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.
To find X% of a number, multiply and divide by 100 — 15% of 200 = (200 × 15) ÷ 100 = 30. For percentage change, use (new − old) ÷ old × 100. A reverse percentage means dividing, not subtracting: a £102 total including 20% VAT is £102 ÷ 1.20 = £85 net. Watch two traps: a rate moving 2% → 3% is 1 percentage point but a 50% increase, and stacked discounts of 20% then 10% give 28% off, not 30% (0.8 × 0.9 = 0.72).
Where do percentages come up in everyday UK life?
Percentages appear on almost every receipt, payslip and statement you handle — VAT, interest, pay rises, discounts and exam results. They are one of the most useful maths tools you have, and one of the most misunderstood. Being comfortable with them 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. For percentages that compound over time, such as savings interest, use the compound interest calculator; to average a set of figures, try the average calculator.
What are the quickest mental shortcuts for percentages?
Two tricks cover most situations: find 10% by shifting the decimal one place, and use the fact that X% of Y = Y% of X. For quick estimates, 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, the X% of Y = Y% of X identity: 4% of 75 is easier as 75% of 4 = 3. Same answer, simpler arithmetic.
What do percentage calculations look like in real life?
Each of the five modes maps to an everyday UK task — VAT, exam marks, pay rises, and stripping VAT back out. Here are four worked scenarios you can reproduce in the calculator above:
"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.
What is the difference between percentage points and percentages?
A percentage point is the arithmetic gap between two percentages; a percentage change is relative — a rate moving 2% to 3% is 1 point but a 50% rise. This is one of the most common sources of confusion in financial news, and both statements are correct — they just measure different things. 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.
Why must you divide, not subtract, for reverse percentages?
Because the percentage was applied to the original value, not the final one — so you reverse it by dividing by (1 ± rate), never by subtracting. 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.
Why don't stacked discounts of 20% and 10% equal 30%?
Because the second discount applies to the already-reduced price, not the original — so 20% then 10% leaves you paying 72% (a 28% saving), not 70%. 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.
How do percentages, fractions and decimals relate?
They are three interchangeable ways of writing the same value — 25% = ¼ = 0.25. These representations are equivalent. 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.
Frequently Asked Questions
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.