Percentage Calculator

Multiply the number by the percentage and divide by 100: B × A ÷ 100. So 10% of 200 is 200 × 10 ÷ 100 = 20. The word percent comes from the Latin per centum, "by the hundred", and that is the whole idea: a percentage is a fraction whose denominator is already fixed at 100. 10% is just another way of writing 10/100, or 0.1. Once you convert the percent into a decimal, every question on this page collapses into ordinary multiplication or division — there is no separate percentage arithmetic to learn. One consequence is a genuinely useful trick: A% of B always equals B% of A, because both are A × B ÷ 100. Nobody wants to compute 4% of 75 in their head, but 75% of 4 is obviously 3. Likewise 16% of 25 is the same as 25% of 16, which is 4.

Divide the part by the whole and multiply by 100: A ÷ B × 100. If 20 out of 200 questions were correct, that is 20 ÷ 200 × 100 = 10%. This is the mode for test scores, completion rates, market share and any "what fraction of the total is this" question. The only real difficulty is deciding which number is the whole — it always goes in the denominator. Getting that backwards is the most common percentage error there is, and the giveaway is a result that looks absurd (1000% instead of 10%). Note that results above 100% are perfectly legitimate. If the "whole" is a comparison figure rather than a genuine total, 250 is 125% of 200. Percentages only have to stay under 100 when the part really is contained in the whole.

If A is B% of some number, recover the whole with A ÷ (B ÷ 100). When $30 is 15% of a total, the total is 30 ÷ 0.15 = $200. This is the mode people get wrong most often, because the instinct is to add the percentage back rather than divide it out. A jacket costs $80 after a 20% discount — the original price is not 80 + 20% = $96. The 20% came off the larger number, so you must divide: 80 ÷ 0.80 = $100. The same trap appears with tax. If a $107 receipt total already includes 7% sales tax, the pre-tax price is 107 ÷ 1.07 = $100, not 107 minus 7% (which would be $99.51). Whenever a percentage has already been applied, you undo it by dividing by the factor, never by subtracting the same percent.

When the quantities being compared are themselves percentages, two different measurements exist and they are constantly confused. A rate that moves from 10% to 15% has risen by 5 percentage points — and by 50 percent. Both are correct descriptions of the same move. The difference is largest when the base is small. Something going from 1% to 2% is a rise of one percentage point, which sounds trivial, and a 100% increase, which sounds alarming. Neither number is wrong; only one of them is usually relevant. A related trap: percentages of a base do not add when they are applied one after another. Two successive 10% increases give 1.10 × 1.10 = 1.21, so +21%, not +20%. Percentages compose by multiplying their factors, not by summing.

Almost every everyday percentage can be built from 10%, which is just the number with the decimal point moved one place left. 10% of 46 is 4.6; from there, 5% is half of that (2.3), 20% is double it (9.2), and 15% is 10% plus half of 10% (6.9). For 1%, move the decimal two places. Tips work the same way: a 20% tip on a $34 check is 3.40 doubled, or $6.80 — no calculator needed. Sales tax, commissions and markups all reduce to the same move. Two checks worth running on any result. A percentage below 100 must make the number smaller; a percentage above 100 must make it bigger. And the part must be smaller than the whole unless you are genuinely comparing two independent quantities. If your answer breaks either rule, you have almost certainly divided by the wrong number.