Choosing the right calculation
Percentage questions look alike but ask different things. “What is 15% of 80?” gives a part. “12 is what percent of 80?” gives a rate. “From 80 to 92” asks for a change. Use the selector at the top to match your question.
Each result shows its working underneath, so you can see exactly which numbers went where and reuse the method by hand.
Everyday uses
Percentages show up in discounts, tips, tax, interest, test scores, pay rises and statistics. Working out a sale price means reducing a number by a percentage. Comparing this year with last year means a percentage change. Splitting a bill means a percentage of a total.
For money-specific cases, the ROI and inflation calculators build on the same ideas.
Common mistakes
Mixing up percentage points and percent: going from 4% to 6% is a rise of 2 percentage points, but a 50% increase in the rate. Using the wrong base is the other frequent error: percentage change always divides by the starting value, not the ending one.
A worked example
A student scores 42 out of 60, which is 42 ÷ 60 × 100 = 70%. A salary of 40,000 rises by 4.5% to 40,000 × 1.045 = 41,800. A price that goes from 80 to 100 has risen 25%, but the same price falling from 100 back to 80 has dropped 20%, because the starting value is different.
Questions people ask
How do I calculate a percentage of a number?
Divide the percentage by 100 and multiply by the number. 20% of 150 = 0.20 × 150 = 30.
How do I find what percent one number is of another?
Divide the first number by the second and multiply by 100. 30 out of 120 = 30 ÷ 120 × 100 = 25%.
How do I calculate percentage change?
Subtract the old value from the new value, divide by the old value and multiply by 100. From 80 to 100 is (100 − 80) ÷ 80 × 100 = +25%. A negative result means a decrease.
Why is a 25% increase not undone by a 25% decrease?
The second percentage is applied to a bigger number. 100 up 25% is 125, and 125 down 25% is 93.75. To return to 100 you need a 20% decrease.
How do I find the original number before a percentage?
Divide the amount by the percentage written as a decimal. If 45 is 15% of a number, the number is 45 ÷ 0.15 = 300. To undo a discount or tax, divide by (1 − rate) or (1 + rate).