How to Calculate a Percentage

Multiply the number by the percentage and divide by 100.

• 15% of 200: 200 x 15 / 100 = 30
• 7.5% of 80: 80 x 7.5 / 100 = 6
• 120% of 50: 50 x 120 / 100 = 60

A shortcut for mental arithmetic: 10% is the number with the decimal point moved one place to the left. So 10% of 240 is 24, 5% is half of that, 12, and 15% is the two together, 36.

Divide the part by the whole and multiply by 100.

• 30 out of 200: 30 / 200 x 100 = 15%
• 18 correct answers out of 24: 18 / 24 x 100 = 75%
• 45 out of 30: 45 / 30 x 100 = 150%

The whole is the number after 'of'. Mixing up the part and the whole is the most common mistake in this sum.

Subtract the old value from the new value, divide by the old value and multiply by 100. A positive answer is an increase, a negative answer a decrease.

• From 80 to 100: (100 - 80) / 80 x 100 = 25% increase
• From 100 to 80: (80 - 100) / 100 x 100 = 20% decrease

Notice that the same difference of 20 gives two different percentages. The change is always measured against where you started.

For a discount, work out the percentage of the price and subtract it. For 25% off 80: 80 x 25 / 100 = 20, so you pay 60. Faster: a 25% discount means you pay 75%, so 80 x 0.75 = 60.

Finding the original price is the other way round. If you paid 60 after a 25% discount, divide by 0.75: 60 / 0.75 = 80. Adding 25% to 60 gives 75, which is wrong.

• Up and down do not cancel out. A price that rises 20% and then falls 20% ends at 96% of where it began, not 100%.
• Two discounts do not add up. 20% off followed by 10% off is 28% in total, because the second discount is taken from the lower price.
• Percent and percentage points are different. If an interest rate goes from 2% to 3%, it rose by 1 percentage point, but by 50 percent.