Percentage Calculator
Pick the question, enter the two numbers you know, and the percentage calculator shows the answer together with the formula and every step of the working.
Source: Department for Education – National curriculum in England: mathematics programmes of study, KS3 “Ratio, proportion and rates of change” (percentage change, original value problems). Updated: .
How it is calculated
How percentages work
Percent means “per hundred”: 1% = 1/100 = 0.01. Every percentage question links three quantities – the whole (100%), the percentage P and the part. The core equation is part = whole × P ÷ 100; if you know two of them, you can find the third.
How to calculate a percentage
- Find your question in the list, for example “What is 15% of 200?” or “Percentage change from 80 to 100?”.
- Type your own numbers into the two boxes of that line – every line calculates on its own.
- The result appears straight away, together with the formula and every step of the working.
Example: 15% of $250 is 250 × 15 / 100 = $37.50. A price rising from $80 to $92 is an increase of (92 − 80) / 80 × 100 = 15%. And 42 out of 50 marks is 42 / 50 × 100 = 84%.
The three percentage formulas
| You want | Formula | Example |
|---|---|---|
| P% of a number | part = whole × P ÷ 100 | 15% of 200 = 200 × 15 ÷ 100 = 30 |
| the original whole | whole = part × 100 ÷ P | 30 is 15% of 30 × 100 ÷ 15 = 200 |
| what percent | P = part ÷ whole × 100 | 30 out of 200 = 30 ÷ 200 × 100 = 15% |
On a calculator, turn the percentage into a decimal first: 15% of 200 = 200 × 0.15 = 30.
Percentage change, increase and decrease
Percentage change = (new − old) ÷ old × 100. A price rising from $80 to $100 is a 20 ÷ 80 × 100 = 25% increase. Falling from $100 to $80 is only a 20% decrease, because the change is always measured against the starting value.
Increase by P%: new value = X × (1 + P ÷ 100). Adding 20% VAT to £100 gives 100 × 1.2 = £120. Decrease by P%: new value = X × (1 − P ÷ 100). 25% off $80 is 80 × 0.75 = $60.
Reverse percentages: to find the original price, divide by the multiplier – £120 ÷ 1.2 = £100. Taking 20% off £120 would wrongly give £96.
Percent vs. percentage points
If an interest rate goes from 4% to 5%, it has risen by 1 percentage point but by 25 percent (1 ÷ 4 × 100). Percentage points measure the gap between two percentages; percent measures the relative change.
The result is shown with up to four decimal places (six in the working); rounded answers are marked with “≈”. Percentage difference between two values on an equal footing (dividing by their average) is a different measure and is not calculated here.
More percentage tools: work out the final price with the discount calculator, solve ratios with the rule of three calculator, turn fractions into decimals with the fraction calculator, or average your marks with the GPA calculator.
Frequently asked questions
How do I calculate a percentage of a number?
Multiply the number by the percentage and divide by 100: 15% of 200 = 200 × 15 ÷ 100 = 30. Or multiply by the decimal: 200 × 0.15.
How do I work out what percent one number is of another?
Divide the part by the whole and multiply by 100: 30 out of 200 = 30 ÷ 200 × 100 = 15%.
How do I calculate percentage increase?
(new − old) ÷ old × 100. From 80 to 100: 20 ÷ 80 × 100 = 25%. A negative result means a decrease.
How do I take a percentage off a price?
Multiply by (1 − P ÷ 100). 25% off $80 = 80 × 0.75 = $60, a saving of $20.
How do I find the original price before a percentage increase?
Divide by the multiplier: a price of £120 including 20% VAT was £120 ÷ 1.2 = £100 before tax.
Why does +25% and then −25% not bring me back to the start?
The second change is based on the new, larger value: 100 × 1.25 = 125, then 125 × 0.75 = 93.75 – an overall drop of 6.25%.
How do I calculate a percentage of my marks or grade?
Divide the marks you scored by the total marks and multiply by 100: 42 out of 50 is 42 / 50 × 100 = 84%. In the calculator, choose “Y is what percent of X?”.
How do I calculate a percentage in Excel?
Divide the part by the whole, e.g. =A2/B2, and format the cell as Percentage. For 15% of a number, use =A2*15%.
Sources and legal basis
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