Percentage Calculator
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Four calculations cover almost every percentage question: what X% of Y is, what share one number represents of another, the percentage change between two values, and the reverse question — finding the whole when you only know a part. Pick a mode, type the two numbers and read the answer, along with the related figures that usually come next, such as the discounted price or the multiplier behind a percentage change.
The four percentage formulas
Every percentage problem reduces to one of four shapes. To find a percentage of a number, multiply by the rate divided by 100: 20% of 150 is 150 × 0.20 = 30. To find what share one number is of another, divide and multiply by 100: 34 out of 40 is 85%. To measure change, subtract, divide by the starting value and multiply by 100: from 80 to 100 is a 25% increase. And to reverse a percentage, divide by the rate: if 150 is 20% of a total, the total is 150 ÷ 0.20 = 750.
Notice that the third and fourth formulas depend on which number is the base. Going from 100 down to 80 is a 20% drop, while going from 80 back up to 100 is a 25% rise — same two numbers, different denominators.
| 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% |
| Change from X to Y | (Y − X) ÷ X × 100 | 80 to 100 = +25% |
| Y is X% of what? | Y ÷ (X ÷ 100) | 150 is 20% of 750 |
Mental math shortcuts
Ten percent of any number is that number with the decimal point moved one place left: 10% of 480 is 48. One percent moves it two places: 1% of 480 is 4.80. Every common rate is built from those two. Five percent is half of ten. Twenty percent is double. Fifteen percent is ten plus half of ten. Thirty-five percent is three tens plus a five.
Two more shortcuts pay off constantly. First, discounts are one multiplication, not two: a 30% discount means multiplying by 0.70, and a 20% increase means multiplying by 1.20. Second, percentages commute — 8% of 50 equals 50% of 8, which is 4. Whenever one side is a round number, flip the calculation.
Percentage points are not percent
The most frequent mistake in percentage work is treating a difference between two rates as a percentage change. When a rate moves from 4% to 5%, it rose by one percentage point but changed by 25%, because 1 divided by 4 is 0.25. Both statements are true and they measure different things, which is why careful writing uses the abbreviation "pp" for the arithmetic gap.
The second trap is adding successive changes. Two consecutive 10% increases produce 21%, not 20%, because 1.1 × 1.1 = 1.21. Stacked discounts behave the same way: 30% off followed by an extra 10% off is 37% total, since 0.7 × 0.9 = 0.63. And percentages do not reverse symmetrically — a 20% discount followed by a 20% increase leaves you at 96% of the original price, and a 50% loss needs a 100% gain just to break even.
Frequently asked questions
How do I calculate a percentage of a number?
Multiply the number by the rate and divide by 100, or convert the rate to a decimal and multiply once. For 20% of 150: 150 × 0.20 = 30. Use the first mode of the calculator above.
How do I work out a percentage change?
Subtract the starting value from the ending value, divide by the starting value and multiply by 100. From 80 to 100 that is (100 − 80) ÷ 80 × 100 = +25%. The calculator also shows the multiplier, 1.25, which is often the more useful number.
What is a reverse percentage?
It is finding the whole when you know a part and its rate. If a 20% deposit was 150, the full price is 150 ÷ 0.20 = 750. Choose the "Y is X% of what total?" mode.
What is the difference between percent and percentage points?
Percentage points measure the arithmetic gap between two rates; percent measures the relative change. A move from 4% to 5% is one percentage point and a 25% increase at the same time.
Results are displayed with up to two decimal places, so repeating decimals appear rounded. Modes that involve division return zero when the reference value is zero.
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Also available in Portuguese: Calculadora de Porcentagem