Percentage Calculator — All Types in One Tool
Five modes cover every percentage problem you will ever meet: find a percentage of a number, work out what percentage one value is of another, calculate percentage change, reverse a percentage back to the original, or find the difference between two values. Step-by-step workings shown for every calculation.
Why percentages matter in everyday UK life
Percentages are one of the most useful maths tools you have — and one of the most misunderstood. They appear everywhere: VAT on your shopping receipts, interest rates on your mortgage and savings accounts, pay rises at review time, discounts in the sales, and exam results for your children. Being comfortable with percentages means you can sense-check figures at a glance instead of taking them on trust.
Despite their ubiquity, most people only ever use one or two types of percentage calculation. The full set — percentage of a number, what percentage, percentage change, reverse percentage, and percentage difference — each has a specific formula, and confusing one with another leads to real mistakes. This calculator handles all five so you never have to remember which formula applies.
Two mental maths shortcuts worth knowing
For quick mental estimates, two tricks cover most situations. First, find 10% by shifting the decimal point one place. 10% of £85 is £8.50. Need 20%? Double it: £17. Need 15%? Add half of 10%: £8.50 + £4.25 = £12.75. Second, remember the X% of Y = Y% of X identity. Finding 4% of 75 is easier thought of as 75% of 4: three-quarters of 4 = 3. Same answer, simpler arithmetic.
Four UK real-world examples
"What is 20% of £85?" — This is VAT on a net price. The answer is (85 × 20) ÷ 100 = £17 VAT, making the VAT-inclusive total £102.
"I scored 67 out of 80 — what percentage is that?" — (67 ÷ 80) × 100 = 83.75%. Whether that earns a grade boundary depends on the exam, but at least you know the raw percentage.
"My salary went from £28,000 to £31,500 — what % increase?" — ((31,500 − 28,000) ÷ 28,000) × 100 = 12.5% increase. The same formula handles a discount: a jacket was £120, now £84 — ((84 − 120) ÷ 120) × 100 = −30% (30% off).
"This receipt shows £102 including 20% VAT. What was the net price?" — Divide by 1.20: £102 ÷ 1.20 = £85. Many people make the mistake of subtracting 20% of £102 (= £20.40) to get £81.60 — which is wrong, because the 20% was applied to £85, not to £102.
A common mistake to avoid: confusing percentage points with percentages. If a mortgage rate rises from 2% to 3%, that is a rise of 1 percentage point — but it is a 50% increase in the rate itself. News reports often use these interchangeably, and the difference matters when you are calculating the actual cost impact.
Percentage points vs percentages — an important distinction
This is one of the most common sources of confusion in financial news. A percentage point is the arithmetic difference between two percentage figures. A percentage expresses a relative change. If the Bank of England base rate rises from 2% to 3%, that is a 1 percentage point rise. But expressed as a percentage change, the rate has increased by 50% (because 1 is 50% of 2). Both statements are mathematically correct — they just measure different things. When a newspaper says "interest rates rose by 1%", they almost always mean 1 percentage point, not a 1% relative change in the rate.
Reverse percentages — why you must divide, not subtract
The most frequent reverse percentage mistake is this: a coat costs £84 after a 30% discount, so people subtract 30% of £84 (£25.20) to get £58.80 and call it the original price. That is wrong. The 30% was taken off the original price, not the sale price. The correct method is to divide by (1 − 0.30) = 0.70: £84 ÷ 0.70 = £120. The same logic applies to VAT — to find the net price from a VAT-inclusive total, divide by 1.20 (for 20% VAT), not subtract 20% of the gross.
Stacking discounts — why 20% + 10% ≠ 30%
Retailers sometimes advertise stacked discounts: "take a further 10% off our already discounted price". A 20% discount leaves you paying 80% of the original. A further 10% off that means you pay 90% of the already-discounted price: 0.80 × 0.90 = 0.72. You pay 72% of the original — a combined saving of 28%, not 30%. The more discounts you stack, the further the combined figure falls below the simple sum. This is why multiplying the remaining fractions is always more accurate than adding the discount percentages.
Percentage vs fraction vs decimal
These three representations are equivalent and interchangeable. 25% = ¼ = 0.25. To convert a percentage to a decimal, divide by 100 (move the decimal point two places left). To convert a decimal to a percentage, multiply by 100. Fractions and decimals are often easier to work with in multi-step calculations — convert percentages to decimals first, do the maths, then convert back if a percentage is needed for the final answer.
Percentage Calculator — FAQ
Multiply the number by the percentage, then divide by 100. For example, 15% of 200 = (200 × 15) ÷ 100 = 30. Or use the shortcut: find 10% by moving the decimal point one place left, then adjust. 10% of 200 is 20, so 15% is 20 + (20 ÷ 2) = 30.
The formula is ((new value − old value) ÷ old value) × 100. A positive result is an increase; a negative result is a decrease. For example, a salary rising from £28,000 to £31,500 is ((31,500 − 28,000) ÷ 28,000) × 100 = 12.5% increase.
A reverse percentage finds the original value before a percentage was applied. If a price has already been increased by 20%, divide by 1.20 to find the original. If it was decreased by 20%, divide by 0.80. Never subtract the percentage directly — that gives the wrong answer because the percentage was applied to the original, not the result.
Percentage points measure the arithmetic difference between two percentages. Percentages measure relative change. If an interest rate rises from 2% to 3%, it has risen by 1 percentage point, but the rate has increased by 50% relative to the original 2%. The distinction matters enormously in finance and news reporting.
Divide by (1 + rate ÷ 100). To remove 20% VAT from a VAT-inclusive price of £120, divide by 1.20 to get £100. Do not subtract 20% of £120 (£24) from £120 — that gives £96, which is wrong because the VAT was calculated on the net price, not on the gross.
Divide the part by the whole, then multiply by 100. If you scored 67 out of 80 on an exam, the percentage is (67 ÷ 80) × 100 = 83.75%. This works for any part-to-whole relationship: market share, survey responses, budget allocation, and so on.
No. Two successive discounts do not add up. A 20% discount leaves 80% of the price, and a further 10% discount leaves 90% of that remaining amount. So 0.80 × 0.90 = 0.72, meaning you pay 72% of the original price — a combined discount of only 28%, not 30%.
Disclaimer: This calculator is provided for general guidance and educational purposes only. Results are based on the values you enter and standard mathematical formulas. Always verify important calculations independently before making financial decisions.