How to Calculate Percentage Increase

Percentage increase tells you how much a value has grown compared with where it started. It is used for prices, wages, traffic, populations and almost anything that changes over time.

The formula

Percentage increase = (new value − original value) ÷ original value × 100

The original value is always the divisor. That is the step people most often get wrong.

Example 1: a price rise

A subscription goes from 40 to 46.

1. Change: 46 − 40 = 6
2. Divide by the original: 6 ÷ 40 = 0.15
3. Multiply by 100: 15%

Example 2: growth in visitors

A site had 80 visitors a day and now has 100. The change is 20, and 20 ÷ 80 = 0.25, so traffic is up 25%.

Adding a percentage to a number

To increase a number by a percentage, multiply it by 1 plus the percentage as a decimal.

New value = original × (1 + percentage ÷ 100)

Increase 200 by 15%: 200 × 1.15 = 230. The amount added is 30.

Going backwards

If a price is 46 after a 15% rise, the original was not 46 minus 15%. Divide by the multiplier instead: 46 ÷ 1.15 = 40.

Why increase and decrease are not symmetrical

A 25% increase followed by a 25% decrease leaves you below where you began.

The decrease is calculated on 125, a larger base, so it takes away more than the increase added. To undo a 25% increase you need a decrease of 20%, because 25 ÷ 125 = 0.2.

Common mistakes

• Dividing by the new value instead of the original.
• Reporting an increase when the number actually fell. A negative result means a decrease.
• Starting from zero. Percentage change from 0 is undefined, because you cannot divide by zero.

Use the percentage increase calculator to check your working.

Try it yourself

1. A value rises from 250 to 310. What is the percentage increase?
2. Increase 80 by 12.5%.
3. A price is 60 after a 20% rise. What was it before?

Answers: (1) 24%; (2) 90; (3) 50 (60 ÷ 1.2).