Percentage Calculator
Work out percentages, percentage change and reverse percentages in seconds. Every answer comes with the working, so you can check the maths and learn the formula.
Four Ways to Work Out a Percentage
A percentage is simply a fraction of 100. Almost every percentage question you will meet — a discount, a tax rate, a test score, a pay rise — is one of the four calculations below. Use the calculator to get an instant answer, then read the matching formula to see how it works.
Find a percentage of a number
The most common calculation: working out a tip, a discount, VAT, or a share of a total. Turn the percentage into a decimal by dividing it by 100, then multiply by the number. For example, 20% of 250 is 50.
Result = (Percentage ÷ 100) × NumberExpress one number as a percentage of another
Use this when you have a part and a whole, such as a test score or a share of a budget. Divide the part by the whole, then multiply by 100. For example, 45 out of 60 is 75%.
Percentage = (Part ÷ Whole) × 100Work out a percentage increase or decrease
This measures how much a value has changed relative to where it started — a price rise, a pay increase, a drop in sales. Always divide by the original value, not the new one. From 80 to 100 is a 25% increase.
Change = ((New − Old) ÷ Old) × 100Reverse a percentage
Use this when you know the final figure and need the original — stripping VAT out of a gross price, or finding the pre-sale price of a discounted item. Divide by 1 plus the decimal for an increase, or 1 minus the decimal for a discount.
Original = Final ÷ (1 ± Percentage ÷ 100)Percentage Calculator
Pick a calculation and enter your numbers
Percentage Formulas
Every percentage formula on one page, with a worked example for each. Handy for homework, invoices, and everyday sums.
| What you want | Formula | Worked example | Typical use |
|---|---|---|---|
| Percentage of a number | (P ÷ 100) × N | 20% of 250 = 50 | Tips, discounts, commission |
| One number as a percentage of another | (Part ÷ Whole) × 100 | 45 of 60 = 75% | Test scores, market share |
| Percentage increase | ((New − Old) ÷ Old) × 100 | 80 → 100 = +25% | Pay rises, price rises |
| Percentage decrease | ((Old − New) ÷ Old) × 100 | 100 → 80 = −20% | Sale prices, falling costs |
| Add a percentage to a number | N × (1 + P ÷ 100) | 100 + 20% = 120 | Adding VAT or a markup |
| Subtract a percentage from a number | N × (1 − P ÷ 100) | 100 − 20% = 80 | Applying a discount |
| Reverse an increase | Final ÷ (1 + P ÷ 100) | 120 ÷ 1.2 = 100 | Removing VAT from a gross price |
| Reverse a decrease | Final ÷ (1 − P ÷ 100) | 80 ÷ 0.8 = 100 | Finding a pre-sale price |
| Percentage difference between two values | (|A − B| ÷ ((A + B) ÷ 2)) × 100 | 40 vs 60 = 40% | Comparing two figures with no baseline |
| Convert a fraction to a percentage | (Numerator ÷ Denominator) × 100 | 3/8 = 37.5% | Fractions, ratios, odds |
Percentage FAQ
Answers to the questions people most often get stuck on when working with percentages.
Divide the percentage by 100 to turn it into a decimal, then multiply it by the number. To find 15% of 200, calculate 15 ÷ 100 = 0.15, then 0.15 × 200 = 30. The same method works for any percentage, including those above 100%.
Percentage points measure the simple gap between two percentages, while percentage change measures the relative difference. If an interest rate rises from 4% to 5%, that is a rise of 1 percentage point, but a percentage increase of 25%. News reports often mix the two up, so it is worth checking which one a figure refers to.
Divide the final figure by 1 plus the percentage expressed as a decimal. If a price of £150 already includes a 20% increase, the original price was 150 ÷ 1.20 = £125. For a discount, divide by 1 minus the decimal instead: an item reduced by 25% to £60 originally cost 60 ÷ 0.75 = £80.
Each percentage is applied to a different base. Adding 10% to 100 gives 110, but taking 10% off 110 removes 11 rather than 10, leaving 99. The increase is calculated on the smaller figure and the decrease on the larger one, so the two never cancel out exactly.
Yes. An increase of more than 100% simply means the value has more than doubled — going from 50 to 150 is a 200% increase. A percentage decrease, however, cannot exceed 100%, because a fall of 100% takes the value all the way to zero.
For a decimal, multiply by 100: 0.375 becomes 37.5%. For a fraction, divide the top number by the bottom number and then multiply by 100: 3 ÷ 8 = 0.375, which is 37.5%. To go the other way, divide the percentage by 100.