Percentage Calculator

Quick answer

To work out a percentage: multiply the number by the percentage and divide by 100. So 15% of £240 is 240 × 15 ÷ 100 = £36. The calculator above handles the three everyday variants: X% of Y, what percent X is of Y, and percentage change between two numbers.

Use the percentage calculator above

Enter your figures in the tool above and pick the type of sum you want. The result updates instantly, so you can try a few scenarios, for example comparing a "20% off" deal against "three for two". The sections below show the formula behind each calculation and walk through real UK examples step by step.

How a percentage calculator works

"Per cent" simply means "out of 100". So 25% is 25 out of 100, or 0.25 as a decimal. Every percentage sum comes down to converting between that decimal and your real-world numbers. There are three core calculations, and this percentage calculator handles all of them.

1. Find a percentage of a number. Multiply the number by the percentage written as a decimal.

• Result = number × (percentage ÷ 100)
• Example: 15% of 240 = 240 × 0.15 = 36

2. Find what percentage one number is of another. Divide the part by the whole, then multiply by 100.

• Percentage = (part ÷ whole) × 100
• Example: 18 out of 60 = (18 ÷ 60) × 100 = 30%

3. Find the percentage change between two numbers. Subtract the old value from the new value, divide by the old value, then multiply by 100. A positive answer is an increase, a negative answer is a decrease.

• Change = ((new − old) ÷ old) × 100
• Example: from 200 to 250 = ((250 − 200) ÷ 200) × 100 = +25%

The one rule that trips people up: the change is always measured against the original value, not the new one. That is why a price that rises 25% and then falls 25% does not return to where it started, as the worked examples below show.

Worked examples with the maths shown

A 20% sale discount

You are eyeing a coat priced at £85 with 20% off. Work out the discount, then the price you pay.

• Discount = 85 × 0.20 = £17
• You pay = 85 − 17 = £68

A quicker route is to multiply by what is left after the discount: 85 × 0.80 = £68. Our discount calculator does this for any sale price, and handles "stacked" offers where a second reduction is taken off the already-reduced price.

Sarah checks her 4% pay rise

Sarah earns £30,000 and is offered a 4% rise. She wants the new salary and the extra in cash.

• Increase = 30,000 × 0.04 = £1,200
• New salary = 30,000 + 1,200 = £31,200

That £1,200 is the gross figure. Income Tax and National Insurance will take a slice before it reaches her bank account, so the take-home gain is smaller. To see the after-tax effect, run the numbers through the pay rise calculator or check the full deductions with the income tax calculator.

Working backwards from VAT

VAT in the UK is charged at the standard rate of 20% on most goods and services. If you have a VAT-inclusive total of £120 and want the net price, you cannot just take 20% off £120, because the 20% was added to the smaller net figure, not the gross one.

• Net price = gross ÷ 1.20 = 120 ÷ 1.20 = £100
• VAT = 120 − 100 = £20

A handy shortcut for the 20% rate: the VAT inside a gross price is the gross divided by 6 (120 ÷ 6 = £20). For reduced and zero rates, or to add VAT to a net invoice, use the dedicated VAT calculator.

Reverse percentages: finding the original number

Sometimes you know the result and the percentage but need the starting figure. Say a discounted item costs £68 after 20% off, and you want the original price. Divide by the proportion you actually paid:

• Original = 68 ÷ 0.80 = £85

The same logic applies to a salary after a deduction, a bill after a surcharge, or a total after a percentage was added. Identify whether the percentage was added or taken away, then divide by 1.20 (for +20%) or 0.80 (for −20%) accordingly. Getting the direction wrong is the most common reverse-percentage error.

Where percentages show up in UK money

Percentages run through almost every financial decision you make in Britain:

• Tax and pay: Income Tax bands, the 8% employee National Insurance rate, and pension contributions are all percentages of your earnings.
• Shopping and bills: sale discounts, VAT at 20%, and energy or insurance price changes year on year.
• Borrowing and saving: mortgage and loan interest rates (APR), and savings rates (AER) are quoted as annual percentages.
• Investing: returns, fund charges and dividend yields are all expressed as percentages.

For interest that builds on itself over time, a flat percentage is not enough, because each year earns interest on the previous year's interest. The compound interest calculator handles that growth properly for savings and investments.

Percentage points are not the same as percent

This catches people out constantly. If a savings rate moves from 4% to 5%, that is a rise of one percentage point, but a 25% increase in the rate itself (1 ÷ 4 = 25%). News headlines often blur the two. When you read that a rate "went up 1%", check whether they mean one percentage point or a 1% relative change, because the difference can be large for mortgages and loans.

The same care applies to tax. Moving from a 20% to a 40% band does not mean your whole income is suddenly taxed at 40%, only the slice above the threshold is. Percentages describe slices, not the whole, far more often than people assume.

Common mistakes to avoid

• Measuring change against the wrong base. Percentage change is always relative to the original value. A rise from 200 to 250 is +25%, but a fall from 250 to 200 is −20%, not −25%.
• Assuming an up-then-down cancels out. £100 up 25% is £125; then down 25% is £93.75, not £100, because the second percentage is taken off a bigger number.
• Subtracting a percentage from a gross price. To strip VAT from £120 you divide by 1.20, not multiply by 0.80.
• Adding percentages that shouldn't be added. A 10% then a further 10% is not 20%; it is 1.10 × 1.10 = 21%.
• Confusing percentage points with percent, as covered above.

If you want to read more on how proportions and rates work in plain English, the MoneyHelper guide on budgeting and everyday money is a reliable, independent starting point, and VAT rules are set out on gov.uk.

These calculations are estimates for guidance only and are not personal tax or financial advice. For decisions with real money at stake, double-check against the official source or speak to a qualified adviser.

Who should use this calculator

This covers the five percentage questions that actually come up, kept separate because mixing them up is where mistakes happen: what is X% of Y, the percentage change between two numbers, adding or subtracting a percentage, working backwards to the original figure before a change, and compounding a percentage over several periods.

The fourth of those — finding the original value — is the one people get wrong most often. If a price rose by 20% to reach £120, the original was not £96. You cannot undo a percentage increase by subtracting the same percentage, because the two are calculated on different starting figures. This tool handles that reversal correctly.

What this calculator assumes

• Percentage change is measured relative to the starting value: the difference divided by the original, not by the new figure.
• Reversing a change divides rather than subtracts — undoing a 20% rise means dividing by 1.2.
• Growth over multiple periods compounds: each period applies to the result of the last, so 10% twice is 21% overall, not 20%.
• Results are shown to a sensible number of decimal places rather than rounded to whole numbers.

Limitations — what it does not cover

• Percentage points versus percent. A rate moving from 4% to 5% is a rise of one percentage point but a 25% increase — different statements, and this tool reports the arithmetic, not which one you meant.
• VAT specifically. Removing VAT is a reverse-percentage calculation, but the VAT calculator handles the rates and rounding rules properly.
• Tax band percentages, which apply progressively to slices of income rather than to the whole amount.
• Averaging percentages, which is rarely valid unless the underlying quantities are the same size.

Related calculators

Once you have your percentage, put it to work. Try the markup calculator for setting prices with a profit margin, the discount calculator for sale savings, or the VAT calculator to add or remove 20% VAT on any figure.

The four percentage formulas, with worked examples

The reverse formula is exactly how VAT is removed from a gross price, and percentage change is how pay rises and inflation are measured.