Percentage Calculator
Three percentage tools in one. Switch between modes to find a percentage of a number, work out what percentage one value is of another, or calculate the percentage change between two numbers.
How Percentage Calculator works
Finding a percentage of a number
To find X% of Y, multiply Y by X and divide by 100. For example, 15% of 200 is 200 × 15 ÷ 100 = 30. This is the most common percentage calculation — used for everything from tipping in a restaurant to calculating tax on a purchase. Mentally, you can often break it down: 10% of 200 is 20, so 15% is 20 + 10 = 30.
Working out what percentage one number is of another
To find what percentage X is of Y, divide X by Y and multiply by 100. For example, 30 is what percentage of 200? That is 30 ÷ 200 × 100 = 15%. This calculation is useful when you want to express a part as a share of a whole — such as what percentage of your salary you save, or what fraction of a class scored above average.
Calculating percentage change
Percentage change measures how much a value has risen or fallen relative to its original level. The formula is ((new value − original value) ÷ |original value|) × 100. A positive result is an increase; negative is a decrease. For example, a price rising from £80 to £100 is a 25% increase. Percentage change is direction-sensitive: a 25% increase followed by a 25% decrease does not return to the original value.
Reverse percentage (finding the original value)
If you know the result after a percentage increase or decrease and want to find the original, divide by (1 + rate/100) for an increase or (1 − rate/100) for a decrease. For example, a price including 20% VAT is £120. The original price before VAT is 120 ÷ 1.20 = £100. This is the reverse percentage technique used in tax and discount calculations.
Common uses of percentage calculations
Percentages appear throughout everyday finance: income tax rates, mortgage interest, VAT, discounts, investment returns, inflation, exam grades, and pay rises all involve percentage arithmetic. The three modes in this calculator cover the full range of percentage problems you are likely to encounter.
Frequently asked questions
How do I calculate 20% of a number?
Multiply the number by 0.20, or multiply by 20 and divide by 100. For example, 20% of 350 is 350 × 0.20 = 70. A quick mental shortcut: 20% is simply double 10%, and 10% of any number is just the number with its decimal point moved one place to the left.
What is the formula for percentage change?
Percentage change = ((new value − original value) ÷ original value) × 100. Always divide by the original (starting) value. A positive result means an increase; a negative result means a decrease. For example, going from 80 to 100 is (100 − 80) ÷ 80 × 100 = 25% increase.
How do I calculate percentage increase?
To find the percentage increase, subtract the original value from the new value, divide by the original value, and multiply by 100. To apply a percentage increase to a value, multiply by (1 + rate/100). So a 15% increase on £200 is £200 × 1.15 = £230.
What is the difference between percentage change and percentage points?
Percentage change is relative (e.g., a tax rate rising from 20% to 25% is a 25% increase). Percentage points measure the absolute difference between two percentages (the tax rate rose by 5 percentage points). Confusing these two is a common error in financial reporting.
How do I work backwards from a percentage?
If a value after a 20% increase is £120, the original is £120 ÷ 1.20 = £100. If a value after a 15% discount is £85, the original is £85 ÷ 0.85 = £100. Divide by (1 + rate/100) for increases, or (1 − rate/100) for decreases.
Related calculators