How to calculate percent change

Percent change compares how much something changed with where it started: (new − original) ÷ original × 100. A price going from $50 to $60 is a 10 ÷ 50 = 20% increase. This page shows the method for increases and decreases, a calculator, finding the new amount after a percent change, and the classic traps.

How to calculate percent change, step by step

  1. Find the change: new − original. $60 − $50 = $10.
  2. Divide by the original amount: 10 ÷ 50 = 0.2.
  3. Multiply by 100: 20%. A positive change is an increase, a negative change a decrease.

Percent change calculator

Type the original and the new amount.

Worked examples

Increase: 40 to 50

Change 10; 10 ÷ 40 = 0.25: 25% increase.

Decrease: $80 to $60

Change −20; 20 ÷ 80 = 0.25: 25% decrease.

Finding the new amount: $30 increased by 15%

15% of 30 is 4.50, so 34.50. Shortcut: 30 × 1.15 = $34.50.

After a discount: $120 with 25% off

120 × 0.75 = $90.

Why +20% then −20% doesn’t get back to the start

$100 up 20% is $120. Down 20% from $120 is $24 off, giving $96, not $100. Each percent is of a different original amount. This is why the original always goes on the bottom.

Common mistakes

50 → 60 is 16.7%Divided by the new amount (10 ÷ 60).Fix: always divide by the original: 10 ÷ 50 = 20%.
50 → 60 is 10%Gave the change as the percent.Fix: the change is 10; as a percent of 50 it is 20%.
+20% then −20% = 0Assumed the percents cancel.Fix: the second percent is of a new amount.
Decrease written as a positiveLost the direction.Fix: say “increase” or “decrease” with the percent.

How to teach it at home

Price watch

Track a price over a few weeks and work out the percent change.

Growth charts

A child’s height from 120 cm to 126 cm is a 5% increase.

Sales

Compare “25% off” with “$20 off” for a $70 item.

By grade

Worksheets and practice

Percent change worksheet, page 1

Percent change worksheet: printable PDF with an answer key. · Make a fresh test

Tax, tip and interest (PDF) · All percentages

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Questions parents ask

How do you calculate percent change?

(new − original) ÷ original × 100. From 50 to 60: 10 ÷ 50 × 100 = 20% increase.

How do you calculate a percent decrease?

The same way; the change is negative. From 80 to 60: 20 ÷ 80 = 25% decrease.

Why do you divide by the original amount?

Percent change describes the change compared with where you started.

How do you increase a number by a percent?

Multiply by 1 plus the percent as a decimal: 30 increased by 15% is 30 × 1.15 = 34.5.

What grade learns percent change?

Grade 7 (7.RP.A.3).