How to calculate percentage change (increase and decrease)

Increase: a plant grows from 80 cm to 92 cm. Change $= 12$; $\tfrac{12}{80} \times 100 = 15\%$ increase.

Decrease: a phone falls from £120 to £90. Change $= -30$; $\tfrac{-30}{120} \times 100 = -25\%$, a 25% decrease.

Check any example with our percentage calculator, which has a percentage change mode.

A multiplier turns a percentage change into one multiplication:

So £250 increased by 4% is $250 \times 1.04 = 260$, so £260, and £250 decreased by 20% is $250 \times 0.8 = 200$, so £200.

A coat costs £96 after a 20% increase. What was the original price?

The new price is 120% of the original, so original $\times 1.2 = 96$, and original $= 96 \div 1.2 = 80$, so £80.

The classic mistake is taking 20% off £96, which gives £76.80. That's wrong because the 20% was 20% of the original, not of £96.

For a change that repeats each year, multiply by the multiplier once per year, which means using a power:

£1,000 growing at 3% a year for 2 years: $1000 \times 1.03^2 = 1060.9$, so £1,060.90. Simple interest would give £1,060, because it doesn't earn interest on interest. Depreciation works the same way with a multiplier below 1. See exponential growth and decay.

If an interest rate rises from 10% to 12%, it has gone up by 2 percentage points, but by 20 percent ($\tfrac{2}{10} \times 100$). News reports mix these up, and exam questions sometimes test the difference.

• Dividing by the new value instead of the original.
• Finding the change but forgetting to multiply by 100.
• Taking a percentage off the new value in a reverse percentage question.
• Adding percentages over several years (3% for 2 years is not 6% when it compounds).

1. Find the percentage change from 25 to 30.
2. Find the percentage change from 120 to 90.
3. After a 10% discount, a game costs £45. What was the original price?
4. Increase 360 by 35%.

Answers: 20% increase, 25% decrease, £50, 486. More practice in the percentages topic guide.