How to Calculate a Percentage

"Percent" means "per hundred". 25% is 25 out of every 100, which is the same as the fraction 25/100 or the decimal 0.25.

To turn a percent into a decimal, divide by 100. In practice that means moving the decimal point two places to the left:

Every percent problem involves three numbers: a part, a whole and a percent. If you know two of them, you can always find the third.

Formula: Part = Percent × Whole ÷ 100. Use it for questions like "What is 15% of 80?"

1. Turn the percent into a decimal: 15% = 0.15.
2. Multiply by the whole: 0.15 × 80 = 12.

This is the formula behind sales tax, tips and discounts. A 6% tax on a $35 purchase is 0.06 × 35 = $2.10.

Formula: Percent = Part ÷ Whole × 100. Use it for questions like "18 is what percent of 24?"

1. Divide the part by the whole: 18 ÷ 24 = 0.75.
2. Multiply by 100: 0.75 × 100 = 75%.

This is how a test score becomes a grade: 36 correct out of 40 is 36 ÷ 40 × 100 = 90%. The whole is the number that comes after "of" or "out of".

Formula: Whole = Part ÷ Percent × 100. Use it for questions like "9 is 30% of what number?"

1. Divide the part by the percent to find 1%: 9 ÷ 30 = 0.3.
2. Multiply by 100 to find 100%: 0.3 × 100 = 30.

Check it: 30% of 30 is 0.3 × 30 = 9. ✓ This formula answers "I paid $12 and that was 40% of the original price. What was the original?" (12 ÷ 40 × 100 = $30).

Most percents can be built from a few easy pieces:

• 10%: move the decimal point one place left. 10% of 64 = 6.4.
• 5%: half of 10%. 5% of 64 = 3.2.
• 1%: move the decimal point two places left. 1% of 64 = 0.64.
• 50%, 25%, 20%: divide by 2, 4 or 5.

Then add the pieces together. For an 18% tip on $40: 10% is $4, 5% is $2, and 1% is $0.40, so 3% is $1.20. Adding them up, $4 + $2 + $1.20 = $7.20.

The swap trick: X% of Y always equals Y% of X. 4% of 75 sounds hard, but 75% of 4 is easy: 3.

Formula: Percent change = (New − Old) ÷ Old × 100. A positive answer is an increase; a negative answer is a decrease.

Two mistakes to avoid:

• Always divide by the old value. Dividing by the new value gives a different, wrong answer.
• Percent is not the same as percentage points. An interest rate going from 4% to 5% rises by 1 percentage point, but that is a 25% increase in the rate ((5 − 4) ÷ 4 × 100).

The Percentage Change Calculator works these out for you, and Percent Change vs Percentage Points explains the difference in more depth.

Any 4 function calculator handles all three formulas. The safest method is to type the percent as a decimal:

• 15% of 80: 80 × 0.15 = → 12
• 18 is what % of 24: 18 ÷ 24 × 100 = → 75
• 9 is 30% of what: 9 ÷ 30 × 100 = → 30

The % key is a shortcut, but it works differently from brand to brand, especially with + and −. If you use it, test it first: 200 × 10 % should show 20.

Try each one, then open the answer to check your working.

1. What is 20% of 45?
   Show answer

   0.2 × 45 = 9
2. 12 is what percent of 48?
   Show answer

   12 ÷ 48 × 100 = 25%
3. 18 is 40% of what number?
   Show answer

   18 ÷ 40 × 100 = 45
4. A $70 jacket is 30% off. What do you pay?
   Show answer

   0.3 × 70 = $21 off, so you pay 70 − 21 = $49
5. A price goes from $40 to $50. What is the percent increase?
   Show answer

   (50 − 40) ÷ 40 × 100 = 25%
6. Write 7/20 as a percentage.
   Show answer

   7 ÷ 20 = 0.35, and 0.35 × 100 = 35%