How To Calculate Percentage: Formulas, Examples and Shortcuts
Percentages appear everywhere: discounts in shops, marks in exams, interest on loans, tax on bills and growth in business. A percentage simply means "out of 100", and once you know three or four formulas you can solve almost every percentage problem in your head or with a calculator. This guide explains the formulas with clear examples and common shortcuts. For instant answers use our free percentage calculator.
What Is A Percentage?
The word percent means per hundred. 25% means 25 out of 100, which is the same as 25/100 or 0.25. To turn a percentage into a decimal divide by 100, and to turn a decimal into a percentage multiply by 100.
The Four Main Percentage Formulas
| What you want | Formula | Example |
|---|---|---|
| X% of Y | X / 100 x Y | 15% of 200 = 30 |
| X is what % of Y | X / Y x 100 | 30 is 15% of 200 |
| Percentage increase | (New - Old) / Old x 100 | 80 to 100 = 25% increase |
| Percentage decrease | (Old - New) / Old x 100 | 100 to 80 = 20% decrease |
How To Calculate X% Of A Number
Divide the percentage by 100 and multiply by the number. To find 18% of 450: 18 / 100 x 450 = 81. A quick trick is to find 10% by moving the decimal point one place (45), then build up: 18% = 10% + 5% + 3% = 45 + 22.5 + 13.5 = 81.
How To Find What Percent One Number Is Of Another
Divide the part by the whole and multiply by 100. If you scored 42 out of 60, your percentage is 42 / 60 x 100 = 70%.
Percentage Increase And Decrease
Subtract the old value from the new value, divide by the old value and multiply by 100. A price that rises from 80 to 100 has increased by (100 - 80) / 80 x 100 = 25%. If it then falls from 100 back to 80, the decrease is 20%, not 25%. The base is different each time, which is why percentage changes are not symmetrical.
Discounts And Tax
- Sale price = Price x (1 - Discount%). A 20% discount on 5,000 gives 5,000 x 0.8 = 4,000.
- Price with tax = Price x (1 + Tax%). 18% tax on 1,000 gives 1,180.
- Original price from sale price = Sale price / (1 - Discount%).
Common Mistakes
- Adding a percentage increase and decrease directly. +20% then -20% does not return you to the start (100 becomes 120, then 96).
- Dividing by the wrong base when finding percentage change; always divide by the old value.
- Mixing percentage points with percent. Going from 10% to 12% is 2 percentage points but a 20% increase.
Quick Percentage Table
| Percent | Fraction | Decimal |
|---|---|---|
| 10% | 1/10 | 0.1 |
| 25% | 1/4 | 0.25 |
| 50% | 1/2 | 0.5 |
| 75% | 3/4 | 0.75 |
| 12.5% | 1/8 | 0.125 |
Frequently Asked Questions (FAQs)
How do I calculate a percentage of a number?
Divide the percentage by 100 and multiply by the number. For example, 15% of 200 is 15 / 100 x 200 = 30.
How do I calculate percentage increase?
Subtract the old value from the new value, divide by the old value and multiply by 100.
How do I calculate percentage decrease?
Subtract the new value from the old value, divide by the old value and multiply by 100.
How do I find what percent one number is of another?
Divide the first number by the second and multiply by 100.
How do I calculate a discount?
Multiply the price by the discount percentage divided by 100 to get the saving, then subtract it from the price.
Why is +20% then -20% not back to the start?
Because the second percentage is taken from the new, larger value. 100 becomes 120, and 20% of 120 is 24, leaving 96.