Five percentage calculators on one page

Multiply the number by the percentage and divide by 100: 15% of 200 is 200 × 15 ÷ 100 = 30. Turning the percentage into a decimal first gives the same answer, 200 × 0.15 = 30. For mental maths, 10% is the number with its decimal point moved one place to the left, so 10% of 200 is 20, 5% is half of that, and 15% is the two added together.

Divide the first number by the second and multiply by 100: 30 ÷ 200 × 100 = 15, so 30 is 15% of 200. The order matters: 200 ÷ 30 × 100 is 666.67%, which answers a different question. Put the part you are asking about first and the whole it belongs to second, such as marks scored out of marks available.

Take the starting value away from the new one, divide by the starting value and multiply by 100. From 200 to 250 is (250 − 200) ÷ 200 × 100 = 25%, an increase. Going back from 250 to 200 is (200 − 250) ÷ 250 × 100 = −20%, a decrease: the same 50 is a smaller share of 250 than of 200, so a rise and the fall that undoes it are never the same percentage. The calculator divides by the size of the starting value, so a move from −50 to −25 reads as a 50% increase. A change from zero has no percentage, because any amount is infinitely more than nothing, and the calculator says so instead of showing a number.

Divide the amount you know by the percentage it represents and multiply by 100. If 30 is 15% of something, that something is 30 ÷ 15 × 100 = 200. The same method removes a tax or a mark-up: a price of 1,180 that includes 18% tax is 118% of the pre-tax price, so the pre-tax price is 1,180 ÷ 118 × 100 = 1,000. Taking 18% off 1,180 instead gives 967.6, which is wrong, because the 18% was charged on 1,000, not on 1,180.

A percentage point is the plain difference between two percentages; a percentage change compares that difference with the starting figure. An interest rate that goes from 4% to 5% has risen by 1 percentage point but by 25%, because 1 is a quarter of 4. Rates, poll results and market shares are usually reported in points. To get the percentage change between two rates, enter them as plain numbers in the change calculator; the point change is one taken away from the other.