ToolsKit

How to Calculate Percentage Increase and Decrease

The percentage change formula with worked examples, why +25% and −20% are not opposites, and the mistakes that give wrong answers.

The formula

Percentage change = (new value − old value) ÷ old value × 100. A positive result is an increase and a negative result is a decrease.

Example: a price rises from 80 to 100. The change is 100 − 80 = 20. Divide by the old value: 20 ÷ 80 = 0.25, so the price increased by 25%.

Percentage decrease

Use the same formula. If the price falls from 100 to 80, the change is 80 − 100 = −20, and −20 ÷ 100 = −0.20, so the price decreased by 20%.

The two answers differ (25% and 20%) because each one is measured against a different starting value. Going up 25% and then down 20% brings you back to where you began: 80 → 100 → 80.

More worked examples

Salary: 4,000 to 4,300 is a change of 300. 300 ÷ 4,000 = 0.075, an increase of 7.5%.

Website visits: 1,250 to 1,000 is a change of −250. −250 ÷ 1,250 = −0.20, a decrease of 20%.

Discount: 20% off a price of 50 takes off 20% of 50 = 10, leaving 40. Going from 50 to 40 is, again, a 20% decrease.

Common mistakes

Dividing by the new value instead of the old value. The starting value is always the base.

Mixing up percent and percentage points. If an interest rate moves from 4% to 5%, it rose by 1 percentage point, but by 25% in relative terms (1 ÷ 4).

Starting from zero. A change from 0 is undefined because you cannot divide by zero, so the ToolsKit calculator reports an error instead of a number.

Negative starting values. ToolsKit divides by the absolute value of the old number, so going from −50 to −25 is shown as an increase of 50%. Check that this matches the meaning in your situation.

Check your result

Enter the old and new values in the Percentage Change Calculator to confirm a hand calculation. It shows "Increase of …%" or "Decrease of …%" rounded to two decimals. For a plain "what is X% of Y" question use the Percentage Calculator, and for prices use the Discount Calculator.

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