Percentage Calculator

A percentage calculator answers the everyday sums that are easy to get wrong in your head: what is 15% of a bill, what percentage one number is of another, how much something has gone up or down, what a price is with VAT added or taken off, and what the original figure was before a percentage change. Our free calculator puts all of these in one place, shows the formula and your working for every answer, and explains the difference between percent and percentage points. Results update as you type and everything runs in your browser.

How to use the Percentage calculator

1. 1 Pick what you want to work outChoose one of the six modes, such as X% of Y, percentage change or reverse percentage. Each mode keeps its own numbers, so you can switch back and forth.
2. 2 Type your numbersFill in the boxes. You can include commas, decimals, a pound sign or a percent sign and the calculator will ignore the symbols.
3. 3 Read the answer and the sentenceThe big number is your result, and the sentence underneath explains it in plain English so you can check it makes sense.
4. 4 Check the formula and workingThe dark box shows the general formula and the same sum with your numbers in it, which is handy for homework, reports or checking a spreadsheet.
5. 5 Adjust decimal places and copyChoose how many decimal places to show, then copy the answer sentence to paste into an email, a document or a message.

The six percentage calculations, explained

Percent means per hundred, so 20% is 20 out of every 100, or 0.2 as a decimal. Almost every percentage problem is one of a small number of patterns, and once you know which one you are dealing with, the formula is simple. The calculator covers the six you are most likely to need.

• X% of Y: multiply Y by X and divide by 100. 20% of 150 is 150 × 20 ÷ 100 = 30.
• X is what percent of Y: divide X by Y and multiply by 100. 30 out of 120 is 30 ÷ 120 × 100 = 25%.
• Percentage change: subtract the old value from the new, divide by the old value and multiply by 100. From 80 to 100 is (100 − 80) ÷ 80 × 100 = a 25% increase.
• Add or subtract a percentage: multiply by 1 plus or minus the percentage as a decimal. £250 plus 20% is £250 × 1.2 = £300.
• Reverse percentage: divide the final figure by 1 plus or minus the percentage as a decimal to find the original. £120 including 20% VAT is £120 ÷ 1.2 = £100 before VAT.
• Percentage points: subtract one percentage from another to find the gap. A rate going from 4% to 5% has risen by 1 percentage point.

Percentage increase and decrease

Percentage change always compares the difference with the starting value, not the end value. That is why going from 80 to 100 is a 25% increase, but going from 100 back to 80 is a 20% decrease. The gap is 20 both times, but it is compared with a different starting point. Use the swap button to see this instantly.

It also explains why a rise and a fall of the same percentage do not cancel out. If a price goes up 10% from £100 to £110 and then falls 10%, it drops to £99, not £100, because the 10% fall is taken from the higher figure. A 50% fall needs a 100% rise to get back to where it started. Keep this in mind when reading about share prices, house prices or sales figures.

A change from zero has no percentage, because you cannot divide by zero. If a new product line sold nothing last year and £5,000 this year, describe the change as an amount rather than a percentage. The calculator will tell you if the starting value is zero.

Adding and removing VAT

VAT is one of the most common reasons people need a percentage calculator in the UK. The standard rate is 20% and there is a reduced rate of 5% for some goods and services. To add 20% VAT to a net price, multiply by 1.2. To find the VAT on a net price, multiply by 0.2.

Removing VAT is where most mistakes happen. To find the price before VAT from a price that includes it, divide by 1.2, not take off 20%. Taking 20% off £120 gives £96, which is wrong. Dividing £120 by 1.2 gives £100, which is right, and the VAT is the £20 difference. A quick way to find the VAT inside a gross price at 20% is to divide by 6, since the VAT is one sixth of the total. The reverse percentage mode has one-click buttons for removing 20% and 5% VAT.

Reverse percentages and discounts

A reverse percentage works back from a figure after a change to the figure before it. As well as VAT, it is useful for discounts, pay rises and price increases. If a coat costs £60 in a sale with 25% off, the original price was £60 ÷ 0.75 = £80, not £60 plus 25%, which would give £75.

The same logic applies to pay. If your salary is £31,200 after a 4% rise, your old salary was £31,200 ÷ 1.04 = £30,000. If a supplier tells you prices have gone up 8% and the new price is £540, the old price was £500. Choose increase or decrease, enter the final amount and the percentage, and the calculator shows both the original figure and the size of the change.

Percent versus percentage points

When you compare two percentages, there are two different ways to describe the change, and mixing them up can be seriously misleading. A percentage point is the simple difference between two percentages. Percent describes the change relative to where you started.

If the Bank of England raises Bank Rate from 4% to 5%, it has gone up by 1 percentage point. But 1 is a quarter of 4, so the rate is 25% higher. Both statements are true, but saying interest rates rose by 1% would be wrong, or at least unclear. The same applies to election results, unemployment figures, conversion rates and survey answers. A website conversion rate rising from 2% to 3% is a rise of 1 percentage point but a 50% improvement, and that is a big difference when you are reporting to a client or a board.

The percentage points mode shows both figures together so you can choose the right one, and the panel beside the result gives two worked examples to refer back to.

Tips for accurate percentages

Round at the end, not along the way. If you round intermediate results, small errors can add up, especially when you chain several percentage changes together. The calculator keeps full precision and only rounds what it displays, using the number of decimal places you choose.

Always check that the answer makes sense. A discount should make a price smaller, a percentage of a number below 100% should be smaller than the number, and a reverse percentage after an increase should be smaller than the final figure. The plain-English sentence under each result is there to help you spot a sum that has gone the wrong way. For spreadsheets, the same formulas work in Excel and Google Sheets, for example =B2*20/100 or =(C2-B2)/B2 formatted as a percentage.

Be careful with averages of percentages. If one shop grows sales by 10% and another by 30%, the combined growth is not necessarily 20%, because the shops may have very different sales to begin with. Work out the totals first and then calculate the percentage change on the combined figures. The same caution applies to averaging interest rates, test scores and survey results from groups of different sizes.

Finally, say clearly what the percentage is of. A headline such as prices up 12% means little until you know which prices, over what period and compared with when. Giving the starting figure, the new figure and the period alongside the percentage makes your numbers far easier for readers to trust and check.

Examples you can copy

15% tip on £48            £48 × 0.15 = £7.20
£36 out of £240            36 ÷ 240 × 100 = 15%
Rent £950 to £1,000        (1,000 − 950) ÷ 950 × 100 = +5.26%
£80 plus 20% VAT           £80 × 1.2 = £96
£96 including 20% VAT      £96 ÷ 1.2 = £80 before VAT
Rate 4% to 5%              +1 percentage point, +25%

X% of Y            =Y*X/100
X as % of Y        =X/Y*100
% change           =(New-Old)/ABS(Old)*100
Add X%             =Y*(1+X/100)
Remove X%          =Final/(1+X/100)

Common mistakes to avoid

Frequently asked questions