Free Online Calculator
Find a percentage of a number, see what percent one number is of another, and calculate percentage change, discounts and increases.
Find a percentage of a number, such as 15% of 80.
Enter a percentage and a number.
Work out what share one number is of another, such as 18 out of 60.
Enter two numbers.
Find the percentage increase or decrease from an old value to a new value.
Enter the old and the new value.
Add or take away a percentage, such as a 25% discount or an 8% tax.
Enter a number and a percentage.
This guide explains the formulas behind each calculator above, with worked examples and the mistakes people make most often.
A percentage is a way of writing a number as a part of 100. The word comes from the Latin per centum, meaning "by the hundred". So 25% means 25 out of every 100, which is the same as the fraction 1/4 and the decimal 0.25.
Percentages make it easy to compare amounts of different sizes. Saying that 18 of 60 students passed is harder to interpret than saying that 30% passed, because you can compare 30% with the result from a class of any other size.
To find a percentage of a number, turn the percentage into a decimal by dividing it by 100, then multiply it by the number.
Formula
Result = (Percentage ÷ 100) × Number
Example: 15% of 80
15 ÷ 100 = 0.15
0.15 × 80 = 12
So 15% of 80 is 12.
To see what share one number is of another, divide the part by the whole and multiply by 100. This is how test scores, completion rates and survey results are usually expressed.
Formula
Percentage = (Part ÷ Whole) × 100
Example: 18 out of 60
18 ÷ 60 = 0.3
0.3 × 100 = 30
So 18 is 30% of 60.
Percentage change compares a new value with an old one. Subtract the old value from the new value, divide by the old value, then multiply by 100. A positive result is an increase and a negative result is a decrease. The old value is the starting point, so it cannot be zero.
If a price falls from 80 to 60, the change is (60 − 80) ÷ 80 × 100 = −25%, which is a 25% decrease.
Formula
Change (%) = (New value − Old value) ÷ Old value × 100
Example: a price rises from 50 to 65
65 − 50 = 15
15 ÷ 50 = 0.3
0.3 × 100 = 30, so the price rose by 30%.
To add a percentage to a number, multiply the number by 1 plus the percentage as a decimal. To take a percentage away, multiply by 1 minus the percentage as a decimal. This is the quickest way to work out discounts, sales tax and price rises.
Formula
New value = Number × (1 ± Percentage ÷ 100)
Example: a jacket costs 80 and is 25% off
1 − 0.25 = 0.75
80 × 0.75 = 60
The sale price is 60. Adding 8% sales tax to 45 works the same way: 45 × 1.08 = 48.60.
A 50% increase followed by a 50% decrease does not bring you back to where you started. Starting at 100, a 50% increase gives 150. A 50% decrease of 150 is 75, not 100, because the second percentage is taken from the larger number.
To undo an increase, the decrease has to be smaller in percentage terms. Reversing a 25% increase takes a 20% decrease, because 100 × 1.25 × 0.80 = 100.
If an interest rate rises from 10% to 12%, it has gone up by 2 percentage points. In percentage terms the rise is 20%, because 2 ÷ 10 = 0.2. Mixing up the two is one of the most common sources of misleading statistics, so always check which one a headline or report is using.
You can estimate many percentages in your head by starting from 10%.
Divide the percentage by 100 and multiply by the number. For example, 20% of 150 is 0.20 × 150 = 30.
Subtract the old number from the new number, divide the result by the old number, and multiply by 100. Use the Percentage change calculator above and enter the old value first.
Yes. A value above 100% means more than the original amount. For example, 150% of 40 is 60, and a 150% increase on 40 gives 100.
The formula divides by the old value, and dividing by zero has no answer. When something grows from nothing, describe the change as a plain difference instead of a percentage.
Yes. You can enter decimals and negative numbers. For percentage change, the result is measured against the size of the old value, so moving from −50 to −25 is shown as a 50% increase.
No. Every calculation runs in your browser and your numbers are not sent to our server or stored.
These calculators give mathematical results. For financial, tax or other important decisions, check the figures with a qualified professional.