How to Calculate Percent Change (Increase and Decrease)

Percent change compares a new value to the old one, as a percent of the old value. A positive result is an increase, and a negative one is a decrease.

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The steps

Subtract the old value from the new value to get the change: new − old.
Divide the change by the old value.
Multiply by 100 to make it a percent.
If the result is positive, call it a percent increase. If it is negative, say percent decrease, and drop the minus sign.

A worked example

A price goes from $80 to $92. What is the percent change?

Change: 92 − 80 = 12.
Divide by the old value: 12 ÷ 80 = 0.15.
Multiply by 100: 0.15 × 100 = 15%.
The result is positive, so it is an increase.

The price rose by 15%. Check: 15% of 80 is 12, and 80 + 12 = 92. ✓

Why it works

We divide by the old value because a change is measured against where you started. A $12 rise matters more on an $80 price than on an $800 price, and dividing by the starting amount captures that: 12 out of 80 is 15%, but 12 out of 800 is only 1.5%.

Try it with your own problem

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Common mistakes

Dividing by the new value. Always divide by the starting value.
Thinking up and down are symmetric. A drop from 100 to 50 is −50%, but going back from 50 to 100 is +100%.
Forgetting to multiply by 100. 0.15 is not the same as 15%.
Mixing up percent change and percentage points. A rate going from 4% to 5% rose by 1 percentage point, which is a 25% increase.

Questions people ask

What is the formula for percent change?

(new − old) ÷ old × 100.

What is the percent decrease from 64 to 48?

The change is 48 − 64 = −16. Then −16 ÷ 64 = −0.25, so it is a 25% decrease.

How do I find the new value after a percent increase?

Multiply the old value by 1 plus the percent as a decimal. A 15% increase on 80 is 80 × 1.15 = 92.

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