Arithmetic & Numbers · Grades 6–9

How to Calculate Percentages: 4 Problem Types, Solved

Updated October 3, 2026By Mateuss M.

Short answer: A percentage is a number out of 100. Every percentage problem is one of four types, and each has its own formula: find a part, find a percent, find the whole, or find a change.

1. What is X% of Y?

Divide the percent by 100 and multiply by the number. 15% of 240 is 36.

15% of 240

Answer36

15% of 240 is 36

Step-by-step working 2 steps

1
Turn the percent into a decimal
```
15% = 15 ÷ 100 = 0.15
```
2
Multiply by the number
```
0.15 × 240 = 36
```

2. X is what percent of Y?

Divide the part by the whole, then multiply by 100. If 45 out of 180 questions are correct, the score is 25%.

Part ÷ whole × 100

Answer25%

45 is 25% of 180

Step-by-step working 2 steps

1
Divide the part by the whole
```
45 ÷ 180 = 0.25
```
2
Multiply by 100 to get a percent
```
0.25 × 100 = 25%
```

3. X is Y% of what number?

Work backwards: divide the part by the percent written as a decimal. If 30 is 12% of a number, that number is 250.

Finding the original value

Answer250

30 is 12% of 250

Step-by-step working 2 steps

1
Turn the percent into a decimal
```
12% = 12 ÷ 100 = 0.12
```
2
Divide the part by that decimal
```
30 ÷ 0.12 = 250
```

4. Percent increase and decrease

Subtract old from new, divide by the old value, multiply by 100. Going from 80 to 100 is a change of +25%. Going back from 100 to 75 is −25%.

Percent change from 80 to 100

Answer+25%

That is a percent increase.

Step-by-step working 3 steps

1
Find the change
```
100 − 80 = 20
```
2
Divide the change by the old value
```
20 ÷ 80 = 0.25
```
3
Multiply by 100
```
0.25 × 100 = 25%
```

Always divide by the old value. That is why a rise followed by an equal-sized fall does not bring you back to the start.

Common mistakes

Picking the wrong base

Ask yourself “percent of what?” before you calculate. The base is the number the percent is taken from.

Forgetting to divide by 100

A percent must be turned into a decimal (or a fraction over 100) before multiplying.

Reversing a percent change

Undoing a 25% rise needs a fall of 20%, not 25%, because the base is different.

Put it into practice. Try your own numbers in the Percentage Calculator and compare each step with the method above.

Frequently asked questions

How do I find a percentage on a calculator?

Press the number, × , the percent as a decimal, then = . Or use the percentage calculator, which also shows the steps.

What is the difference between percent and percentage points?

Going from 10% to 12% is a 2 percentage-point rise, but a 20% increase in the rate itself.

Written and reviewed by Mateuss M.

Mateuss M. writes and reviews mathematical content for CalcSolver, focusing on online calculators, formulas, equations, and practical math tools. He reviews calculator functionality, calculation methods, formulas, examples, and explanations to help ensure that each tool is clear, useful, and easy to understand.

How-to guides

How to Calculate Percentages: 4 Problem Types, Solved

1. What is X% of Y?

2. X is what percent of Y?

3. X is Y% of what number?

4. Percent increase and decrease

Common mistakes

Picking the wrong base

Forgetting to divide by 100

Reversing a percent change

Frequently asked questions

Written and reviewed by Mateuss M.

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