Three ways to calculate any percentage — instantly.
A percentage is a way of expressing a number as a fraction of 100. To find X% of Y, multiply Y by X and divide by 100. For example, 20% of 150 = (150 × 20) ÷ 100 = 30. Alternatively, convert the percentage to a decimal by dividing by 100, then multiply: 20% = 0.20, and 0.20 × 150 = 30. This approach is often faster for mental math.
To find what percentage X is of Y, divide X by Y and multiply by 100. For example, to find what percentage 30 is of 150: (30 ÷ 150) × 100 = 20%. This is useful for calculating test scores (you got 45 out of 60 — what percentage is that?), tracking progress toward goals, or comparing proportions between different groups.
Percentage change = ((New Value − Old Value) ÷ Old Value) × 100. A positive result is a percentage increase and a negative result is a percentage decrease. For example, if a price goes from $80 to $100: ((100 − 80) ÷ 80) × 100 = 25% increase. If it goes from $100 to $80: ((80 − 100) ÷ 100) × 100 = −20% decrease. Note that a 25% increase followed by a 20% decrease does not return you to the original value — this asymmetry trips people up frequently.
Percentages appear constantly in daily life. Sales tax is added as a percentage of your purchase price. Discounts and sales are expressed as percentage reductions. Bank interest rates on savings accounts and loans are annual percentages. Nutritional labels show daily value percentages for vitamins and minerals. Election results and poll numbers are expressed as percentages. Investment returns are measured in percentage gains or losses. Understanding how to quickly calculate percentages is one of the most practically useful math skills you can have.
A common source of confusion is the difference between a percentage change and a change in percentage points. If an interest rate rises from 2% to 3%, it has increased by 1 percentage point, but it has increased by 50% (because 1 is 50% of 2). Politicians and media outlets sometimes use these interchangeably in misleading ways. If someone says unemployment "fell by 2%" it could mean it fell from 10% to 9.8% (a 2% relative decrease) or from 10% to 8% (a 2 percentage point decrease) — very different things. Always check which meaning is intended.