Percentages are everywhere: sales tax, discounts, tips, test scores, raises and price changes. This percentage calculator answers the four most common percentage questions and shows the formula for each, so you can see how the result was worked out.
Quick answer: X% of Y = Y × X ÷ 100 (20% of 150 = 30). X is what % of Y = X ÷ Y × 100 (30 of 150 = 20%). % change = (new − old) ÷ old × 100 (80 → 100 = +25%). Add a %: number × (1 + % ÷ 100) ($59.99 + 8.25% tax = $64.94).
How to use the percentage calculator
- Choose a tab: X% of Y, X is what % of Y, % change or Add / subtract %.
- Enter the two numbers. Labels change to tell you what each box means.
- Press Calculate. The result appears with the full calculation and, for changes, the difference.
Percentage formulas
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | Y × X ÷ 100 | 20% of 150 = 30 |
| X is what percent of Y? | X ÷ Y × 100 | 30 of 150 = 20% |
| Percent change from A to B | (B − A) ÷ A × 100 | 80 → 100 = +25% |
| Increase A by X% | A × (1 + X ÷ 100) | 80 + 25% = 100 |
| Decrease A by X% | A × (1 − X ÷ 100) | 1,250 − 20% = 1,000 |
| Original price before X% off | Sale price ÷ (1 − X ÷ 100) | $60 after 25% off = $80 |
Percent off chart
Below the calculator you will find a chart of sale prices for common prices and discounts. A few examples:
| Original price | 10% off | 20% off | 25% off | 50% off |
|---|---|---|---|---|
| $20 | $18.00 | $16.00 | $15.00 | $10.00 |
| $50 | $45.00 | $40.00 | $37.50 | $25.00 |
| $100 | $90.00 | $80.00 | $75.00 | $50.00 |
| $200 | $180.00 | $160.00 | $150.00 | $100.00 |
Worked examples
Sales tax
A $59.99 item with 8.25% sales tax: 59.99 × 1.0825 = $64.94. The tax itself is 59.99 × 0.0825 = $4.95.
Test score
42 correct answers out of 50: 42 ÷ 50 × 100 = 84%.
Price increase
Rent goes from $1,600 to $1,720: (1,720 − 1,600) ÷ 1,600 × 100 = 7.5% increase.
Increase then decrease
A price rises 20% and then falls 20%: 100 → 120 → 96. The net change is −4%, because the second percentage is taken from a larger number.
Common mistakes
- Dividing by the wrong number in percent change. Always divide by the starting (old) value.
- Adding and subtracting the same percentage and expecting to get back to the start.
- Confusing percent with percentage points when comparing rates.
- Reversing a discount by adding it back. Divide by (1 − discount) instead.
Need another everyday calculation? Find your exact age with the age calculator, estimate your daily calories with the calorie calculator, or convert units with the length and weight converters.
Frequently asked questions
How do I calculate a percentage of a number?
Multiply the number by the percentage and divide by 100. 20% of 150 = 150 × 20 ÷ 100 = 30. A quick shortcut is to move the decimal: 10% of 150 is 15, so 20% is twice that, 30.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100. 30 out of 150 = 30 ÷ 150 × 100 = 20%. This is how you turn a test score of 42 out of 50 into 84%.
How do I calculate percent change?
Subtract the old value from the new value, divide by the old value and multiply by 100. From 80 to 100: (100 − 80) ÷ 80 × 100 = 25% increase. From 100 to 80 the change is −20%, not −25%, because the starting value is different.
How do I add a percentage to a number?
Multiply the number by 1 plus the percentage as a decimal. Adding 8.25% sales tax to $59.99: 59.99 × 1.0825 = $64.94. To subtract a percentage, multiply by 1 minus the decimal: a $1,250 item at 20% off costs 1,250 × 0.80 = $1,000.
What is 15% of 80?
15% of 80 is 12 (80 × 15 ÷ 100). That makes 15% tips easy: 10% of the bill plus half of that again.
What is the difference between percent and percentage points?
Percentage points measure the simple difference between two percentages; percent measures the relative change. If an interest rate rises from 4% to 5%, it went up 1 percentage point, which is a 25% increase in the rate.
How do I reverse a percentage to find the original price?
Divide by 1 minus the discount (or 1 plus the increase). If a sale price of $60 is after 25% off, the original price was 60 ÷ 0.75 = $80. Subtracting 25% of $60 from $60 would give the wrong answer.
Can a percentage be more than 100%?
Yes. A value can grow by more than 100%: going from 50 to 150 is a 200% increase. A part cannot be more than 100% of a whole, but a change or a ratio can.
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