Percentage & Rule of Three
Work out a percentage of a number, find what percent one value is of another, measure a percent change, apply a discount or markup, and solve direct or inverse rule of three problems.
How the percentage calculator works
Pick a tab and fill in the numbers; only positive numbers are supported, because the minus sign is ignored. Percent of a number multiplies the rate by the value and divides by 100, so 15% of 200 is 30. What percent divides the part by the total and multiplies by 100, so 25 out of 200 is 12.5%. Percent change subtracts the start from the end, divides by the start and multiplies by 100: going from 100 to 135 is +35%. Increase or decrease multiplies the value by 1 plus or minus the rate divided by 100, so taking 20% off 250 leaves 200.
The rule of three links two pairs of quantities. In direct proportion both grow together: if 3 kg cost 12, then 5 kg cost 20, found as X = B × C ÷ A = 12 × 5 ÷ 3. In inverse proportion one grows while the other shrinks: if 4 workers take 6 days, then 3 workers take 8 days, found as X = A × B ÷ C = 4 × 6 ÷ 3. Type A and B as the known pair, C as the new first quantity, and the calculator returns X. A or C equal to zero in the divisor is rejected.
Two classic mistakes are worth avoiding. A 50% rise followed by a 50% fall does not bring you back to the start: 100 becomes 150 and then 75, because the second percentage applies to a larger base. Also keep percentage points apart from percent: moving from 10% to 12% is a rise of 2 percentage points, but a 20% increase in the rate itself. Results are shown with at least two decimals, or as many as you typed, up to six.