Solve every common percentage problem in one place: percent of a number, what percent X is of Y, percentage increase and decrease, and reverse percentage.
Four different calculations get called “percentage” problems, and mixing them up is the source of most percentage errors. This tool handles all four: finding a percentage of a number, expressing one number as a percentage of another, measuring change between two values, and working backwards from a discounted price.
Where
Almost every percentage mistake comes from applying the number to the wrong base. Three examples worth internalising:
Pick the calculation type
Choose from percentage of a number, X is what percent of Y, percentage increase/decrease, or reverse percentage.
Enter your numbers
Results update live as you type. Negative numbers and decimals are supported.
Check the working
Every result shows the arithmetic used, so you can verify it or reproduce it by hand.
Shopping and discounts
Work out sale prices, compare stacked coupons, and find the original price from a marked-down tag.
Business reporting
Calculate growth rates, margins and month-over-month changes correctly, including negative bases.
Grades and test scores
Convert marks out of any total into a percentage, and find what score you need on a remaining assessment.
Tips and splitting bills
Quick gratuity maths, or check that a service charge on a receipt matches the advertised rate.
Divide the percentage by 100 and multiply by the number. For 15% of 80: (15 ÷ 100) × 80 = 12. A quick mental shortcut is that 10% is the number with the decimal moved one place left, so 10% of 80 is 8, and half of that (5%) is 4, giving 12.
If a rate rises from 4% to 6%, that is an increase of 2 percentage points but a 50% increase in relative terms. News reports frequently confuse the two, which can make a change sound far larger or smaller than it is.
Percentages apply to different bases. Losing 50% of $100 leaves $50. Gaining 50% of $50 only returns you to $75. To get back to $100 from $50 requires a 100% gain. This asymmetry is why large losses are so damaging to investments.
Divide the final price by (1 minus the discount as a decimal). An item costing $85 after a 15% discount was originally $85 ÷ 0.85 = $100. Use the reverse percentage mode above for this.
No. A 20% discount followed by another 10% is not 30% off. The second discount applies to the already-reduced price: 0.80 × 0.90 = 0.72, so the total is 28% off. Stacked percentages always total less than their sum.