To find a percentage of a number, multiply the number by the percentage and divide by 100. So 15% of 240 is 240 × 15 ÷ 100 = 36. To find what percent one number is of another, divide the part by the whole and multiply by 100.
What a percentage means
“Per cent” means “out of 100”. So 25% is 25 out of every 100, which is the same as the fraction 1/4 or the decimal 0.25. Once you are happy converting between these three forms, most percentage questions become easy.
| Percentage | Decimal | Fraction |
|---|---|---|
| 10% | 0.10 | 1/10 |
| 25% | 0.25 | 1/4 |
| 50% | 0.50 | 1/2 |
| 75% | 0.75 | 3/4 |
How to find a percentage of a number
The formula is: x% of y = y × x ÷ 100.
Worked example: what is 15% of 240?
- Divide 15 by 100 to get 0.15
- Multiply 240 × 0.15 = 36
If you take 15% off 240 instead, you are left with 240 − 36 = 204. The Percentage of a number tool shows both the answer and the remainder.
How to find what percent one number is of another
The formula is: (part ÷ whole) × 100.
Worked example: you score 45 out of 180. 45 ÷ 180 = 0.25, and 0.25 × 100 = 25%. This is useful for marks, budgets (what share of your pay goes on rent?) and survey results. The What percent tool does the division for you.
Mental maths shortcuts
You can do many percentages in your head by building from 10% and 1%.
- 10%: move the decimal point one place left (10% of 240 is 24)
- 5%: half of 10% (12)
- 1%: move the decimal point two places left (2.4)
- 15%: 10% plus 5% (24 + 12 = 36)
- 20%: double 10% (48)
Other quick ones: 50% is half, 25% is a quarter, and 75% is three quarters. To check a result, ask whether it is sensible: 15% of 240 should be a bit more than a tenth, and 36 is.
Percentages in everyday money
Percentages crop up wherever money does. VAT at the standard 20% rate is a percentage of the net price, which VAT explained: adding and removing VAT covers in detail. Pay rises, discounts and price changes use a related idea, the percentage change, explained in Percentage change, increases and discounts. If you are converting pay between hourly and yearly figures, Hourly rate to salary, and how to work out overtime shows how multipliers such as 1.5 work.
Note: These are general maths methods. For tax, loans or other money decisions, check the figures with the provider or official guidance.
Common mistakes to avoid
- Dividing by the wrong number. In “what percent is 45 of 180”, the whole (180) goes underneath, not the part.
- Forgetting to multiply by 100 at the end, which leaves you with a decimal.
- Mixing up “percent of” with “percentage points”. A rise from 4% to 6% is 2 percentage points, not 2%.
- Adding percentages that apply to different bases, such as two successive discounts.
Worked examples you can try
Practice makes the methods stick. Try these, then check them with the calculators:
- A restaurant bill is £64 and you want to leave 10%. That is £6.40.
- You have saved £450 of a £1,800 target. 450 ÷ 1,800 × 100 = 25% of the way there.
- A report is 140 pages and you have read 35. That is 25%.
- Rent of £900 out of take-home pay of £2,400 is 900 ÷ 2,400 × 100 = 37.5%.
Notice that the same two formulas cover every case. Decide which number is the whole, which is the part, and whether you need the part or the percentage.
Percentages of percentages and repeated steps
If a quantity changes by a percentage twice, multiply the factors rather than adding the percentages. A 10% rise followed by another 10% rise gives 1.1 × 1.1 = 1.21, so 21% overall. This idea underpins interest and discounts, which are explored in Percentage change, increases and discounts.
Try the calculator
Use Percentage of a number to find a percentage of any amount and What percent to find what share one number is of another. They give instant results as you type.
Open the free Percentage of a number
Step-by-step: how to work out a percentage by hand
Whichever question you face, the same routine works. Write the question as a sentence, label each number as the part, the whole or the percentage, then pick the matching formula.
- Identify the whole. This is the total, the original price or the full amount. It is usually the number that follows “of” in the question.
- Identify what is missing. Either you want the part (a percentage of a total), the percentage (how big is this part?) or the whole (what total would make this part a certain percentage?).
- Convert the percentage to a decimal by dividing by 100, so 35% becomes 0.35.
- Calculate using the table below.
- Sense-check. If you asked for a small percentage, the answer should be much smaller than the whole.
| You know | You want | Calculation |
|---|---|---|
| Whole and percentage | The part | whole × percentage ÷ 100 |
| Part and whole | The percentage | part ÷ whole × 100 |
| Part and percentage | The whole | part ÷ percentage × 100 |
Working backwards: finding the whole from a percentage
The third row catches many people out. Suppose 18 is 30% of a number. The whole is 18 ÷ 30 × 100 = 60. Check it: 30% of 60 is 18.
A very common version of this is removing a percentage that has already been added. If a price including 20% VAT is £120, the original is not £120 minus 20%. The £120 is 120% of the net price, so the net price is 120 ÷ 1.2 = £100 and the VAT is £20. Taking 20% off £120 would give £96, which is wrong. VAT explained: adding and removing VAT walks through adding and removing VAT, and Percentage increase and decrease, and reverse percentages covers the same trap for discounts and pay rises.
The pattern is simple: if something has been increased by x%, divide by (1 + x ÷ 100) to undo it. If it has been reduced by x%, divide by (1 − x ÷ 100). So a coat sold for £68 after a 15% reduction started at £68 ÷ 0.85 = £80.
Worked example 2: a household budget in percentages
Percentages are a handy way to compare budgets of different sizes. Take monthly take-home pay of £2,600 and the following spending:
| Item | Amount | Share of pay |
|---|---|---|
| Rent | £950 | 36.5% |
| Food | £320 | 12.3% |
| Transport | £180 | 6.9% |
| Bills and phone | £260 | 10.0% |
| Savings | £260 | 10.0% |
| Everything else | £630 | 24.2% |
| Total | £2,600 | 100% |
Each share is the item divided by £2,600 and multiplied by 100, rounded to one decimal place. Because of rounding, the shares may add to 99.9% or 100.1%, which is normal. Totalling the shares is a good check that you have not missed an item.
Once you have shares, you can ask a new question: if pay rose to £2,860, what would £260 of savings be as a share? 260 ÷ 2,860 × 100 = 9.1%, so a fixed amount shrinks as a percentage when income grows.
Percentages in other settings
- Tips and service charges: 12.5% of £48 is 48 × 0.125 = £6.
- Interest: 4% a year on £1,000 is £40 in the first year, before interest on interest. Over several years, the repeated-step rule applies, as Compound interest explained, with examples shows.
- Profit margins: a margin is profit as a percentage of the selling price, whereas a markup is profit as a percentage of the cost. Mixing them up is common, and Break-even point and profit margin: how to work them out explains the difference.
- Test scores: 34 out of 40 is 34 ÷ 40 × 100 = 85%.
- Statistics in the news: always ask what the percentage is of. “Up 50%” from a tiny base can still be a small number.
Checking your answer with estimation
A quick estimate catches most slips before they reach a bill or a report. Round the numbers to something easy, calculate, then compare.
- 19% of £412: round to 20% of £400, which is £80. The exact answer is £78.28, so the estimate is close.
- 48 out of 160: that is 3 out of 10, so about 30%. The exact answer is 30%.
- 7.5% of £2,000: find 10% (£200), then take away a quarter of it (£50) to get £150.
If your exact answer is far from the estimate, recheck which number you divided by. Another habit that helps is to think about whether the answer should be bigger or smaller than the starting number. A discount must give a smaller figure, and a markup must give a bigger one. If you get the opposite, you have probably used 0.85 where you needed 1.15, or the other way round.
Glossary of percentage terms
- Base or whole: the number the percentage is taken of.
- Percentage point: the arithmetic gap between two percentages.
- Percentage change: the difference between new and old, divided by old, times 100.
- Multiplier: the decimal you multiply by, such as 1.15 for a 15% increase or 0.85 for a 15% decrease.
- Reverse percentage: working back from a changed figure to the original.
Frequently asked questions
How do I calculate 20% of a number?
Multiply the number by 0.2. For £80, that is £16. You can also find 10% and double it.
How do I turn a fraction into a percentage?
Divide the top number by the bottom number and multiply by 100. For example, 3/8 = 0.375, which is 37.5%.
Can a percentage be more than 100?
Yes. 150% of 40 is 60. It simply means more than the whole, which happens with growth or when comparing a new value to an old one.
What is the difference between a percentage and a percentage point?
A percentage point is a simple subtraction between two percentages. Going from 10% to 12% is a rise of 2 percentage points, but a 20% increase in relative terms.
How do I find a percentage with a calculator that has a percent key?
Keys differ between devices, so the most reliable method is to type the number, multiply by the percentage as a decimal (0.15 for 15%) and press equals. That works on any calculator.
How do I work out the original price after a discount?
Divide the sale price by the multiplier. If something is 25% off, the multiplier is 0.75, so a £60 sale price came from £60 ÷ 0.75 = £80.
Why is 10% off followed by 10% off not 20% off?
The second 10% is taken from the already reduced price. Two 10% reductions multiply as 0.9 × 0.9 = 0.81, which is 19% off, not 20%.
How do I round a percentage?
Round at the end, not part way through the working. For everyday use, one decimal place is usually enough, and whole numbers are fine for rough comparisons.