Percentages & Fractions

How to Calculate a Percentage: 3 Easy Methods

By Math Solving Space · · 2 min read

On this page
  1. What a percentage means
  2. Method 1: Find a percentage of a number
  3. Method 2: Find what percent one number is of another
  4. Method 3: Find the percentage change
  5. Working backwards: finding the original amount
  6. Common mistakes
  7. Practice questions
  8. Frequently asked questions

To find a percentage of a number, turn the percentage into a decimal and multiply. For example, 20% of 150 is 0.20×150=300.20 \times 150 = 30. The same idea, used in slightly different ways, answers almost every percentage question you will meet.

What a percentage means

"Per cent" means "out of 100". So 20% means 20 out of every 100, which is the fraction 20100\frac{20}{100} or the decimal 0.200.20.

Percentage=PartWhole×100\text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100

Every method below is a rearrangement of this one formula.

Method 1: Find a percentage of a number

  1. Divide the percentage by 100 to get a decimal.
  2. Multiply the decimal by the number.

Example: 20% of 150.

20%=20100=0.20.2×150=3020\% = \frac{20}{100} = 0.2 \qquad 0.2 \times 150 = 30

Method 2: Find what percent one number is of another

  1. Divide the part by the whole.
  2. Multiply by 100.

Example: You scored 45 out of 60 on a test. What percentage is that?

4560×100=0.75×100=75%\frac{45}{60} \times 100 = 0.75 \times 100 = 75\%

Method 3: Find the percentage change

  1. Subtract the old value from the new value to get the change.
  2. Divide the change by the old value.
  3. Multiply by 100.
Percentage change=New−OldOld×100\text{Percentage change} = \frac{\text{New} - \text{Old}}{\text{Old}} \times 100

Example (increase): A price rises from 80 to 92.

92−8080×100=1280×100=15%\frac{92 - 80}{80} \times 100 = \frac{12}{80} \times 100 = 15\%

Example (decrease): A value falls from 250 to 200.

200−250250×100=−50250×100=−20%\frac{200 - 250}{250} \times 100 = \frac{-50}{250} \times 100 = -20\%

A negative answer means a decrease, so this is a 20% decrease.

Working backwards: finding the original amount

After a 20% discount, a jacket costs 64. What was the original price?

A 20% discount leaves 80% of the price, so 0.8×Original=640.8 \times \text{Original} = 64.

Original=640.8=80\text{Original} = \frac{64}{0.8} = 80

Check: 20% of 80 is 16, and 80−16=6480 - 16 = 64. ✓

Common mistakes

Mistake Fix
Dividing by the new value in percentage change Always divide by the old (starting) value.
Taking 20% off 64 to "undo" a discount Divide by 0.8 instead; a 20% cut and a 20% rise do not cancel.
Forgetting to multiply by 100 4560=0.75\frac{45}{60} = 0.75 is a decimal; multiply by 100 to get 75%.

Practice questions

  1. What is 15% of 240?
  2. What percentage is 18 of 72?
  3. A plant grows from 50 cm to 65 cm. What is the percentage increase?

Answers: 1) 36 2) 25% 3) 30%

Frequently asked questions

How do I calculate a percentage quickly in my head?

Find 10% by dividing by 10, then scale it. For example, 30% of 70 is three lots of 7, which is 21.

Is X% of Y the same as Y% of X?

Yes. For example, 8% of 50 and 50% of 8 are both 4, because multiplication works in either order.

Why do I divide by the old value for percentage change?

The change is measured relative to where you started, so the starting (old) value is the whole.

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