren't symmetric because the denominator is different in each direction).

What's the difference between 'percent of' and 'percentage'?

'Percent of' is the absolute portion (25% of 80 is 20). 'What percentage' is the ratio (20 is 25% of 80). Both are computed here, as separate modes.

How do I add a percentage to a number?

Use the X +/- Y% mode with direction set to +. 100 + 20% becomes 120 (the 20% is taken of the original 100). For subtraction, flip the direction: 100 - 20% becomes 80.

How do I work out a price before VAT?

Use the 'X is Y% of what' mode. A receipt for 120 with 20% VAT means the pre-tax price was the value V where 120 = (100% + 20%) * V, so 120 / 120 * 100 = 100. Equivalently: 120 - (120 / 1.20 * 0.20) = 100. The reverse-percentage mode does the first form for you.

Percent vs. percentage points - what's the catch?

Confusing the two is the most common percent error in the news. Going from 50% to 55% is a 5 percentage-point rise (subtract the numbers) but a 10% relative rise (the change is 5/50 = 10% of the original). Headlines that quote one and imply the other are the source of most 'wait, what?' arguments.

Percentage Calculator

Five percent modes in one tool: X% of Y, percent change, reverse percentage, plus add or subtract a percent.

What is X percent of Y?

Result

Pick a mode, type the numbers, read the answer. Five modes cover the most-searched percentage questions: X% of Y (discounts, tips), X is what % of Y (scoring, share-of), percent change from X to Y (year-over-year movements), X is Y% of what number (reverse VAT, working back from a part), and X +/- Y% (apply a tax, raise or markup). The formula used appears under every result so the maths is auditable, not magic.

How to use it

Pick a mode
Five modes cover the common questions: X% of Y, X is what % of Y, percent change, reverse (X is Y% of what), and X +/- Y%.
Enter the two numbers
Type X and Y. For the +/- mode, also pick the direction (+ or -). The answer updates with every keystroke.
Read the result and the formula
The result appears in the highlighted card. Underneath, the formula trace shows the exact calculation - useful for sanity-checking or pasting into a report.

What is it?

A percentage calculator answers the five everyday percent questions in one place: what is X% of Y; what fraction X is of Y; how much Y has moved from X; what whole gives X as Y% of itself; and what Y +/- X% becomes. The arithmetic is trivial - divide, multiply, subtract - but doing it under time pressure or on a phone keypad is where the mistakes happen. The formula trace below each result lets you spot a typo before it ships.

When to use it

Discounts and sale prices ('30% off $80'), VAT or sales-tax (add or strip), tipping a restaurant bill, grading an exam, performance reviews ('revenue up 12% YoY'), reverse-engineering a pre-tax price from a tax-inclusive total, applying a raise or markup, working out what fraction one number is of another. Pairs especially well with the discount and tip calculators.

Common mistakes

Confusing 'percent of' with 'percentage points' - a change from 50% to 55% is a 5-point rise but a 10% relative rise. Inverting the percent-change formula: it's (new - old) / old, not the other way round. Dividing by zero - if the old value is 0, the percent change is undefined. And forgetting that consecutive percentages don't add: +20% then -20% is -4%, not 0%.

FAQ

How is percent change calculated?: Percent change = ((new - old) / old) * 100. A negative result means a decrease. From 80 to 100 is +25%; from 100 to 80 is -20% (the percentages aren't symmetric because the denominator is different in each direction).
What's the difference between 'percent of' and 'percentage'?: 'Percent of' is the absolute portion (25% of 80 is 20). 'What percentage' is the ratio (20 is 25% of 80). Both are computed here, as separate modes.
How do I add a percentage to a number?: Use the X +/- Y% mode with direction set to +. 100 + 20% becomes 120 (the 20% is taken of the original 100). For subtraction, flip the direction: 100 - 20% becomes 80.
How do I work out a price before VAT?: Use the 'X is Y% of what' mode. A receipt for 120 with 20% VAT means the pre-tax price was the value V where 120 = (100% + 20%) * V, so 120 / 120 * 100 = 100. Equivalently: 120 - (120 / 1.20 * 0.20) = 100. The reverse-percentage mode does the first form for you.
Percent vs. percentage points - what's the catch?: Confusing the two is the most common percent error in the news. Going from 50% to 55% is a 5 percentage-point rise (subtract the numbers) but a 10% relative rise (the change is 5/50 = 10% of the original). Headlines that quote one and imply the other are the source of most 'wait, what?' arguments.