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Common Percentage Calculations Explained

The three most frequently needed percentage calculations are: what is X per cent of Y, what percentage is X of Y, and what is the percentage change from X to Y. To find a percentage of a number, multiply the number by the percentage and divide by 100. For example, 15 per cent of 200 equals 30. To find what percentage one number is of another, divide the first number by the second and multiply by 100. So 30 out of 200 is 15 per cent.

Percentage change calculations are particularly useful for comparing prices, wages, investment returns and other figures over time. The formula is the difference divided by the original value, multiplied by 100. If a price rises from 50 to 60 pounds, the percentage increase is 20 per cent. If it falls from 60 to 50, the percentage decrease is approximately 16.7 per cent. Note that the same absolute change of 10 pounds produces different percentages depending on the starting point, which is an important concept in financial analysis.

Percentages in Everyday UK Life

Sale discounts are one of the most common uses of percentage calculations. A 30 per cent discount on a 120-pound item saves 36 pounds, bringing the price to 84 pounds. VAT at 20 per cent adds 20 pounds to a 100-pound net price. Income tax at the basic rate of 20 per cent on 10,000 pounds of taxable income equals 2,000 pounds. Understanding these calculations helps you make informed financial decisions and verify that you are being charged correctly.

Interest rates on savings and loans are expressed as percentages. A savings account paying 4.5 per cent AER on a 10,000-pound balance earns approximately 450 pounds per year before tax. A mortgage at 5 per cent interest on a 200,000-pound balance costs approximately 10,000 pounds in interest per year. APR on credit cards and loans includes fees as well as interest, making it a more comprehensive comparison tool than the headline interest rate alone.

Avoiding Common Percentage Mistakes

A frequent error is assuming that a percentage increase followed by the same percentage decrease returns to the original number. A price that rises by 20 per cent from 100 to 120 pounds, then falls by 20 per cent, drops to 96 pounds, not 100. This is because the 20 per cent decrease is calculated on the higher base of 120. Similarly, successive discounts are not additive: two 20 per cent discounts are not the same as a single 40 per cent discount, but rather equivalent to a 36 per cent total reduction.

For VAT-specific percentage calculations, try our dedicated VAT calculator, or convert between units using the unit converter. For UK tax rate information, visit GOV.UK.