How to Calculate Percentages
A percentage is just a way of expressing a part out of 100. Almost every percentage question is one of three types, and once you can spot which type you are looking at, the maths is easy.
Percent of a number
To find a percentage of a number, turn the percent into a decimal and multiply. What is 20% of 500? Multiply 500 by 0.20 to get 100.
What percent one number is of another
Divide the part by the whole and multiply by 100. If 30 out of 200 questions were correct, that is 30 / 200 x 100 = 15%. The same method turns any "x out of y" into a percentage, from a test score to a completion rate.
Percent increase and decrease
Take the difference, divide by the original, and multiply by 100. A price rising from 200 to 260 is (260 - 200) / 200 x 100 = a 30% increase. The same idea works for a drop: from 260 back to 200 is a decrease of about 23%, not 30%, because the starting number is different.
How to add or remove a percentage
Often you want the new total, not the percentage alone. To add 20% to 50, multiply by 1.20 to get 60. To take 30% off 80, multiply by 0.70 to get 56. The one-step multipliers are worth memorising: adding x% is multiplying by (1 + x/100), and removing x% is multiplying by (1 - x/100). That single trick covers most tax, tip and discount maths.
How to reverse a percentage
This is the one that trips people up. If a jacket costs 60 after 20% off, the original was not 60 plus 20%. Because the discount came off the larger original, you divide: the sale price is 80% of the original, so 60 / 0.80 = 75. The same reverses tax: a 120 total that already includes 20% tax started at 120 / 1.20 = 100. Whenever a percentage has already been applied, divide by the multiplier instead of adding the percentage back.
The mistake almost everyone makes
A percentage increase and the matching decrease are not equal. Add 30% to a number and you have to remove about 23% to get back, not 30%. And a percentage point is not a percent: moving from 10% to 12% is 2 percentage points, but that is a 20% relative increase. Reporters and adverts blur these two constantly, so it is worth keeping them straight.
Quick mental tricks
- 10% of anything: move the decimal one place left. 10% of 250 is 25.
- 5% is half of 10%, and 20% is double it.
- 1% is two places left. 1% of 250 is 2.5.
- X% of Y equals Y% of X, so 8% of 50 is the same as 50% of 8, which is 4.
Let a calculator do it
The Percentage Calculator handles all three types in one place. For price changes, try the Percentage Increase Calculator or the Discount Calculator.
Frequently asked questions
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100. 30 out of 200 is 30 / 200 x 100 = 15%.
How do I add or remove a percentage?
To add x%, multiply by (1 + x/100); to remove x%, multiply by (1 - x/100). Adding 20% to 50 gives 60; taking 30% off 80 gives 56. Simply subtracting the percentage does not reverse it correctly.
How do I reverse a percentage to find the original?
Divide, do not add. If 60 is the price after 20% off, the original is 60 / 0.80 = 75. If 120 includes 20% tax, the pre-tax figure is 120 / 1.20 = 100.
What is a percentage point?
The raw gap between two percentages. Going from 10% to 12% is 2 percentage points, but a 20% increase in relative terms.