There are three percentage questions people usually ask, and each has a short formula. To find a percent of a number, divide the percent by 100 and multiply. To find what percent one number is of another, divide and multiply by 100. To find a percent change, divide the difference by the starting value and multiply by 100. The percentage calculator handles all three.
Here is each one worked out.
Percent of a number
This answers “what is 15% of 200?”. Turn the percent into a decimal by dividing by 100, then multiply by the number.
15% becomes 0.15, and 0.15 × 200 = 30. So 15% of 200 is 30. The same method gives a tip, a tax amount or a discount: 20% of an 80 bill is 0.20 × 80 = 16.
What percent one number is of another
This answers “30 is what percent of 120?”. Divide the first number by the second, then multiply by 100.
30 ÷ 120 = 0.25, and 0.25 × 100 = 25%. So 30 is 25% of 120. This is how you turn a score into a percentage, or work out what share of a total something is.
Percent increase or decrease
This answers “what is the percent change from 50 to 75?”. Subtract the old value from the new value, divide by the old value, then multiply by 100.
(75 − 50) ÷ 50 = 0.5, and 0.5 × 100 = 50%. So going from 50 to 75 is a 50% increase. If the value falls, the result is negative: from 80 to 60 is (60 − 80) ÷ 80 × 100 = −25%, a 25% decrease.
A common mistake is to divide by the new value instead of the old one. The change is always measured against where you started, so the old value is the denominator.
Reversing a percentage
Sometimes you know the result and want the original. If a price is 20% off and now costs 64, the 64 is 80% of the original, so the original is 64 ÷ 0.80 = 80. The rule is to divide by the decimal that remains after the change, not to add the same percent back.
Where this comes up
Percentages turn up wherever you compare a part with a whole:
- Shopping, for discounts and the saving compared with the full price.
- Bills, for tips, service charges and tax added to a total.
- Results, for marks as a percentage and growth between two figures.
For lowest-terms comparisons of two quantities rather than a single percent, see how to simplify a ratio, or open the percentage calculator to try these now.