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How to Calculate Percentages (With Examples)
Percentage means “per hundred.” Every percentage calculation comes down to one of three formulas, and once you know them, you can handle tips, discounts, tax, grade scores, and any other situation where percentages come up.
Formula 1: what is X% of Y?
\[\text{Result} = \frac{X}{100} \times Y\]This is the most common percentage calculation. You use it every time you figure out a tip at a restaurant, a sale price, or how much tax to expect on a purchase. The idea is straightforward: convert the percentage to a decimal by dividing by 100, then multiply by the number.
For example, 18% of 240 is 0.18 x 240 = 43.2. And 7.5% of $85 is 0.075 x 85 = $6.38 (rounded). The percentage calculator can handle these instantly if you want to double-check your mental math.
This formula also works in reverse. If a store advertises 30% off a $160 item, the discount is 0.30 x 160 = $48, so the sale price is $160 - $48 = $112. The same logic applies to tax: if sales tax is 8.25%, the tax on a $45 purchase is 0.0825 x 45 = $3.71.
Formula 2: what percent is X of Y?
\[\text{Percentage} = \frac{X}{Y} \times 100\]You use this when you have two numbers and want to know the ratio as a percentage. Test scores are a common example: if you scored 42 out of 50 on an exam, your percentage is (42 / 50) x 100 = 84%. The key is to put the “part” on top and the “whole” on the bottom. Mixing them up is the most common mistake, and it produces wildly different answers. “25 is what percent of 200” gives 12.5%, while “200 is what percent of 25” gives 800%.
This formula comes up frequently outside of school as well. If a business spent $3,200 on marketing out of a $40,000 budget, marketing consumed (3,200 / 40,000) x 100 = 8% of the budget. If 17 out of 60 survey respondents chose option A, that is (17 / 60) x 100 = 28.3%. The operation is always the same: divide the part by the whole, then multiply by 100.
Formula 3: percent change
\[\text{Percent change} = \frac{\text{New} - \text{Old}}{\text{Old}} \times 100\]A positive result means an increase and a negative result means a decrease. The important detail is that you always divide by the old (original) value, not the new one. This matters because the same dollar difference produces different percentages depending on direction. Going from $50 to $75 is a 50% increase, but going from $75 to $50 is only a 33.3% decrease. The base changes, so the percentage changes. The percentage change calculator is useful when comparing data across time periods.
Consider a real-world example. A company’s revenue went from $820,000 last year to $943,000 this year. The percent change is (943,000 - 820,000) / 820,000 x 100 = 123,000 / 820,000 x 100 = 15% growth. If instead revenue dropped from $943,000 to $820,000, the decline would be (820,000 - 943,000) / 943,000 x 100 = -13%. The same $123,000 difference produces a different percentage because the starting value changed.
Mental math shortcuts
You do not need a calculator for most common percentages. Start by finding 10%, which is simply moving the decimal point one place to the left. 10% of $350 is $35. From that anchor point, you can scale: 5% is half of 10% ($17.50), 20% is double ($70), and 15% is 10% plus half again ($52.50). For 1%, move the decimal two places left. 1% of $350 is $3.50, so 3% is $10.50 and 7% is $24.50.
Another useful trick is reversing the numbers. 8% of 50 is the same as 50% of 8, which is 4. This works because multiplication is commutative. Whenever one of the two numbers is easier to take a percentage of, swap them. 4% of 75 is the same as 75% of 4, which is 3. For a complete reference on how percentages relate to fractions and ratios, see the percentages, fractions, and ratios guide.
Quick reference table
| Base number | 10% | 15% | 20% | 25% | 50% |
|---|---|---|---|---|---|
| 50 | 5 | 7.5 | 10 | 12.5 | 25 |
| 100 | 10 | 15 | 20 | 25 | 50 |
| 150 | 15 | 22.5 | 30 | 37.5 | 75 |
| 200 | 20 | 30 | 40 | 50 | 100 |
| 500 | 50 | 75 | 100 | 125 | 250 |
| 1,000 | 100 | 150 | 200 | 250 | 500 |
Common mistakes to avoid
Mixing up the base number is the most common error. Always put the “part” on top and the “whole” on the bottom when using Formula 2. Getting this backwards flips the answer entirely.
With percent change, always divide by the original value. The same $25 difference between 50 and 75 gives different percentages depending on which direction you are calculating.
The other frequent mistake is forgetting to multiply by 100. The formula (X / Y) gives you a decimal like 0.36. Multiply by 100 to convert it to 36%.
One less obvious error is stacking percentages incorrectly. A 20% increase followed by a 20% decrease does not return you to the original number. Starting at 100, a 20% increase gives 120. A 20% decrease of 120 gives 96, not 100. The second percentage applies to the new base, not the original. This same logic explains why a stock that drops 50% needs a 100% gain to recover, not a 50% gain.