Three everyday percentage questions
Percent means “per hundred”, so 15% is 15 out of every 100, or 0.15 as a decimal. Almost every percentage problem is one of three types, and this calculator handles them all. To find a percentage of a number, multiply: 15% of 240 is 0.15 × 240 = 36. To find what percent one number is of another, divide and multiply by 100: 36 is 36 ÷ 240 × 100 = 15% of 240. To find the percentage change from one value to another, divide the difference by the starting value: going from 80 to 100 is (100 − 80) ÷ 80 × 100 = a 25% increase.
Choose the question from the menu, enter A and B, and the answer appears along with the working so you can check it or copy the method for homework.
Increase and decrease by a percentage
Adding or removing a percentage is common with prices, raises and recipes. To increase B by A%, multiply B by (1 + A ÷ 100). A $50,000 salary with a 4% raise becomes 50,000 × 1.04 = $52,000. To decrease, multiply by (1 − A ÷ 100): a $80 item reduced by 25% costs 80 × 0.75 = $60. For shopping-specific scenarios with stacked discounts and tax, the discount and sales tax calculators are more convenient.
Common percentage mistakes
Percentage changes are not symmetrical. If a stock falls 50% and then rises 50%, it is not back where it started: $100 falls to $50, and a 50% rise takes it only to $75. You would need a 100% gain to recover. Similarly, a 20% increase followed by a 20% decrease leaves you 4% lower than you started.
Another frequent confusion is between percentage change and percentage points. If an interest rate goes from 4% to 5%, it has risen by one percentage point, but by 25% in relative terms. News reports and financial documents often mix the two, so it is worth checking which is meant. Finally, a percentage change from zero is undefined, because you cannot divide by zero; the calculator will warn you if A is zero in that mode.
Where percentages show up
Percentages are everywhere: interest rates, tax rates, test scores, nutrition labels, battery levels, survey results and sports statistics. Converting between fractions, decimals and percentages is a useful skill: 1/4 is 0.25 or 25%, 1/3 is about 33.3%, and 1/8 is 12.5%. When you compare two quantities of very different sizes, a percentage is often clearer than a raw difference. A $10 price rise on a $20 item (50%) is far more significant than a $10 rise on a $1,000 item (1%), even though the dollar amount is the same.
Frequently asked questions
How do I calculate a percentage of a number?
Multiply the number by the percentage and divide by 100. For example, 15% of 240 is 240 × 15 ÷ 100 = 36.
How do I calculate percentage increase?
Subtract the old value from the new value, divide by the old value and multiply by 100.
What is the difference between percent and percentage points?
Percentage points are the simple difference between two percentages. Percent change is the relative difference. From 4% to 5% is 1 point, or a 25% increase.
Why can’t I calculate a percentage change from zero?
Because it requires dividing by the starting value, and division by zero is undefined.