Calculate percentages quickly and accurately. This calculator handles three common percentage problems: finding a percentage of a number, calculating the percentage change between two values, and finding what percentage one number is of another.
To find X% of Y, multiply Y by X and divide by 100. For example, 15% of 200 = 200 × 15 ÷ 100 = 30.
Percentage change = (New Value − Old Value) ÷ Old Value × 100. A positive result means an increase, a negative result means a decrease. For example, a price going from £80 to £100 is a 25% increase.
Divide X by Y and multiply by 100. For example, 30 is what percentage of 200? 30 ÷ 200 × 100 = 15%.
Percentages appear constantly in daily life and understanding them helps make better financial and practical decisions. Shop discounts are expressed as percentages — knowing that 20% off £50 saves you £10 helps compare deals quickly. Interest rates on savings accounts, mortgages, and loans are percentages determining how much you earn or owe. VAT at 20% adds a fifth to most UK purchases, so a £100 pre-VAT item costs £120. Salary increases, inflation rates, and investment returns all use percentages to show relative changes. Restaurant tips are typically 10-15% of the bill. Battery levels, phone storage, and download progress use percentages to show completion. Tax rates, nutritional information, probability forecasts, and exam scores all rely on percentages. Without understanding percentages, you might struggle to compare savings rates (is 4.5% on £10,000 better than 5% on £8,000?), evaluate discounts (which is better: 30% off or buy one get one half price?), or assess financial risk (what does a 2% chance of default actually mean?). Percentage fluency also prevents being misled by marketing — "50% extra free" sounds more impressive than "33% off" but they're mathematically identical for the same original amount. Understanding compound percentages is especially crucial: a 50% increase followed by a 50% decrease doesn't return you to the starting point (it leaves you 25% down). Mastering percentage calculations removes this cognitive load and enables quick mental math for comparing options, calculating tips, or working out sale prices without reaching for a calculator.
This crucial distinction confuses many people but matters enormously in finance and statistics. Percentage change refers to the relative change expressed as a percentage of the original value. If interest rates increase from 2% to 3%, the percentage point change is 1 percentage point (simply 3 minus 2), but the percentage change is 50% (the increase of 1 is 50% of the original 2%). This difference becomes dramatic with larger numbers: if your council tax rises from £1,500 to £1,650, that's a £150 or 10% increase — both tell you something useful. But if you read "council tax up 10%" you know it's proportional to your current bill, whereas "council tax up £150" is an absolute amount affecting everyone the same. Politicians and media often exploit this confusion. "Unemployment fell by 2 percentage points" (e.g., from 8% to 6%) sounds less impressive than "unemployment fell by 25%" (the 2 point fall represents a 25% reduction from the original 8%). Similarly, "crime increased by 0.5 percentage points" sounds small, but if crime was at 1% that's actually a 50% increase in the crime rate. When evaluating claims, always check whether the figure quoted is percentage points (absolute difference) or percentage change (relative difference) as they can paint very different pictures of the same situation. In finance, understanding this prevents costly mistakes: if your investment falls 50% then rises 50%, you haven't broken even — you're down 25% overall (£100 falls to £50, then rises to £75).
Percentage change from a positive number to a negative number, or between two negative numbers, creates mathematical complications that confuse even spreadsheets. The standard formula (New − Old) / Old × 100 works fine for positive to positive: profits rising from £100k to £150k is a 50% increase. But if profits fall from £50k to a loss of £20k, the formula gives (−20 − 50) / 50 × 100 = −140%. This mathematically correct answer is hard to interpret: does "−140%" meaningfully describe the change? Some contexts use absolute values to avoid negatives in the denominator: |−20 − 50| / |50| = 140% decline. For negatives to negatives, if losses shrink from −£30k to −£10k, you've improved by £20k but percentage formulas break down because dividing by a negative flips the sign. The pragmatic approach is describing the absolute change (£20k improvement) rather than forcing a percentage that doesn't illuminate. Similarly, going from zero to any value is technically infinite percentage growth, which isn't useful for comparison. In business reporting, when numbers cross zero it's clearer to say "moved from £X profit to £Y loss" or "losses narrowed from £X to £Y" rather than calculating misleading percentages. This is why financial statements often show both absolute changes (£ difference) and percentage changes (% difference), omitting percentage when crossing zero or between negative values. When building spreadsheets or reports, implement logic to handle zero and negative denominators appropriately rather than displaying meaningless percentages.
A jacket originally priced at £80 has a 25% discount. How much do you pay? Calculate 25% of £80: 0.25 × 80 = £20 discount. Final price: £80 − £20 = £60. Alternatively, 25% off means you pay 75%, so 0.75 × 80 = £60 directly. If there's then a further 10% off the sale price (common in multi-buy promotions), it's 10% off £60 = £6 discount, paying £54 total. Note this isn't 35% off the original price (which would be £52) — sequential discounts multiply rather than add.
Your £35,000 salary increases by 4%. New salary = £35,000 × 1.04 = £36,400. That's a £1,400 increase, or £116.67 extra monthly before tax. If inflation is 6%, your real purchasing power has actually decreased by roughly 2% despite the nominal increase — you can buy 2% less with your new salary than you could with the old one before prices rose. This shows why percentage comparisons matter: a 4% raise sounds good until compared against 6% inflation.
You invested £5,000 which grew to £6,200 over two years. What's your percentage return? Gain = £6,200 − £5,000 = £1,200. Percentage return = (£1,200 / £5,000) × 100 = 24% total return over two years. Annualized, this is approximately 11.4% per year (not simply 12%, as compound interest means the second year's growth includes gains from the first year). This matters when comparing investments with different time periods — a 30% gain over three years (9.1% annually) is less attractive than 20% over one year.
Don't add percentages that apply to different bases: if a product decreases 10% then increases 10%, you don't end up at the starting point. Starting at £100, minus 10% = £90, plus 10% of £90 = £99, not £100. The base changed. Similarly, averaging percentages without weighting is misleading: if investment A gains 50% on £1,000 and investment B loses 20% on £10,000, the average percentage (15% gain) hides that you've actually lost money overall (−£1,500 loss on £11,000 invested). Always calculate the actual monetary result then convert to percentage if needed. Beware of small sample sizes inflating percentages: crime rising from 2 incidents to 4 incidents is a 100% increase that sounds alarming but represents just 2 additional incidents. Percentage points versus percentage change confusion causes frequent misunderstandings in media reports — a 2 percentage point rise from 3% to 5% is actually a 67% increase in relative terms. Don't confuse percentage of a total with percentage increase: scoring 75% on a test means you got 75 out of 100, not that your score increased by 75%. Understanding reverse percentages prevents mistakes: if a retailer increases prices 20% then offers a "20% sale," you're not back to the original price — you're still paying 96% of it (1.20 × 0.80 = 0.96). When calculating tips, remember that percentage applies to the pre-tax amount in the US but post-tax in the UK. Finally, don't fall for the base rate fallacy: a test that's 99% accurate giving a positive result doesn't mean 99% chance you have the condition — it depends on how rare the condition is in the population. These nuances separate percentage literacy from superficial understanding.