How to calculate percentage: method and shortcuts
To calculate a percentage, divide the part by the whole and multiply by 100. To find a percentage of a number, multiply by the percentage and divide by 100.
Percentages turn up in a sales report, on a VAT invoice, at the till, and in a numerical test. This is how to calculate percentage, quickest route first. Try one question now, or practise with ten drill questions.
Percentage formula: which number is the part, and which is the whole?
A percentage says how many hundredths one amount is of another. Decide which amount you are describing, the part, and which one you are comparing it with, the whole. Divide part by whole, then multiply by one hundred.
Formula
Percentage = (Part) divided by (Whole) × 100
- Part is the amount you are describing.
- Whole is what it is compared with: the total, the maximum, the starting figure.
Worked example
You score 36 out of 48 in a practice test. What percentage is that?
Dividing the other way, 48 ÷ 36, gives 1.33. A mark can never be more than 100% of its own total, so a result over 100% is the sign to turn the division round.
- Divide part by whole: 36 ÷ 48 = 0.75
- Multiply by 100: 0.75 × 100 = 75
Your score is 75%.
Check it: 75% is three quarters, and a quarter of 48 is 12, so three quarters is 36.
How to find a percentage of a number, such as VAT on an invoice?
A percentage of an amount is the whole scaled down to hundredths and taken that many times. That is how to calculate percentage of a number, whether the number is money, people or minutes.
Formula
Part = Whole × (Percentage) divided by (100)
- Percentage is the figure without its % sign.
Worked example
An invoice is 85 euros before VAT, and VAT is 20%. How much VAT is added?
Multiplying 85 by 20 gives 1700 and stops. That skips the division by 100, and a VAT charge far bigger than the invoice itself should have warned you.
- Turn the percentage into a decimal: 20 ÷ 100 = 0.2
- Multiply the invoice by it: 85 × 0.2 = 17 euros
The VAT is 17 euros.
Check it: 10% of 85 is 8.5, so 20% is twice that, 17.
How to work out percentage in your head: what is the quick way?
Nobody at a shop till reaches for the formula. Everything below starts from ten per cent, which is easy because it only moves the decimal point.
- Ten per cent: slide the point. On a 240 euro jacket, 10% is 24 euros, which is 240 ÷ 10.
- Five per cent: halve that. Half of 24 is 12, so 5% off the jacket is 12 euros.
- One per cent: slide two places. 1% of 240 is 2.4, so 3% is three of those.
- Build the rest from those. 15% is 10% plus 5%, so 24 + 12 = 36 euros.
- Swap the two numbers. 6% of 50 is the same as 50% of 6, and half of 6 is 3.
- Know when the swap fails. 17% of 12 swaps to 12% of 17, which is no easier. It comes to 2.04.
Percentage questions in a test: where do people lose the mark?
The usual trap is a percentage of a percentage. The second percentage applies to the smaller group the first one made, not to everyone.
Formulas
Group = Whole × (First %) divided by (100)
Answer = Group × (Second %) divided by (100)
- First % picks out the group, and Second % is taken from that group alone.
Worked example
A firm has 250 staff. 40% work part time, and 30% of the part-timers are in sales. How many part-timers are in sales?
Taking 30% of all 250 staff gives 75. It is a tidy number, so nothing warns you, and the mark is gone.
- Find the part-timers: 40% of 250 = 100
- Take the second percentage of that group: 30% of 100 = 30
30 part-timers work in sales.
Check it: 30 of the 250 staff is 12%, which is below 40%, as a slice of a slice must be.
Want a mixed set instead of one skill? The button below opens the numerical practice page. Its 12-question diagnostic runs on a 12-minute clock, and the clock starts only when you press start on that page.
Of, change or difference: which percentage is your question?
Three questions share the % sign and divide by different things. A percentage of something is what this page teaches. A rise or fall divides by the old figure. A difference between two peers has no old figure, so say which one you divided by.
- A figure went up or down and you want how much, in percent: percentage change, measured from the old figure
- You know the price after a rise or a cut and need the price before: reverse percentages
- Every numerical formula on one page: the formulas reference
- Sharing a total in parts rather than hundredths: ratios
Want a mixed set instead of one skill? The button below opens the numerical practice page. Its 12-question diagnostic runs on a 12-minute clock, and the clock starts only when you press start on that page.
How we write, check and mark the practice questions is set out on the Methodology page.