Percentage Calculator
Calculate percentages, percentage increase, percentage decrease, and percentage of a number.
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How to Calculate a Percentage
A percentage is just a fraction with 100 on the bottom. "Per cent" literally means "per hundred", so 25% is another way of writing 25/100, or 0.25. Almost every percentage problem you'll meet is one of four questions, and this calculator handles all four. The hard part is usually working out which one you're being asked — so here is each of them, with the formula and a worked example.
1. What is X% of Y?
This is the one people need most: a discount, a tip, a commission, a tax. Convert the percentage to a decimal by dividing by 100, then multiply.
- Formula: (X ÷ 100) × Y
- Example: What is 15% of 80? (15 ÷ 100) × 80 = 0.15 × 80 = 12.
2. X is what percent of Y?
Use this when you have two numbers and want to know how one relates to the other — a test score, a share of a total, a completion rate.
- Formula: (X ÷ Y) × 100
- Example: 18 is what percent of 24? (18 ÷ 24) × 100 = 0.75 × 100 = 75%.
3. Percentage increase
The change from an original value to a larger new value, expressed as a percentage of where you started.
- Formula: ((New − Original) ÷ Original) × 100
- Example: A rent of 1,200 rises to 1,320. ((1320 − 1200) ÷ 1200) × 100 = (120 ÷ 1200) × 100 = 10%.
4. Percentage decrease
The same idea in the other direction — a price drop, a weight loss, a fall in energy use.
- Formula: ((Original − New) ÷ Original) × 100
- Example: A jacket marked at 90 is reduced to 63. ((90 − 63) ÷ 90) × 100 = (27 ÷ 90) × 100 = 30%.
Common Percentages at a Glance
Some percentages have shortcuts worth memorising, because they let you check the calculator's answer in your head.
| Percentage | Shortcut | Example (of 240) |
|---|---|---|
| 1% | Move the decimal point two places left | 2.4 |
| 5% | Find 10%, then halve it | 12 |
| 10% | Move the decimal point one place left | 24 |
| 20% | Find 10% and double it | 48 |
| 25% | Divide by 4 | 60 |
| 50% | Halve it | 120 |
| 75% | Halve it, then add half again | 180 |
Mistakes That Catch People Out
A percentage rise and fall of the same size don't cancel
If a 100 item rises 20% to 120, then falls 20%, it does not return to 100 — it lands at 96. That's because the second 20% is taken from the larger number. This is why a stock that drops 50% needs a 100% gain to break even, not another 50%.
Percentage points are not percentages
If an interest rate moves from 4% to 5%, that's a rise of one percentage point, but a 25% increase in the rate. News reports mix these up constantly, and the difference can be enormous.
Stacked discounts don't add up
"30% off, then a further 20% off at the till" is not 50% off. The second discount applies to the already-reduced price: 100 becomes 70, then 56 — a total of 44% off, not 50%.
Averaging percentages needs care
You can't usually average percentages directly unless the groups they came from are the same size. Scoring 90% on a 10-mark quiz and 60% on a 100-mark exam is not an average of 75% — it's 9 + 60 = 69 marks out of 110, or about 63%.
Reversing a Percentage
A common real-world problem: you know the price after a discount or a tax, and you want the price before. Don't apply the percentage again in reverse — divide instead.
- Remove a 20% tax from a gross price: divide by 1.20. A gross 60 means a net of 50, and 10 of tax.
- Find the original price before a 30% discount: divide the sale price by 0.70. A sale price of 56 came from an original 80.
Frequently Asked Questions
How do I work out a percentage without a calculator?
Break it into 10% and 1% pieces. To find 17% of 250: 10% is 25, so 5% is 12.50, and 1% is 2.50, giving 2 × 1% = 5. Add them: 25 + 12.50 + 5 = 42.50. Splitting a percentage into round chunks makes almost any figure workable in your head.
Can a percentage be more than 100?
Yes. Anything above 100% simply means "more than the whole". If a business grows from 40 customers to 120, that's a 200% increase — it added twice its original size on top of what it already had. Percentages above 100 only look strange when you'd expect a share of a fixed total, such as a share of the vote.
What's the difference between percentage change and percentage difference?
Percentage change has a clear starting point and compares against it. Percentage difference is used when neither value is "first" — you divide the gap by the average of the two values instead. For most everyday questions, percentage change is what you want.
Why does my percentage answer have so many decimal places?
Because most divisions don't come out evenly. This calculator rounds to two decimal places, which is more than enough for money and everyday use. If you're chaining several calculations, round only at the very end — rounding at each step compounds the error.