“What is 25% of 200?” is the most common percentage question there is, and it is the one every other percentage calculation is built on. Once you can find a part of a whole, you can find a discount, a tip, a tax amount, a commission or a share of a bill — they are all the same operation wearing different clothes.
The word itself tells you the method. Per cent means “per hundred”, so a percentage is simply a fraction with 100 on the bottom. 25% is 25/100, which is 0.25. To find 25% of something, you multiply it by 0.25. That is the whole idea, and everything below is just that idea applied.
When you need this
Working out a share. A sales commission of 8% on $4,500 of revenue, a 3% platform fee on a payout, a 15% deposit on a purchase price. In each case you have a total and a rate, and you want the slice.
Checking someone else’s arithmetic. An invoice says a 12% service charge came to $84 on a $600 job. Is that right? 12% of 600 is 72, not 84 — so no, and it is worth asking why.
Scaling a recipe, a budget or a forecast. “Cut the marketing line by 30%” means finding 30% of the line and removing it. Finding the 30% is step one.
Worked examples
25% of 200. Divide 25 by 100 to get 0.25. Multiply 200 by 0.25. The answer is 50. You can also see it as a quarter, because 25% is a quarter — and a quarter of 200 is obviously 50. Recognising the common fractions is the fastest route to a sanity check.
8% of 4,500. Divide 8 by 100 to get 0.08. Multiply 4,500 by 0.08 to get 360. Or work it in steps: 1% of 4,500 is 45, so 8% is 45 × 8 = 360. The “find 1% first” route is usually the easiest one to do in your head, because finding 1% is just moving the decimal point two places left.
150% of 40. Percentages above 100 are perfectly legal and mean exactly what they say. 150/100 is 1.5, and 40 × 1.5 = 60. If a figure has grown to 150% of what it was, it is now one and a half times the original.
0.5% of 900. Divide 0.5 by 100 to get 0.005. Multiply by 900 to get 4.5. Small percentages trip people up because the decimal shifts twice; the “1% first” method handles it cleanly — 1% of 900 is 9, so half of one per cent is 4.5.
Where people go wrong
Multiplying by the percentage instead of the decimal. Typing 200 × 25 gives 5,000, which is a hundred times too big. The division by 100 is not optional. If an answer looks absurdly large, this is almost always why.
Confusing “25% of 200” with “200 increased by 25%”. The first is 50. The second is 250. This calculator answers the first question; the increase by a percentage calculator answers the second. The difference has caused a great many pricing errors, and it is worth being deliberate about which one you actually want.
Assuming percentages of different totals are comparable. 10% of one department’s budget and 10% of another’s are the same rate but potentially wildly different amounts. A percentage is meaningless until you know what it is a percentage of.
Forgetting that the order does not matter. 25% of 200 and 200% of 25 both equal 50. Multiplication is commutative, and this occasionally gives you a much easier sum than the one you were handed. 4% of 75 looks awkward; 75% of 4 is obviously 3.
Doing it without the calculator
Anchor on the easy ones and build. 50% is half, 25% is a quarter, 10% is the decimal point moved one place, 1% is two places. Almost any percentage can be assembled from those: 35% is 25% + 10%, 15% is 10% + half of 10%, 90% is the whole thing minus 10%. Our guide on doing percentages in your head works through the full set of shortcuts, and what percent one number is of another covers the reverse direction.