How do you calculate a percentage increase?
Short answer
Percentage increase = (new value − original value) ÷ original value × 100. For example, a price rising from 80 to 100 is an increase of 20, and 20 ÷ 80 × 100 = 25%. Always divide by the original value, not the new one.
Step by step
- Find the increase: new value minus original value.
- Divide the increase by the original value.
- Multiply by 100 to turn the decimal into a percentage.
- If the answer is negative, it is a percentage decrease.
Worked example
A school had 450 students last year and 513 this year. Find the percentage increase.
- Increase: 513 − 450 = 63
- 63 ÷ 450 = 0.14
- 0.14 × 100 = 14%
Common mistakes
- Dividing by the new value instead of the original value.
- Forgetting to multiply by 100 and giving 0.14 as the answer.
- Adding percentages over several years. Two increases of 10% are a 21% increase in total, not 20%.
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