How to calculate percentages
A percentage is a way of expressing a number as a part of one hundred. Once you see that percent simply means per hundred, the three things people usually need become straightforward: finding a percentage of a number, working out what percentage one number is of another, and measuring a percentage change. This guide covers all three with worked examples.
What a percentage really means
The word percent comes from per hundred. So 25 percent means 25 out of every 100, the same as the fraction 25/100 or the decimal 0.25. This single idea, that a percentage is just hundredths, is the key to every percentage calculation. To turn a percentage into a decimal, divide by 100 (move the decimal two places left); to go the other way, multiply by 100.
Finding a percentage of a number
This is the most common task: what is 15 percent of 80? Convert the percentage to a decimal and multiply.
- Convert the percentage to a decimal by dividing by 100. Here, 15 percent becomes 0.15.
- Multiply the decimal by the number: 0.15 × 80 = 12.
- The answer is 12, so 15 percent of 80 is 12.
20 percent becomes 0.20. Then 0.20 × 45 = 9. The tip is 9 dollars.
What percentage one number is of another
Sometimes you have the part and the whole and want the percentage. Divide the part by the whole, then multiply by 100.
- Divide the part by the whole. For 12 out of 80, compute 12 ÷ 80 = 0.15.
- Multiply by 100 to get a percentage: 0.15 × 100 = 15 percent.
- So 12 is 15 percent of 80.
You answered 18 of 24 questions correctly. Then 18 ÷ 24 = 0.75, and 0.75 × 100 = 75 percent.
Percentage increase and decrease
To measure a change in percentage terms, find the difference, divide by the original value, then multiply by 100.
- Subtract to find the change. Going from 80 to 100 is a change of 20.
- Divide the change by the original amount: 20 ÷ 80 = 0.25.
- Multiply by 100: a 25 percent increase.
A jacket falls from 60 dollars to 45 dollars. The change is 15, and 15 ÷ 60 = 0.25, so the price dropped 25 percent.
Quick mental shortcuts
Ten percent is easy: move the decimal one place left, so 10 percent of 250 is 25. From there you can build others: 5 percent is half of 10 percent, 20 percent is double, and 15 percent is 10 percent plus 5 percent. To find 1 percent, move the decimal two places. These building blocks let you estimate most percentages in your head.
- Percent means per hundred, so every percentage is a fraction out of 100.
- To find a percentage of a number, convert to a decimal and multiply.
- To find what percentage one number is of another, divide the part by the whole and multiply by 100.
- For percentage change, divide the difference by the original value.
- Ten percent (move the decimal one place) is the anchor for quick mental math.
Handy percentage references
See the Fraction to Percentage Chart, or use the Percentage Calculator for any values.
FAQ
How do I find 15 percent of a number?
Convert 15 percent to 0.15 and multiply by the number. For 80, that is 0.15 × 80 = 12.
How do I work out a percentage increase?
Subtract the old value from the new value, divide by the old value, then multiply by 100. From 80 to 100 is 20 ÷ 80 = 25 percent.
What is the easiest way to estimate percentages?
Start with 10 percent by moving the decimal one place left, then add or halve to reach other percentages such as 5 or 20 percent.