Percentage Calculator
Seven everyday percentage questions, each written as a sentence. Type into any row and the answer, with the working, updates as you go.
The formulas
X% of Y is Y × X ÷ 100. X as a percent of Y is X ÷ Y × 100. Percent change from an old value to a new one is (new − old) ÷ |old| × 100, so a positive answer is an increase and a negative one a decrease.
Reversing a change trips people up: if a price fell 20% to 96, the original was 96 ÷ 0.8 = 120, not 96 × 1.2 = 115.2. A 20% cut followed by a 20% rise leaves you 4% below where you started.
Percentage points measure the gap between two percentages. A rate that moves from 3.5% to 4.25% has risen 0.75 percentage points, which is a 21.4% relative increase. Percent difference compares two values with no “before” and “after”, dividing by their average so the order doesn’t matter.
Questions
How do I calculate a percentage of a number?
Multiply the number by the percentage and divide by 100. 15% of 240 is 240 × 15 ÷ 100 = 36. Moving the decimal point helps for mental math: 10% of 240 is 24, so 5% is 12 and 15% is 36.
What is the difference between percent change and percent difference?
Percent change has a direction: it measures from an old value to a new one and divides by the old value. Percent difference compares two values as equals and divides by their average, so swapping them gives the same answer.
How do I add 20% to a price?
Multiply by 1.2. To take 20% off, multiply by 0.8. Use the “increased by / decreased by” row to see the result and the amount added or removed.
How do I remove VAT or sales tax from a total?
Divide by 1 plus the rate. A total of 120 with 20% VAT included was 120 ÷ 1.2 = 100 before tax. The “original value” row does this for any rate.
Why is a 50% drop followed by a 50% rise not back to even?
Each percentage applies to a different base. 100 falls 50% to 50, then rises 50% of 50 to 75. To recover a 50% loss you need a 100% gain.