How to Calculate Percentage: Formulas, Examples and Easy Tricks

What is a percentage?

A percentage is a number written as a part of 100. The word comes from the Latin for per hundred, and the sign is %. So 40 percent means 40 out of every 100, which is the same as the fraction 40/100 or the decimal 0.40.

Percentages make different amounts easy to compare. Scoring 18 out of 20 and 45 out of 50 are hard to compare at a glance, but 90 percent on both shows that the results are equal.

The three basic percentage formulas

Almost every percentage problem uses one of three formulas. Learn these and you can solve most everyday questions.

• Percent of a number. Result = (percent / 100) x number. This answers questions such as what is 15 percent of 200.
• What percent is one number of another. Percent = (part / whole) x 100. This answers questions such as what percent of 180 is 45.
• Find the whole from a part. Whole = part / (percent / 100). This answers questions such as 30 is 20 percent of what number.

How to calculate a percentage of a number

• Step 1: Convert the percent to a decimal. Divide the percent by 100. For 15 percent, 15 / 100 = 0.15.
• Step 2: Multiply by the number. Multiply the decimal by the number you are working with. For 200, 0.15 x 200 = 30.
• Step 3: Read the result. So 15 percent of 200 is 30.

How to find what percent one number is of another

Divide the part by the whole, then multiply by 100. For example, a student scores 45 marks out of 180. Divide 45 by 180 to get 0.25, then multiply by 100. The score is 25 percent.

Always put the part on top and the whole at the bottom. Swapping them is the most common reason for a wrong answer.

How to calculate percentage increase and decrease

To find a percentage change, subtract the old value from the new value, divide the result by the old value and multiply by 100. The formula is: change = ((new - old) / old) x 100. A positive answer is an increase and a negative answer is a decrease.

• Increase example. A price rises from 80 to 100. The change is 100 - 80 = 20. Divide 20 by 80 to get 0.25, so the price went up by 25 percent.
• Decrease example. A price falls from 100 to 80. The change is 80 - 100 = -20. Divide -20 by 100 to get -0.20, so the price went down by 20 percent.
• Notice the difference. Going from 80 to 100 is a 25 percent rise, but going back from 100 to 80 is only a 20 percent fall. The old value is different each time.

Adding and removing a percentage: discounts, tax and tips

• Add a percentage. Multiply by 1 plus the decimal. To add 15 percent tax to 200, calculate 200 x 1.15 = 230.
• Take off a percentage. Multiply by 1 minus the decimal. A 25 percent discount on 80 means 80 x 0.75 = 60, so you pay 60 and save 20.
• Go back to the original price. If a price of 230 already includes 15 percent tax, divide by 1.15 to get the original price: 230 / 1.15 = 200. Do not subtract 15 percent of 230, because that gives the wrong answer.

Percent or percentage points?

These two are often confused. If an interest rate moves from 10 percent to 15 percent, it has gone up by 5 percentage points. In relative terms, it has risen by 50 percent, because 5 is half of 10.

News articles and reports use both, so read carefully. A change of 5 percentage points is a simple difference between two percentages, while a change of 50 percent describes how large that difference is compared with the starting value.

Easy tricks for mental maths

• 10 percent. Divide the number by 10. 10 percent of 80 is 8.
• 1 percent. Divide the number by 100. 1 percent of 350 is 3.5.
• 5 percent. Find 10 percent and halve it. 5 percent of 80 is 4.
• 15 percent. Add 10 percent and 5 percent. 15 percent of 80 is 8 + 4 = 12.
• 25 percent and 50 percent. 25 percent is a quarter, so divide by 4. 50 percent is half, so divide by 2.

Common percentage mistakes

• Adding and removing the same percent. A 20 percent rise followed by a 20 percent fall does not return to the start. 100 becomes 120, then 96. The second change applies to a larger number.
• Using the wrong base. A percentage change is always measured against the old value, not the new one.
• Forgetting to divide by 100. 15 percent is 0.15 in a calculation, not 15. Mixing them up makes the answer 100 times too big.
• Adding percentages of different bases. A 10 percent discount and a 10 percent fee on different amounts do not cancel each other out.

Calculate percentages instantly

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