Percentage calculator
The four most common percentage calculations in a single tool.
Calculator inputs
Results
Enter your values and press “Calculate” to see the result.
In short
- What it calculates
- The four most common percentage calculations in a single tool.
- Formula used
A% of B = B × A ÷ 100- Example
- What is 25% of 200?
Percentage calculator
Almost every percentage question boils down to one of four different problems, and mixing them up is what produces odd answers. Pick the one that matches your case and the calculator applies the right formula.
The result includes the exact operation performed so you can check it.
How it works
A percentage is a fraction with denominator 100: 25% is 25/100 = 0.25. Multiplying by a percentage is the same as multiplying by that fraction.
Percentage change is a different matter: it measures the relative change against the starting value, which is why going from 100 to 150 is +50% while going from 150 back to 100 is −33.33%.
Formula
A% of B = B × A ÷ 100
A is what % of B = A ÷ B × 100
Change from A to B = (B − A) ÷ |A| × 100
If A is B% of the total: total = A × 100 ÷ B
Worked example
What is 25% of 200?
200 × 25 ÷ 100 = 50
A 25% discount on £200 brings the price down to £150, because those £50 are taken off.
Explanation
The four questions a percentage answers
What is fifteen per cent of two hundred. What percentage is thirty out of two hundred. Forty is twenty per cent of what number. And how much has one value changed against another. Almost every percentage problem is one of those four, and confusing them is the source of most errors.
Up and down by the same percentage does not return to the start
A hundred rising twenty reaches a hundred and twenty; falling twenty leaves ninety-six. Each percentage applies to a different base. It is the same reason recovering from a fifty per cent fall requires a hundred per cent rise.
Percentage points against percentages
If unemployment goes from eight to ten per cent, it has risen two percentage points but twenty-five per cent in relative terms. Both figures are true and describe the same thing, so identify which is being used before drawing conclusions from a headline.
Working backwards means dividing
To recover the price before a twenty per cent discount you do not add twenty: you divide by 0.8. Adding gives ninety-six instead of a hundred. It is the costliest and commonest error when working with sale prices or tax-inclusive amounts.
Frequently asked questions
How do I find the discount between two prices?
Use the “percentage change” mode: enter the original price as A and the sale price as B. The negative result is the discount applied.
How do I recover the price before the discount?
Use “A is B% of which number”. If you paid £80 after a 20% discount, 80 is 80% of the original: 80 × 100 ÷ 80 = £100.
Does a 100% increase double the amount?
Yes. A 100% increase means multiplying by 2, and a 200% increase multiplies by 3.
What is the difference between a percentage point and a percentage?
Going from eight to ten per cent is a rise of two percentage points, but twenty-five per cent in relative terms. Both describe the same change.
Why does a 20% rise then a 20% fall not return the original price?
Because the fall is calculated on the already increased price. From a hundred you rise to a hundred and twenty and fall to ninety-six.
Need to calculate something else?
These tools are often used alongside this calculator.
Discount
Final price after a discount and exactly how much you save.
Percentage increase
Apply a percentage rise to any amount and see the exact difference.
Rule of three
Solve direct and inverse proportions by entering the three known values.
VAT
Add VAT or sales tax to a net amount at whatever rate you need.
Calculator
Type the whole expression and get the result instantly, brackets and functions included.
Scientific
Trigonometry, logarithms, exponentials and factorials, with a degrees/radians switch.