Percentage Calculator

Percentages express a number as a fraction of 100. This calculator handles four common operations: find X% of a number, find what percentage one number is of another, calculate the percentage change between two values, and reverse-calculate the original from a percentage result.

Percentage change is widely used in finance, statistics and everyday comparisons. The formula is: ((New − Old) ÷ Old) × 100. A positive result means an increase; a negative result means a decrease. The calculator displays both the direction and magnitude clearly.

Reverse percentage is useful for VAT-inclusive prices or sale items. If you know the final value after a percentage increase or decrease, the calculator finds the original amount before the change was applied.

The three core percentage calculations. (1) X% of Y: multiply Y × (X/100). 15% of £80 = 80 × 0.15 = £12. (2) X as a percentage of Y: (X/Y) × 100. £20 of £80 = 25%. (3) Percentage change: ((new − old) / old) × 100. From £80 to £100 = +25%. From £100 to £80 = −20% (NOT −25% — base is different). Always identify the base — most percentage errors come from confusion about what's being compared.

Percentage increase and decrease — asymmetric. A 50% loss requires a 100% gain to recover. Example: £100 → −50% = £50; £50 → needs +100% to get back to £100. Common mistake: 'I lost 30%, I need 30% to recover' — actually need ~43%. Investing implication: drawdowns hurt twice — once when you lose, again because recovery requires larger percentage. Pension implications: a 30% market crash near retirement is catastrophic; same percentage drop early career barely matters thanks to time.

UK VAT and percentage-based tax calculations. Standard VAT 20% (since 4 Jan 2011). To add VAT: multiply by 1.2. To remove VAT from a gross price: divide by 1.2 (NOT subtract 20%). Example: £120 gross ÷ 1.2 = £100 net; VAT = £20 (the 1/6 of gross rule). Reduced VAT 5% (domestic energy): divide by 1.05 to find net. Income tax rates 2026/27: 0% to £12,570; 20% to £50,270; 40% to £125,140; 45% above. Each band applies only to that slice — marginal rates, not effective rates.

Compound growth — why percentages matter for savings. £10,000 at 5% annual: year 1 = £10,500; year 2 = £11,025; year 10 = £16,289; year 30 = £43,219. Compound formula: A = P × (1 + r/100)^n. Rule of 72: dividing 72 by annual return rate gives years to double — 5% doubles in 14.4 years; 8% in 9 years; 10% in 7.2 years. Why inflation matters: 3% inflation over 30 years = £1 becomes worth 41p of today's purchasing power. Real returns (after inflation) typically lag headline returns by 2-3% in UK markets.

Mortgage interest, APR and percentage traps. Mortgage 'rate' (e.g. 4.5% fixed) is annual interest charged on remaining balance. APR (Annual Percentage Rate) includes fees and is higher: a 4.5% rate with £999 fees often becomes 4.6-4.8% APR. Credit card APR is mandatory but misleading — represents annual rate IF you carry balance all year. Pay in full each month: pay 0% interest. Minimum-payment trap: 18.9% APR on £3,000 balance, paying £80/month = 5+ years to clear, £1,500 interest. Always calculate total interest paid, not just rate.