How to Find a Percentage of Any Number by Hand

What a percentage really is

A percentage is a fraction with a denominator of 100. Writing 35% is a short way of writing 35/100, which equals 0.35. In maths, the word "of" almost always means multiply, so "35% of 240" is 0.35 × 240.

part = percent ÷ 100 × wholeThe one formula behind every method in this article.

To turn a percent into a decimal, move the decimal point two places to the left: 18% becomes 0.18, 7% becomes 0.07 and 125% becomes 1.25. To go back, move it two places to the right.

Method 1: multiply by the decimal

Convert the percent to a decimal and multiply. This is exact and works for any percentage, including awkward ones like 17.5%.

Worked example: what is 18% of 250? Convert 18% to 0.18, then 0.18 × 250 = 45. If the multiplication feels heavy, split it: 0.18 × 250 is the same as 18 × 2.5, which is 45.

This method is the best choice when you have pencil and paper, or when the percentage does not break into friendly pieces.

Method 2: build it from 10%, 5% and 1%

For mental maths, find 10% first (move the decimal one place left), then add or subtract simple pieces. Half of 10% is 5%, and one tenth of 10% is 1%.

Worked example: what is 35% of 240? Ten percent of 240 is 24. Thirty percent is 3 × 24 = 72. Five percent is half of 24, which is 12. Add them: 72 + 12 = 84. Check with the decimal method: 0.35 × 240 = 84.

• 25%: find 10%, double it, then add 5%. Or simply take a quarter of the number.
• 90%: find 10% and subtract it from the whole.
• 15%: add 10% and 5%.
• 1%: move the decimal two places left, then multiply for 2%, 3% and so on.

Method 3: swap the numbers

Multiplication does not care about order, so x% of y always equals y% of x. That means you can choose whichever version is easier.

Worked example: what is 8% of 50? Swapping gives 50% of 8, which is half of 8, or 4. Both versions equal 0.08 × 50 = 4. Another: 4% of 75 is the same as 75% of 4, which is 3.

Turning it around: the other two problems

Rearranging the formula gives the other two questions:

percent = part ÷ whole × 100What percent is one number of another?

whole = part ÷ (percent ÷ 100)Finding the whole from a part and its percentage.

What percent is 27 of 36? Divide 27 by 36 to get 0.75, then multiply by 100: 75%.

18 is 30% of what number? Divide 18 by 0.30 to get 60. Check by finding 30% of 60: 0.30 × 60 = 18.

Sanity checks and common mistakes

Before trusting any answer, compare the percentage with a landmark you know: 50% is half, 25% is a quarter, 10% is a tenth, and 100% is the whole number. Any percentage below 100% must give a result smaller than the starting number, and any percentage above 100% a larger one.

Worked example: 51% of 198. Since 51% is just over half, the answer should be just over 99. The exact calculation, 0.51 × 198 = 100.98, passes the check. A result of 10.098 or 1,009.8 would flag a misplaced decimal point straight away.

• Skipping the decimal conversion. 5% of 80 is 0.05 × 80 = 4, not 5 × 80 = 400.
• Dividing in the wrong order. For "what percent is 9 of 12", the part (9) goes on top: 9 ÷ 12 = 0.75, so 75%. Flipping them gives 133%.
• Forgetting that percentages above 100 exist. 150% of 40 is 60, because 150% is 1.5 times the number.
• Mixing up the whole. In "20% more than 50", the percentage applies to 50, giving 60, not to the new total.

For a quick answer or a check, use the percentage calculator, and the percent to decimal calculator if you want to see the conversion step on its own.