How to calculate a percentage step by step

The three-step method

Finding what a percentage of a number is always follows the same structure, no matter what the actual numbers are:

1. Turn the percentage into a fraction of 100: for example, 20% becomes 20/100, or equivalently the decimal 0.20.
2. Multiply that fraction (or decimal) by the amount you're taking the percentage of: 0.20 × 200.
3. The result of that multiplication is the answer: 0.20 × 200 = 40, so 20% of 200 is 40.

A fully worked example

Let's calculate 15% of 80, showing every step separately.

Step 1. Convert 15% to a decimal: 15 ÷ 100 = 0.15.

Step 2. Multiply that decimal by 80: 0.15 × 80.

Step 3. Do the multiplication: 0.15 × 80 = 12.

So 15% of 80 is 12. You can check the result with the percentage calculator by entering 15 and 80 in the first tab: it should show exactly 12.

Mental math shortcuts for round percentages

For the percentages that come up most often (10%, 20%, 25%, 50%), you don't need to multiply by a decimal at all: there are much faster shortcuts you can do in your head.

• 10% of a number: move the decimal point one place to the left (or, for a whole number, drop the last zero if it has one). 10% of 250 is 25.
• 20% of a number: work out 10% first, then double it. 10% of 250 is 25, so 20% is 50.
• 5% of a number: work out 10%, then halve it. 10% of 250 is 25, so 5% is 12.5.
• 25% of a number: divide by 4 (25% is a quarter of the total). 25% of 200 is 50.
• 50% of a number: divide by 2 (50% is half). 50% of 90 is 45.
• 1% of a number: move the decimal point two places to the left. 1% of 250 is 2.5. Useful as a base for building almost any other percentage by adding or multiplying that value.

How to find what percent one number is of another

This is the reverse question: instead of starting from the percentage, you start from two amounts and want to know what percentage one represents of the other.

1. Divide the partial amount by the total amount: for example, if you got 18 out of 20 questions right, divide 18 by 20 = 0.9.
2. Multiply that result by 100 to convert it to a percentage: 0.9 × 100 = 90.
3. The result is the percentage you were looking for: 18 out of 20 correct answers is 90%.

Common mistakes when calculating by hand

The most frequent slip-ups when working out a percentage without a calculator usually come from skipping the step of converting the percentage to a decimal, or from mixing up which number is the part and which is the total.

• Forgetting to divide by 100 before multiplying: multiplying directly by "20" instead of by "0.20" gives a result 100 times too large.
• Reversing which number is the part and which is the total in the reverse calculation: asking "what % is 20 of 40?" is not the same as "what % is 40 of 20?" (50% versus 200%).
• Adding percentages directly when they should be multiplied instead: two successive 10% discounts do not equal a single 20% discount; they equal something slightly less (about 19%), because the second 10% is applied to an already-discounted price.

When to use a calculator instead of doing it by hand

The mental shortcuts on this page work well for round percentages (10%, 20%, 25%, 50%) and simple numbers. But when the values include decimals, uncommon percentages (like 7.3% or 42%), or when you need guaranteed accuracy with no room for error, it's faster and safer to use the percentage calculator on this site: enter the two values and get the exact result instantly, without having to double-check the arithmetic by hand. You can also check the formula reference page if you'd rather see every variant of the formula laid out in one place.

Practice exercises

Try solving these five exercises by hand using the three-step method explained above, then check your result with the calculator. The solutions appear right below each question.

1. What is 30% of 150? Solution: 0.30 × 150 = 45.

2. What is 8% of 250? Solution: 0.08 × 250 = 20.

3. If you got 27 out of 30 questions right on a test, what percentage did you get right? Solution: (27 ÷ 30) × 100 = 90%.

4. A $60 item has a 25% discount. What's the final price? Solution: 60 − (0.25 × 60) = $45.

5. Out of a group of 80 people, 12 are left-handed. What percentage of the group is left-handed? Solution: (12 ÷ 80) × 100 = 15%.

If any of your results don't match the solution, revisit the common mistakes section above, since the slip almost always comes from forgetting to divide by 100, or reversing the order of the two numbers in a reverse calculation. All calculations on this page are illustrative examples: no data is sent to any server, as explained in the privacy policy.