What is a Percentage?
In everyday terms, a percentage is a way to express a part of a whole as an amount out of 100. When we say “50%”, it literally means 50 out of 100 (50 per hundred). Using percentages lets us easily compare portions of different sizes by putting them on the same scale (0 to 100).
For example, suppose you have a pizza cut into 8 equal slices, and you eat 2 slices. You have eaten 2 out of 8 slices. As a percentage of the whole pizza, first find the fraction: 2/8 = 0.25. Now multiply by 100 to get 25%. That means you ate 25% of the pizza. In other words, one quarter of the pizza is gone.
Percentages are used everywhere in daily life. If a store is offering 20% off a price, that means the price is discounted by 20 out of every 100 units of currency. If your phone battery is at 50%, it’s half full. Scoring 90% on a test means you got 90 points out of 100 (or an equivalent ratio like 45 out of 50). The percent symbol % is a shorthand way to indicate that a number is a fraction of 100.
Using percentages makes it easy to understand and compare ratios. Instead of saying “you ate 2 slices out of 8”, saying “25%” immediately conveys that a quarter of the whole pizza was eaten. A percentage provides a quick sense of proportion.
Percentages can also exceed 100% or be less than 1%. For example, if something is 200%, it is twice the whole amount. If you have 0.5%, that’s half of one percent (a very small portion).
Percentages are encountered in many everyday situations, for example:
- Shopping discounts: A store might advertise 20% off a product, meaning you pay 80% of the original price.
- Tips at restaurants: You might leave a tip that is 15–20% of the bill amount.
- Test scores: If you get 90% on a quiz, you scored 90 points out of 100 (or an equivalent ratio).
- Surveys and polls: You often hear things like “60% of people prefer product A.”
- Interest rates: A bank might offer 3% interest on savings (meaning for every $100, you earn $3 per year).
Basic Percentage Formula
Any percentage problem involves three parts: the part, the whole, and the percentage. These are related by a simple formula:
Percentage = (Part / Whole) × 100%
In this formula, the part is the portion or amount of interest, and the whole is the total or maximum amount. The result of (Part/Whole) gives a decimal (or fraction of 1). Multiplying by 100 converts it into a percentage. For example, if 20 students in a class of 50 are wearing glasses, then Percentage = (20/50) × 100% = 40%. So 20 is 40% of 50.
You can rearrange the basic formula to solve for any one of the three values if you know the other two:
- To find the percentage (P) when you know the part and whole: P = (part / whole) × 100%.
- To find the part when you know the percentage and the whole: part = (P/100) × whole.
- To find the whole when you know the part and the percentage: whole = part / (P/100).
How to Calculate a Percentage of a Number
One common task is finding a certain percentage of a given number. For example, you might want to calculate 20% of 50 or 8% of 200. The word “of” in this context means multiplication. The process can be broken down into a couple of simple steps:
- Convert the percentage to a decimal. Divide the percentage by 100. For example, 20% becomes 0.20 (20 ÷ 100 = 0.2).
- Multiply by the number. Take this decimal and multiply it by the number in question. For example, to find 20% of 50, calculate 0.20 × 50.
After performing these steps, the result you get is the portion of the number that corresponds to the given percentage. In our example, 0.20 × 50 = 10. So, 20% of 50 is 10.
Let’s try another example: What is 15% of 200? First, convert 15% to a decimal: 15% = 0.15. Then multiply by 200: 0.15 × 200 = 30. The answer is 30. In other words, 30 is 15% of 200.
In everyday life, this calculation comes up often for things like tips or sales tax. For example, a 20% tip on a $45 bill is 0.20 × 45 = $9 (so you’d tip $9).
You can use the calculator below to compute any percentage of a number yourself:
%
Result will appear here.
How to Calculate What Percentage One Number Is of Another
Another frequent calculation is determining what percentage one number is of another. In other words, you’re finding out how big the first number is relative to the second number in percentage terms. For example: “45 is what percent of 60?”
The method is straightforward and is essentially the reverse of the previous scenario:
- Divide the part by the whole. Divide the first number (the part) by the second number (the whole or total). This gives you a decimal. For example, 45 ÷ 60 = 0.75.
- Multiply by 100. Take the decimal result and multiply it by 100 to convert it to a percentage. In our example, 0.75 × 100 = 75.
Add a percent sign to the result, and that’s the percentage. Using the example above, 45 is 75% of 60.
Let’s apply this to another situation: say you scored 45 points out of 60 on a test. Divide 45 by 60 to get 0.75, then multiply by 100 to get 75. This means you scored 75% of the total points. If the part is larger than the whole, the result will be greater than 100% (which is fine, it just means the part exceeds the whole).
This formula is widely used. For instance, you can calculate the percentage of voters who voted for a candidate by dividing that candidate’s votes by the total votes and multiplying by 100%. Similarly, if a survey says 300 out of 400 people prefer a product, that’s (300/400) × 100 = 75% of respondents.
Try it yourself below:
Result will appear here.
Converting Between Fractions, Decimals, and Percentages
Percentages, decimals, and fractions are all closely related. You can easily convert a value from one form to another:
- Decimal to percentage: Multiply by 100 and add a “%” sign. For example, 0.5 → 0.5 × 100 = 50 → 50%.
- Fraction to percentage: First, divide to get a decimal, then multiply by 100%. For example, 3/4 = 0.75, and 0.75 × 100% = 75%. (Alternatively, since 3/4 = 75/100, you can directly see it is 75%.)
- Percentage to decimal: Remove the “%” and divide by 100. For example, 25% → 25 ÷ 100 = 0.25.
- Percentage to fraction: Put the number over 100 and simplify if possible. For example, 25% = 25/100 = 1/4.
In summary, multiplying by 100 converts a fraction or decimal into a percentage. Conversely, dividing by 100 (or moving the decimal point two places to the left) converts a percentage into a decimal.
How to Calculate Percentage Change (Increase/Decrease)
Percentage change measures how much a value has increased or decreased in comparison to its original value, expressed as a percentage. It’s commonly used for things like price changes, population growth or decline, and other comparisons over time. The calculation for percentage change is:
Percentage Change = (Change / Original Value) × 100%
Here, the “change” is the difference between the new value and the original value. If the new value is greater than the original, the change is positive (an increase). If the new value is smaller, the change is negative (a decrease). The original value is the starting reference point.
Let’s break this down:
- Find the difference: change = new value – original value.
- Divide this difference by the original value.
- Multiply by 100 to convert to a percentage.
The result tells you how large the change is relative to where you started, in percentage terms.
Percentage Increase
If the new value is larger than the original, you have a percentage increase. Use the formula above by plugging in the values. For example, suppose a price increases from $50 to $65. The change is $65 – $50 = $15 (increase). Divide 15 by the original 50 to get 0.3, then multiply by 100 to get 30. This means the price went up by 30%. We call this a 30% increase. Notably, the new value (65) is 130% of the original value (because 100% of 50 plus an additional 30%).
Percentage Decrease
If the new value is smaller than the original, you have a percentage decrease. Again, use the same formula. For example, say a town’s population drops from 20,000 to 16,000. The change is 16,000 – 20,000 = –4,000 (a decrease of 4,000). Now, 4,000 divided by the original 20,000 equals 0.2. Multiply by 100 to get 20. That means a 20% decrease in population. (The new value is 80% of the old value, since it lost 20%.)
Another way to think of this: to apply a percentage change directly, add or subtract that percentage from 100%, then multiply by the original. For a 30% increase, use 100% + 30% = 130% (which is 1.30 as a decimal) and multiply: 50 × 1.30 = 65. For a 20% decrease, use 100% – 20% = 80% (0.80) and multiply. This gets you the new value in one step.
Use the calculator below to find the percentage increase or decrease between any two values:
Result will appear here.
How to Calculate Percentage Difference
Percentage difference is a way to compare two numbers by describing the difference between them relative to their average. This calculation is useful when you want to see how far apart two values are in percentage terms, without indicating an increase or decrease from one specific base value.
The formula for percentage difference is:
Percentage Difference = (|A – B| / ((A + B) / 2)) × 100%
Here, A and B are the two values being compared, and |A – B| is the absolute difference between them. Dividing by the average ((A + B)/2) normalizes this difference with respect to the size of the numbers.
For example, if one value is 8 and the other is 10, the difference is |8 – 10| = 2. The average of 8 and 10 is (8 + 10) / 2 = 9. Now divide the difference by 9: 2/9 ≈ 0.2222. Multiply by 100% to get approximately 22.22%. So the two numbers differ by about 22.22% in relative terms.
Note that percentage difference will give the same result regardless of which value is A or B, because it doesn’t assume one is “original” and the other is “new.” If you do have a clearly defined starting value and ending value, it’s usually more appropriate to use percentage change (increase or decrease) rather than percentage difference.
This measure is often used in science or statistics when comparing two measurements. For instance, you might use percentage difference to compare the populations of two different cities or the results of two experiments, giving a sense of how far apart they are in relative terms.
Percentage Chart: Common Fractions to Percentages
Here is a quick reference for some common fractions and their equivalent percentages (rounded to two decimal places where necessary):
| Fraction | Percentage |
|---|---|
| 1/1 | 100% |
| 1/2 | 50% |
| 1/3 | 33.33% |
| 2/3 | 66.67% |
| 1/4 | 25% |
| 3/4 | 75% |
| 1/5 | 20% |
| 1/6 | 16.67% |
| 1/7 | 14.29% |
| 1/8 | 12.5% |
| 1/9 | 11.11% |
| 1/10 | 10% |
| 1/12 | 8.33% |
| 1/20 | 5% |
You can use this chart to quickly see, for example, that 1/3 of a pie is about 33.33% or that 1/8 is 12.5%. Knowing these common conversions can sometimes help you estimate percentages faster.
Quick Tips and Tricks for Percentage Calculations
With practice, you can do many percentage calculations in your head or simplify them significantly. Here are some handy tricks:
- 50% and 25%: 50% is simply half of any quantity. 25% is one quarter (half of 50%). These are easy fractions of a whole. For example, 50% of 80 is 40 (half of 80), and 25% of 80 is 20 (a quarter of 80).
- 10%, 5%, and 1%: 10% is one-tenth, and 1% is one-hundredth. To find 10% of a number, divide it by 10 (just move the decimal point one place to the left). To find 1%, divide the number by 100 (move the decimal two places left). 5% is half of 10%. Using these: for example, 15% = 10% + 5%. If you can find 10% and 5%, you can get 15% by addition.
- X% of Y = Y% of X: A useful fact is that swapping the percentage and the number gives the same result. For instance, 4% of 50 is the same as 50% of 4. It’s often easier to compute 50% of 4 (which is 2) in your head, so you immediately know that 4% of 50 is also 2.
Example of using these tricks: Suppose you want 15% of $80. 10% of $80 is $8 (just divide by 10). 5% of $80 is half of that, $4. Add them up: $8 + $4 = $12. So, 15% of $80 is $12, done mentally.
Using tricks like these can save time and reduce errors, especially in everyday situations like figuring out tips, discounts, or sales tax in your head.
Examples and Practice Problems
Now, let’s put everything together with some examples. Try to solve these problems yourself, then click on the scenario to see the explanation and answer.
Click a scenario below to see the explanation.
| Scenario |
|---|
| Calculate 15% of 200. |
| 45 is what percent of 60? |
| A price increases from $40 to $50. What is the percentage increase? |
| A population drops from 500 to 350. What is the percentage decrease? |
| What is the percentage difference between 20 and 30? |
Frequently Asked Questions
How do I find the total when a part is a certain percentage of it?
If you know that some amount represents a certain percentage of the total, you can find the total using the percentage formula. Rearranging the formula, Whole = Part ÷ (Percentage/100). In other words, divide the part by the percent (in decimal form). For example, if 30 is 15% of some total, then the total is 30 ÷ 0.15 = 200. (Check: 15% of 200 is 30.)
Can a percentage be greater than 100%?
Yes. A percentage over 100% means the part is more than the whole. For example, scoring 110 points out of 100 possible points would be 110%. Or if a quantity doubles, that’s 200% of the original (an increase of 100%). Percentages above 100% often indicate that something exceeds the standard full amount.
How do I calculate a percentage of a total?
To find what percentage one number is of another (a part of a total), divide the part by the total and multiply by 100%. For instance, if you have 30 out of 50 apples, divide 30 by 50 to get 0.6, and then multiply by 100 to get 60%. So, 30 is 60% of 50.
What’s an easy way to calculate percentages in my head?
Use the quick tricks! Start with 10% (divide by 10) or 1% (divide by 100) depending on the problem, and scale up. For example, to find 15%, combine 10% and 5% (half of 10%). Also, use the fact that X% of Y = Y% of X to make calculations easier when possible. With practice, these mental math techniques become faster.
What is a “percentage point”?
A percentage point is a unit for the difference between two percentage values. It’s used to avoid confusion when talking about changes in percentages. For example, if a tax rate goes from 10% to 12%, we say it increased by 2 percentage points. This is an absolute change. In contrast, calling it a “20% increase” would be ambiguous or misleading (since 2 is 20% of 10). So, percentage points clarify the difference between two percentages, whereas a percent change usually refers to a relative change with respect to the starting value.
What is percentage error?
Percentage error is a way to describe how far an observed value is from an exact or true value, in percentage terms. It’s commonly used in science to report accuracy. The formula is similar to percentage difference, but the comparison is made to an accepted true value: Percentage Error = (|Observed – True| / True) × 100%. For example, if a measured length is 98 cm but the true length is 100 cm, the error is 2 cm. The percentage error would be (2/100) × 100% = 2% error.
End: By understanding how to convert and calculate percentages, you can tackle a wide range of everyday problems, from figuring out discounts and tips to analyzing data and changes over time. The more you practice with percentage calculations, the more intuitive they will become. Percentages are all around us, and mastering them is a very valuable skill that will serve you in school, work, and daily life.