How to use this percentage calculator
- Choose what you want to find: a percent of a number, what percent one number is of another, the percentage change, or the percentage difference.
- Enter the two numbers. Only the two inputs for the chosen question are shown. Decimals and negative numbers are accepted where they make sense.
- Read the answer and the steps. The results show the formula with your numbers filled in, plus useful extras such as the number increased and decreased by the percentage.
- Copy the link to save or share the calculation.
How to calculate percentages by hand
A percent is a number out of 100: 20% means 20 per 100, or 0.2 as a decimal. Every percentage problem is one of four simple formulas.
1. What is X% of Y?
result = X / 100 × Y
- X
- the percentage
- Y
- the number you are taking a percentage of
Example: 20% of 150 = 0.2 × 150 = 30. Adding that to the original gives 150 + 20% = 180; subtracting it gives 120.
2. X is what percent of Y?
percent = X / Y × 100
- X
- the part
- Y
- the whole (cannot be 0)
Example: 30 is what percent of 150? 30 ÷ 150 = 0.2, and × 100 = 20%.
3. Percentage change from X to Y
change = (Y − X) / |X| × 100
- X
- the starting (old) value, not 0
- Y
- the final (new) value
Example: from 80 to 100 is (100 − 80) ÷ 80 × 100 = +25%, a 25% increase. A negative answer is a decrease. Dividing by the absolute value of X keeps the sign meaningful when the starting value is negative: a loss shrinking from −50 to −25 is a +50% change.
4. Percentage difference between X and Y
difference = |X − Y| / ((X + Y) / 2) × 100
- X, Y
- the two values being compared (0 or more)
Example: 80 and 100 differ by 20, and their average is 90, so the percentage difference is 20 ÷ 90 × 100 = 22.22%. Use it when neither value is the “before,” such as comparing two stores’ prices or two measurements.
A shortcut worth knowing
X% of Y always equals Y% of X, so you can flip a hard problem into an easy one: 8% of 25 is the same as 25% of 8, which is a quarter of 8, or 2.
Common percentages of common numbers
Look up a percentage without calculating. Each cell is the percentage in the left column applied to the number at the top.
| Percent | of 20 | of 50 | of 100 | of 200 | of 500 | of 1,000 |
|---|---|---|---|---|---|---|
| 5% | 1 | 2.5 | 5 | 10 | 25 | 50 |
| 10% | 2 | 5 | 10 | 20 | 50 | 100 |
| 15% | 3 | 7.5 | 15 | 30 | 75 | 150 |
| 20% | 4 | 10 | 20 | 40 | 100 | 200 |
| 25% | 5 | 12.5 | 25 | 50 | 125 | 250 |
| 30% | 6 | 15 | 30 | 60 | 150 | 300 |
| 50% | 10 | 25 | 50 | 100 | 250 | 500 |
Percent vs. percentage points
When the thing that changes is itself a percentage, there are two ways to describe the change. If a rate goes from 4% to 5%, it rose by 1 percentage point (the simple difference), but by 25% in relative terms (1 ÷ 4).
Both statements are true, which is why careful writers use “percentage points” for interest rates, tax rates, unemployment rates and poll results. A mortgage rate falling from 7% to 6% is a 1-point drop, or a 14.29% decrease in the rate. When you compare loan offers, the mortgage calculator shows what a point difference means in dollars.
Why percentage increases and decreases don’t cancel out
A percentage is always a share of some base, and after a change the base is different. Increase 100 by 50% and you get 150; decrease that by 50% and you get 75, not 100. The two moves together are a 25% loss.
The same asymmetry means that recovering from a drop takes a larger percentage gain than the drop itself:
| Drop | Value after drop (from 100) | Gain needed to recover |
|---|---|---|
| 10% | 90 | 11.11% |
| 20% | 80 | 25% |
| 25% | 75 | 33.33% |
| 50% | 50 | 100% |
This matters for investments, prices and pay: a 20% pay cut followed by a 20% raise still leaves you below where you started. Over many years, repeated percentage changes compound; see the compound interest calculator and the inflation calculator.
Percent off, discounts, markup and margin
Percent off: multiply the price by (1 − discount). 25% off $80 is $80 × 0.75 = $60, a saving of $20. Successive discounts multiply: 20% off and then an extra 10% off is $80 × 0.8 × 0.9 = $57.60, a combined 28% discount, not 30%. Sales tax is then charged on the discounted price; the sales tax calculator adds it for any state.
Markup vs. margin: both describe the same profit, but against different bases. An item that costs $60 and sells for $80 earns $20. The markup compares that profit with the cost: $20 ÷ $60 = 33.33%. The margin compares it with the selling price: $20 ÷ $80 = 25%. Margin is always smaller than markup for a profitable sale, so confusing the two leads to underpricing.
Tipping is the most common everyday percentage; the tip calculator handles splitting the bill, too.
Frequently asked questions
How do I calculate a percentage of a number?
Divide the percent by 100 to turn it into a decimal, then multiply by the number. For example, 20% of 150 is 0.2 × 150 = 30. For quick mental math, find 10% by moving the decimal point one place left, then scale it: 20% is double 10%, and 5% is half of it.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100. For example, 30 out of 150 is 30 ÷ 150 × 100 = 20%. This is how a test score is turned into a percentage: 42 correct out of 48 questions is 87.5%. The whole cannot be zero.
How do you calculate percentage increase?
Subtract the old value from the new value, divide by the old value, and multiply by 100. Going from 80 to 100 is (100 − 80) ÷ 80 × 100 = +25%. A negative result means a decrease: going from 100 back to 80 is −20%.
What is the difference between percentage change and percentage difference?
Percentage change measures a move from an old value to a new one, so it has a direction and uses the old value as the base. Percentage difference compares two values with no before and after, using their average as the base, so the order does not matter. For 80 and 100, the change is +25% but the difference is 22.22%.
What is a percentage point?
A percentage point is the plain difference between two percentages. If a rate goes from 4% to 5%, it rose 1 percentage point, which is a 25% increase in the rate itself. Describing changes in rates in points avoids this ambiguity, because “up 1%” and “up 1 point” mean very different things.
Why does a 50% gain not make up for a 50% loss?
Because each percentage is taken from a different starting value. 100 up 50% is 150, and 150 down 50% is 75, a net 25% loss. In the other direction, after a 50% drop you need a 100% gain to get back to where you started.
How do I calculate a discount or percent off?
Multiply the price by the discount rate to get the savings, then subtract. 25% off $80 saves $20, so you pay $60; the shortcut is price × (1 − 0.25). Stacked discounts multiply rather than add: 20% off and then another 10% off $80 leaves $57.60, a total discount of 28%, not 30%.