Quick answer: “X% of Y” is Y × X ÷ 100, so 15% of 240 is 36. Percent change is (new − old) ÷ old × 100. A rise from 80 to 100 is +25%, but a fall from 100 back to 80 is −20%, because the base changes.
Percentages are everywhere: discounts, taxes, tips, interest, exam scores and pay rises. The rules are simple, but it is easy to slip on the details, especially with percentage change and with increases followed by decreases.
Fill in the numbers in any of the four rows and the answer updates straight away. Each row is a full sentence, so you can read it aloud to check that it asks the question you meant. Working out a restaurant tip is one of the most common percentage questions; the tip calculator handles that directly, including splitting the total between a group.
The four formulas
X is what % of Y = X ÷ Y × 100
% change from A to B = (B − A) ÷ A × 100
Increase Y by X% = Y × (1 + X ÷ 100) Decrease Y by X% = Y × (1 − X ÷ 100)
A positive percentage change is an increase and a negative one is a decrease. Percentage change is always measured against the starting value, which is why the order of the two numbers matters.
One trap: a 20% increase followed by a 20% decrease does not return you to where you started. 200 up 20% is 240, and 240 down 20% is 192, because the second percentage is taken from a larger number.
A worked example
Example. 15% of 200 is 30. 30 is 15% of 200. A price that rises from 80 to 100 has gone up 25%. A jacket priced at 200 with a 20% discount costs 160.
Real-world examples
A price rise. A monthly plan goes from $80 to $100: (100 − 80) ÷ 80 = 25% more. A discount. A $100 item on sale for $80 is (100 − 80) ÷ 100 = 20% off. The same $20 is 25% of the smaller number and 20% of the larger.
Quick reference
| Percent | Of 240 |
|---|---|
| 5% | 12 |
| 10% | 24 |
| 15% | 36 |
| 20% | 48 |
| 25% | 60 |
| 50% | 120 |
| 75% | 180 |
To find a percentage of any number, multiply by the percent and divide by 100.
Common mistakes to avoid
- Confusing percentage points with percent. A rate that rises from 4% to 6% went up 2 percentage points, which is a 50% increase.
- Using the wrong base. Percent change is always measured against the starting value, not the ending one.
- Assuming an increase and the same decrease cancel out. A 50% rise followed by a 50% fall leaves you at 75% of the start.
Go deeper: read our guide Cups to Grams: A Baking Conversion Guide.
Frequently asked questions
How do I calculate a discount?
Use the last row. Enter the original price and the discount percentage, and read the decrease result. For a 25% discount on 80, enter 80 and 25 to get 60.
What is the difference between percent and percentage points?
If an interest rate goes from 4% to 5%, it has risen by one percentage point, but by 25 percent in relative terms. The second calculator row gives the relative change.
How do I work out the original price before a discount?
Divide the sale price by (1 − discount). If a coat costs 60 after a 25% discount, the original price was 60 ÷ 0.75 = 80.
Why is my percentage change different when I swap the numbers?
Because the change is measured against the starting value. Going from 80 to 100 is +25%, but going from 100 to 80 is −20%.
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Sources and further reading
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