How percentages work
A percentage is a fraction out of 100. So 25% means 25 out of every 100, or one quarter. This calculator covers the five questions people ask most, and shows the working so you can learn the method, not only copy the answer.
The five formulas
- X% of Y = Y × X ÷ 100
- X is what % of Y = X ÷ Y × 100
- Percentage change = (new − old) ÷ old × 100
- Increase by X% = number × (1 + X ÷ 100)
- Decrease by X% = number × (1 − X ÷ 100)
Everyday uses
Check a restaurant service charge, work out how much a fee is of your salary, see how much a price has risen since last year, or turn your marks into a percentage. For a shop sale use the discount calculator, and for GST on a bill try the sales tax calculator.
Remember that percentage points and percent are different. If a bank rate moves from 12% to 15%, that is 3 percentage points, but a 25% relative increase.
Frequently asked questions
How do I calculate a percentage of a number?
Multiply the number by the percentage and divide by 100. For example 15% of 2,000 = 2,000 × 15 ÷ 100 = 300.
How do I find what percent one number is of another?
Divide the first number by the second and multiply by 100. If you scored 450 out of 600, then 450 ÷ 600 × 100 = 75%.
How is percentage change calculated?
Change % = (new value − old value) ÷ old value × 100. A price going from 250 to 275 is (275 − 250) ÷ 250 × 100 = a 10% increase.
Why does a 20% rise followed by a 20% fall not return to the start?
The second percentage is taken from a bigger number. 100 up 20% is 120, and 20% of 120 is 24, so you end at 96, not 100.
Can the result be negative?
Yes. In percentage change mode a negative result means the value went down. If the old value is zero the change cannot be calculated.