What is X% of Y?
Find a percentage of any number.
Increase or decrease a value
Apply a percentage increase or decrease to a number.
X is what % of Y?
Find the percentage one number represents of another.
X is P% of what?
Find the whole number when you know a part and its percentage.
What is a percentage?
A percentage describes a number as a fraction of 100. The symbol % means “per hundred”: 35% is the same as 35 out of 100, 0.35 as a decimal, or 7/20 as a fraction.
How to calculate a percentage
To find a percentage of a number, divide the percentage by 100 and multiply it by the number. For example, 15% of 240 is 0.15 × 240, which equals 36.
The basic relationship is: percentage × original value = result. When working it out by hand, use the percentage as a decimal. For example, if 5% of 30 is 1.5, then 0.05 × 30 = 1.5.
How to find what percentage one number is of another
Divide the first number by the second number, then multiply by 100. For example, 30 is what percentage of 120? Calculate 30 ÷ 120 × 100 = 25%.
How to find the whole number
When you know the part and the percentage it represents, divide the part by the percentage as a decimal. For example, if 10 is 5% of a number, the whole is 10 ÷ 0.05 = 200.
Increasing or decreasing a number by a percentage
To increase a value, multiply it by 1 plus the percentage as a decimal. To decrease a value, multiply it by 1 minus the percentage as a decimal. For example, increasing 500 by 10% gives 500 × 1.10 = 550; decreasing it by 10% gives 500 × 0.90 = 450.
Everyday percentage examples
Percentages are useful for working out discounts, VAT, test scores, progress towards a target and how much of a monthly budget is spent on one cost. For example, if rent is £1,245 and a monthly budget is £4,000, rent uses 31.125% of that budget.
Percentage points are not the same as a percentage change
If a rate moves from 10% to 12%, it has risen by 2 percentage points. Relative to the original 10%, that is a 20% increase. The distinction matters when comparing interest rates, surveys and statistics.
Choose the reference amount explicitly
A percentage is incomplete without its base. A price rising from 80 to 100 increases by 25%, while a fall from 100 to 80 is a 20% decrease. The difference is 20 in both cases, but the starting values differ. State the starting amount before calculating a percentage change.
Frequently asked questions
How do I find 18% of 250?
Convert 18% to 0.18 and multiply by 250 to get 45.
How do I find the whole from a part and percentage?
Divide the part by the percentage written as a decimal. If 45 is 18% of the whole, calculate 45 ÷ 0.18 = 250.
Does a 20% decrease followed by a 20% increase cancel out?
No. Starting from 100, the decrease gives 80 and the subsequent increase gives 96 because the second percentage uses a smaller base.
What is the difference between percent and percentage points?
A rise from 10% to 12% is 2 percentage points, but a 20% increase relative to the original 10%.
Can a percentage be greater than 100?
Yes. For example, 150% of 40 is 60, which is one and a half times the starting amount.