What this calculator does
Percentages show up everywhere: sale prices, tips, sales tax, test scores, salary raises, inflation and investment returns. This calculator answers the seven most common percentage questions. Choose the question from the menu, enter two numbers and the result updates as you type.
- What is X% of Y? For example, what is 15% of 200?
- X is what percent of Y? For example, you scored 30 out of 120. What percent is that?
- X is P% of what number? For example, a $30 deposit is 25% of the price. What is the full price?
- Percentage change from A to B. How much did a value rise or fall, relative to where it started?
- Percentage difference between A and B. How far apart are two values when neither is the "before" value?
- Y decreased by X%. Discounts and markdowns, such as 25% off $80.
- Y increased by X%. Markups, tips and sales tax, such as $50 plus 8% tax.
Percentage formulas
"Percent" means "per hundred", so 1% is 0.01 and 15% is 0.15. Every calculation here comes from that single idea. In the formulas below, X and P are percentages and A, B and Y are ordinary numbers.
X% of Y = X ÷ 100 × Y
X as a percent of Y = X ÷ Y × 100
X is P% of what = X ÷ (P ÷ 100)
Percentage change = (B − A) ÷ A × 100
Percentage difference = |A − B| ÷ ((A + B) ÷ 2) × 100
Y decreased by X% = Y × (1 − X ÷ 100)
Y increased by X% = Y × (1 + X ÷ 100)
The percentage change formula is the same method the U.S. Bureau of Labor Statistics uses to report changes in the Consumer Price Index: subtract the earlier value from the later one, divide by the earlier value, and multiply by 100.
Worked examples
| Question | Calculation | Answer |
|---|---|---|
| What is 20% of 50? | 20 ÷ 100 × 50 | 10 |
| What percent is 45 of 60? | 45 ÷ 60 × 100 | 75% |
| 12 is 40% of what number? | 12 ÷ 0.40 | 30 |
| Change from 50 to 65 | (65 − 50) ÷ 50 × 100 | 30% increase |
| Change from 250 to 200 | (200 − 250) ÷ 250 × 100 | 20% decrease |
| Difference between 50 and 65 | 15 ÷ 57.5 × 100 | 26.09% |
| $80 with 25% off | 80 × 0.75 | $60 |
| $40 plus 7.25% sales tax | 40 × 1.0725 | $42.90 |
Percentage change, percentage difference and percentage points
These three ideas are easy to mix up, and they give different answers.
Percentage change has a direction. It compares a new value with an old one, and the old value is the reference. Going from 50 to 65 is a 30% increase because the rise of 15 is measured against 50.
Percentage difference has no direction. It compares two values on equal terms, such as the prices of the same item in two stores, so it measures the gap against their average. The difference between 50 and 65 is 26.09% whichever value you list first.
Percentage points describe the gap between two percentages. If a savings rate rises from 4% to 5%, it went up by 1 percentage point, but by 25% in relative terms, because 1 is a quarter of 4. News reports about interest rates and polls usually use percentage points.
Common mistakes to avoid
A rise and an equal fall do not cancel out
If a price goes up 10% from $100, it becomes $110. If it then falls 10%, it drops to $99, not back to $100, because the second 10% is taken from the larger number. For the same reason, two discounts applied one after another do not simply add up: 30% off followed by an extra 20% off is 0.7 × 0.8 = 0.56 of the original price, a total discount of 44%, not 50%.
Reversing a percentage needs division
To find the price before an 8% tax was added, divide by 1.08 rather than subtracting 8%. A total of $54 came from $54 ÷ 1.08 = $50. Subtracting 8% of $54 would give $49.68, which is wrong. The "X is P% of what number?" mode handles this kind of question.
Use the right starting point
A percentage change is always measured from the starting value. A fall from 120 to 90 is a 25% decrease, while a rise from 90 back to 120 is a 33.33% increase, even though both moves are 30 units.
Frequently asked questions
- How do I calculate a tip or sales tax?
- Choose "Y increased by X%". Enter the bill as Y and the tip or tax rate as X. The result is the total, and the amount added is the tip or tax itself.
- How do I work out a sale price?
- Choose "Y decreased by X%", enter the original price as Y and the discount as X. The calculator shows the sale price and how much you save.
- Why can't the starting value be zero for a percentage change?
- A percentage change divides by the starting value, and dividing by zero is undefined. When something grows from zero, describe the change in absolute terms instead, for example "up by 15".
- How many decimal places does the calculator show?
- Whole numbers are shown as they are, and other results are rounded to two decimal places. Very small results are shown to three significant figures so that they do not appear as zero.