Percentage Calculator

Percentages express a number as a fraction of 100. This calculator handles four common operations: finding X% of a number, finding what percentage one number is of another, calculating the percentage change between two values, and reverse-calculating the original from a percentage result. Each has a formula worth carrying in your head. To take X% of Y, multiply Y by X divided by 100, so 15% of £80 is 80 times 0.15, which comes to £12. To express X as a percentage of Y, divide X by Y and multiply by 100, so £20 out of £80 is 25%.

Percentage change is widely used in finance, statistics and everyday comparisons. The formula subtracts the old value from the new, divides by the old, then multiplies by 100. A positive result means an increase and a negative one a decrease, and the tool shows both direction and magnitude. The base matters more than people expect. Going from £80 to £100 is a rise of 25%, but coming back down from £100 to £80 is a fall of 20%, not 25%, because the starting point has changed. Most percentage errors trace back to confusion about what is being compared with what.

Reverse percentage is useful for VAT-inclusive prices or sale items. If you know the final value after a percentage increase or decrease, it finds the original amount before the change was applied. That same asymmetry explains a rule which trips up investors. A 50% loss needs a 100% gain to recover, because £100 falling by half leaves £50, and £50 has to double to get back. Lose 30% and you need about 43% to break even, not 30%. Drawdowns hurt twice over, once in the fall and again in the size of the climb back, which is why a 30% crash near retirement does far more damage than the same drop early in a career.

VAT is where reverse percentages earn their keep. The standard rate has been 20% since 4 January 2011, so adding VAT means multiplying by 1.2 and removing it means dividing by 1.2, never subtracting 20%. A gross price of £120 divides down to £100 net with £20 of VAT, the familiar one-sixth of the gross. The reduced rate of 5% on domestic energy behaves the same way, dividing by 1.05. Getting this the wrong way round is the most common VAT mistake on invoices.

Income tax applies percentages in slices rather than in one lump. For 2026/27 nothing is charged up to £12,570, then 20% applies up to £50,270, 40% up to £125,140 and 45% above that. Each rate touches only the slice of income inside its own band, which is why a pay rise crossing a threshold never taxes the whole salary at the higher rate. That distinction, between the marginal rate on the next pound earned and the effective rate across everything, is worth keeping straight whenever a headline quotes a tax percentage.

Compound growth is a percentage applied repeatedly, and the effect is not intuitive. £10,000 at 5% a year becomes £10,500 after one year and £11,025 after two, but £16,289 after ten and £43,219 after thirty. The formula multiplies the starting amount by one plus the rate over 100, raised to the number of years. The Rule of 72 gives a quick estimate of doubling time by dividing 72 by the annual return, so 5% doubles money in 14.4 years, 8% in 9 years and 10% in 7.2. Inflation compounds too, and at 3% over thirty years £1 keeps only 41p of today's buying power, which is why real returns in UK markets typically run about 2% to 3% below the headline figure.

Borrowing hides a second percentage behind the first. A mortgage rate such as 4.5% fixed is the annual interest charged on the balance still outstanding, while the APR folds in fees as well, so a 4.5% deal carrying a £999 arrangement fee often works out at 4.6% to 4.8% APR. Credit card APR is mandatory to display but easy to misread, since it describes the annual cost only if you carry a balance all year. Clear the card in full each month and you pay no interest. Pay the minimum and the arithmetic turns unpleasant, because at 18.9% APR on a £3,000 balance, paying £80 a month takes over five years and costs about £1,500 in interest. Judge borrowing by total interest paid, not by the rate alone.