How to Calculate a Percentage

A percentage is a fraction with a denominator of 100. Fifteen percent means 15 out of every 100, or 0.15. Almost every everyday percentage problem is one of three questions, and each has its own formula.

The three questions

1. What is X% of Y?          X% of Y = (X ÷ 100) × Y
2. A is what percent of B?   Percent = (A ÷ B) × 100
3. A is X% of what number?   Whole = A ÷ (X ÷ 100)

If you keep only one idea, keep this one: divide by 100 to turn a percentage into a decimal, and multiply by 100 to turn a decimal into a percentage.

Question 1: what is X% of Y?

Find 15% of 80. Convert 15% to 0.15, then multiply: 0.15 × 80 = 12.

A quick mental route is to find 10% by moving the decimal point one place, then build up. 10% of 80 is 8, and 5% is half of that, 4, so 15% is 8 + 4 = 12.

Question 2: what percent is A of B?

A test has 72 questions and you answered 18 correctly. Divide the part by the whole: 18 ÷ 72 = 0.25. Multiply by 100 to get 25%.

The part always goes on top. If you reverse them you get the wrong answer, which is the most common slip here.

Question 3: find the whole from a part

A discount saved you 30, and that was 12% of the original price. The original price is 30 ÷ 0.12 = 250.

Checking your answer

• If the percentage is under 100%, the result of "X% of Y" must be smaller than Y.
• 50% is half, 25% is a quarter, and 10% is a tenth. Compare your result with these anchors.
• Work backwards: 12 is 15% of 80, and 15% of 80 is 12, so the two directions agree.

Common mistakes

• Dividing the whole by the part instead of the part by the whole.
• Forgetting to convert 15% into 0.15 before multiplying.
• Treating percentage points and percent as the same thing. A rise from 4% to 5% is one percentage point but a 25% increase.

You can check any of these with the percentage calculator, which shows the working as you type.

Try it yourself

1. What is 35% of 240?
2. 45 out of 60 is what percent?
3. 18 is 24% of what number?

Answers: (1) 84; (2) 75%; (3) 75.