Calculate percentages, changes, and more
Percentages are one of the most frequently used mathematical concepts in everyday life. From calculating discounts while shopping to understanding interest rates, exam results, or nutritional information, percentages help us express proportions in a universally understood way. The word "percent" comes from the Latin "per centum", meaning "out of one hundred". Despite being a basic concept, percentage calculations trip people up more often than you might expect. A common source of confusion is the difference between "percentage of" and "percentage change" -- these are fundamentally different operations. Another frequent mistake is calculating percentages in the wrong direction: if a GBP 50 item is reduced by 20%, the discount is GBP 10 (giving a sale price of GBP 40), but if you then increase GBP 40 by 20%, you get GBP 48, not GBP 50. Percentage increases and decreases are not symmetrical. This calculator supports five common percentage operations, covering virtually every percentage question you might encounter in daily life, at work, or in education. Each variant has a clear purpose, and the formula display shows you exactly how the answer was reached.
To use the percentage calculator: 1. Select the calculation type from the dropdown. The five available variants are: - "What is X% of Y?" -- finds a percentage of a number (e.g. what is 15% of 200?) - "X is what % of Y?" -- finds what percentage one number is of another (e.g. 30 is what percent of 150?) - "% change from X to Y" -- calculates the percentage increase or decrease between two values - "X + Y%" -- adds a percentage to a number (e.g. 100 + 20% = 120) - "X - Y%" -- subtracts a percentage from a number (e.g. 100 - 20% = 80) 2. Enter Value A. This is the first number in your calculation -- its meaning depends on the variant you selected. 3. Enter Value B. This is the second number. Again, its role changes depending on the calculation type. 4. View the result and the formula breakdown. The result shows the answer, and the formula field shows the exact calculation performed so you can verify or learn the method.
Each of the five percentage variants uses a slightly different formula: 1. What is X% of Y? Result = Y x (X / 100) Example: What is 15% of 200? Result = 200 x 0.15 = 30 2. X is what % of Y? Result = (X / Y) x 100 Example: 30 is what % of 150? Result = (30 / 150) x 100 = 20% 3. Percentage change from X to Y: Result = ((Y - X) / X) x 100 Example: Change from 80 to 100: ((100 - 80) / 80) x 100 = 25% increase If the result is positive, it is an increase. If negative, it is a decrease. 4. X + Y%: Result = X x (1 + Y / 100) Example: 100 + 20% = 100 x 1.20 = 120 5. X - Y%: Result = X x (1 - Y / 100) Example: 100 - 20% = 100 x 0.80 = 80 A common real-world application is calculating sale prices. If an item costs GBP 75 and has a 30% discount, use variant 5: 75 x (1 - 0.30) = 75 x 0.70 = GBP 52.50. To find the discount amount separately, use variant 1: 75 x 0.30 = GBP 22.50. Another practical use is comparing prices. If a product was GBP 60 last year and is now GBP 72, the percentage change is ((72 - 60) / 60) x 100 = 20% increase.
Percentage calculations are used extensively in finance (interest rates, returns on investment, tax rates), retail (discounts, markups, VAT), health (body fat percentage, nutritional values), and education (exam scores, grade boundaries). Understanding percentages well is a valuable life skill that saves time and prevents costly mistakes. If you need to work with VAT specifically, our dedicated VAT Calculator handles the standard UK rates automatically.