Percentages show up everywhere: discounts, tips, taxes, grades, interest rates, pay rises. The good news is that almost every percentage question is one of a handful of patterns, and each pattern has a one-line formula. This guide walks through each one with worked examples, then covers the mistakes that trip people up most. You can check any answer with our free percentage calculator.
To find X% of a number, multiply the number by X ÷ 100. For example, 15% of 240 = 240 × 0.15 = 36. To find what percent A is of B, divide A by B and multiply by 100. To find a percentage change, subtract the old value from the new value, divide by the old value, and multiply by 100.
What a percentage is
A percentage is a number written as a part of 100. The word comes from the Latin per centum, meaning "by the hundred". So 25% means 25 out of every 100, which is the same as the fraction 25/100, the simplified fraction 1/4, and the decimal 0.25.
To turn a percentage into a decimal, divide by 100 (move the decimal point two places left). To turn a decimal back into a percentage, multiply by 100. Every formula below is built on this one idea.
| Percent | Fraction | Decimal |
|---|---|---|
| 1% | 1/100 | 0.01 |
| 5% | 1/20 | 0.05 |
| 10% | 1/10 | 0.1 |
| 12.5% | 1/8 | 0.125 |
| 20% | 1/5 | 0.2 |
| 25% | 1/4 | 0.25 |
| 50% | 1/2 | 0.5 |
| 75% | 3/4 | 0.75 |
| 100% | 1 | 1 |
How to find a percentage of a number
Example: what is 15% of 240?
- Convert 15% to a decimal: 15 ÷ 100 = 0.15.
- Multiply: 240 × 0.15 = 36.
The same method works for a tip, a commission or a tax amount. A 20% tip on a bill of 85 is 85 × 0.20 = 17.
🔢 Check your answer
Type any two numbers and get the result with the working shown.
Open the percent-of calculator →How to find what percent one number is of another
Example: you scored 45 out of 180 on a test. What percent is that?
- Divide the part by the whole: 45 ÷ 180 = 0.25.
- Multiply by 100: 0.25 × 100 = 25%.
Always put the part on top and the whole on the bottom. If you reverse them, you get 400% instead of 25%, which is a sign something went wrong. Try it with the what percent is X of Y calculator.
Percentage increase and decrease
A positive result is an increase and a negative result is a decrease.
Increase example: a price rises from 80 to 100.
(100 − 80) ÷ 80 = 0.25, so the price rose 25%.
Decrease example: the same price falls from 100 back to 80.
(80 − 100) ÷ 100 = −0.20, so the price fell 20%.
The gap is 20 in both cases, but the starting point is different. The percentage is always measured against the original value, so the same gap is a bigger percentage of a smaller starting number. Use the percentage change calculator to try your own numbers.
Percentage difference vs percentage change
Percentage change has a clear starting point. Percentage difference is for comparing two numbers when neither one is "the original", such as two prices from two shops or two measurements.
Example: compare 50 and 70.
- The gap is |50 − 70| = 20.
- The average is (50 + 70) ÷ 2 = 60.
- 20 ÷ 60 × 100 = 33.3333%.
Treating 50 as the starting point instead would give a percentage change of 40%. Both are valid, but they answer different questions. The percentage difference calculator gives the same answer whichever number you enter first.
How to add or subtract a percentage
Subtract: Number × (1 − Percentage ÷ 100)
Add example (sales tax): an item costs 85 and tax is 8%. 85 × 1.08 = 91.8.
Subtract example (a markdown): a jacket costs 250 and is 15% off. 250 × 0.85 = 212.5.
This is faster than working out the percentage amount and then adding or subtracting it. Use the add or subtract a percentage calculator for quick checks.
Reverse percentages: find the original
Sometimes you know the result and the percentage, and you need the starting value.
Find the whole from a part
Example: 45 is 20% of what number? 45 ÷ 0.20 = 225.
Find the original price before a discount
Example: a coat costs 68 after 15% off. 68 ÷ 0.85 = 80.
Adding 15% to 68 gives 78.2, which is wrong. The 15% was taken from the original price of 80, not from 68. Use the original price calculator to avoid this.
Discounts and stacked percentages
A discount calculation is just "subtract a percentage". 25% off a price of 100 is 100 × 0.75 = 75, so you save 25.
Stacked discounts do not add up. Take 20% off, then another 10% off:
- After 20% off: 100 × 0.80 = 80.
- After another 10% off: 80 × 0.90 = 72.
The total saving is 28%, not 30%, because the second discount is applied to the lower price. The same rule applies to a percentage of a percentage: 20% of 50% is (20 × 50) ÷ 100 = 10%.
Common percentage mistakes
1. Using the wrong base
Increase 100 by 50% and you get 150. Now decrease that by 50% and you get 75, not 100. To get back to 100 from 150 you need a decrease of 33.3333%. Percentages are only reversible when you remember each one is measured from a different starting number.
2. Confusing percent with percentage points
If an interest rate goes from 4% to 6%, it rose by 2 percentage points, which is a 50% increase in the rate. News and financial reports mix these up often, so check which one is meant.
3. Adding stacked discounts
As shown above, 20% and then 10% off is 28% off in total, not 30%.
4. Dividing by the wrong number
For "what percent is X of Y", the whole goes on the bottom. For percentage change, the original goes on the bottom. Writing down which number is the base before you calculate prevents most errors.
Mental math shortcuts
| Percent | Shortcut | Example |
|---|---|---|
| 1% | Move the decimal two places left | 1% of 250 = 2.5 |
| 10% | Move the decimal one place left | 10% of 250 = 25 |
| 5% | Half of 10% | 5% of 250 = 12.5 |
| 15% | 10% plus 5% | 15% of 80 = 8 + 4 = 12 |
| 20% | Double 10%, or divide by 5 | 20% of 80 = 16 |
| 25% | Divide by 4 | 25% of 200 = 50 |
| 50% | Divide by 2 | 50% of 90 = 45 |
| 12.5% | Divide by 8 | 12.5% of 64 = 8 |
Successive percentage changes and percentage points
Two changes in a row do not add up. A 10% rise followed by a 10% fall does not return to the start: 100 × 1.10 × 0.90 = 99, a net fall of 1%. The second percentage is taken from the new, larger value. Multiply the growth factors instead: Final = Start × (1 + p1/100) × (1 + p2/100) × ...
A percentage point is the plain difference between two percentages. If an interest rate moves from 4% to 5%, that is 1 percentage point higher, but a 25% relative increase (1 ÷ 4). News stories often mix the two up, so check which one is meant.
Tips, tax and splitting a bill
Add tax and tip to the pre-tax bill, then divide by the number of people. For a 100 bill with 8% tax and an 18% tip split four ways: tax = 8, tip = 18, total = 126, so each person pays 31.5. Many people tip on the pre-tax amount, which is how the calculator works.
How to use the percentage calculator
- Pick the question that matches yours. Use the jump buttons at the top of the percentage calculator to go straight to one of 12 tools.
- Type your numbers. The answer and the working update as you type. There is no submit button.
- Set decimals and currency. The settings bar lets you choose 0 to 6 decimal places and a currency symbol for price tools.
- Copy or share. "Copy result" copies the answer with its working. "Copy link" makes a link that reopens the calculator with your numbers filled in, handy for sending a calculation to someone else.
- Reset restores the example values for that tool.
Your numbers stay in your browser and are never sent to a server.
Practice problems
Try each one first, then open the answer.
1. What is 35% of 260?
91. 260 × 0.35 = 91.
2. 18 is what percent of 24?
75%. 18 ÷ 24 = 0.75, and 0.75 × 100 = 75%.
3. A salary goes from 40,000 to 43,000. What is the percentage increase?
7.5%. (43,000 − 40,000) ÷ 40,000 = 0.075.
4. A 120 item is on sale at 30% off, and then you add 5% tax to the sale price. What do you pay?
88.2. 120 × 0.70 = 84, and 84 × 1.05 = 88.2.
5. After a 20% discount, a bag costs 56. What was the original price?
70. 56 ÷ 0.80 = 70.
🧮 Free Percentage Calculator
Twelve calculators in one page: percent of a number, percent change, difference, discounts, reverse percentages, tip splitting and more, with the steps shown.
Open the Percentage Calculator →Frequently asked questions
Conclusion
Percentages become easy once you spot which pattern you are looking at: a percentage of a number, what percent one number is of another, a change from an original value, or a reverse problem that starts from the result. Write down the base before you calculate, and remember that percentages taken from different bases do not simply add or cancel. When you want a quick check, use the free percentage calculator.