Percentage calculator
Choose the sum you need, enter two numbers and see the answer with the working. It covers a percentage of a number, one number as a percentage of another, the percentage change between two figures, and adding or taking off a percentage.
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The four sums
What is X% of Y? Divide X by 100 and multiply by Y. 15% of £240 is 0.15 × 240, which is £36.
X is what percentage of Y? Divide X by Y and multiply by 100. £36 out of £240 is 36 ÷ 240 × 100, which is 15%.
Percentage change from X to Y. Take the old figure from the new one, divide by the old figure and multiply by 100. A salary that goes from £30,000 to £31,500 has risen by 1,500 ÷ 30,000 × 100, which is 5%. A negative answer is a fall.
Increase or decrease Y by X%. Multiply Y by 1 plus the percentage, or 1 minus it for a decrease. £240 plus 20% is 240 × 1.2, which is £288.
Common mistakes
A rise and a fall of the same percentage do not cancel out. If a price goes up 10% and then down 10%, it ends lower than it started, because the second 10% is taken from a bigger number.
To find a price before a percentage was added, divide rather than subtract. If £288 includes 20% on top, the price before it was 288 ÷ 1.2, which is £240. Taking 20% off £288 gives £230.40, which is wrong.
Percentage points and per cent are different. A rate that goes from 4% to 5% has risen by one percentage point, which is a 25% rise in the rate itself.
Where percentages come up with money
- Pay rises. The take-home pay calculator shows how much of a rise you keep after tax.
- Interest rates. The compound interest calculator shows what a rate does over time.
- Rising prices. The inflation calculator gives the percentage change in prices between two years.
- Electricity costs. Use the electricity cost calculator to see what a change in your unit rate means for an appliance.
- Loan costs. The loan repayment calculator turns an APR into a monthly payment.
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For a short practice question about comparing prices, try Which pack costs less? and choose the lower price per unit.