What Is a Percentage?
A percentage shows how much of something you have compared with a whole. The word percent means “per hundred,” so 25% means 25 out of 100. It can also be written as the fraction 25/100 or the decimal 0.25.
We use percentages when talking about discounts, grades, taxes, interest, budgets, survey results, and changes in price. They are useful because they put different values on the same scale and make them easier to compare.
Percentage Formulas
Most percentage questions involve three values: the part, the whole, and the percentage. If you know two of them, you can usually find the third.
| What you want to find | Formula |
|---|---|
| Percentage of a number | Result = (Percentage ÷ 100) × Number |
| The whole number | Whole = (Part ÷ Percentage) × 100 |
| What percent A is of B | Percentage = (Part ÷ Whole) × 100 |
| Percentage change | Change = ((Final − Starting) ÷ |Starting|) × 100 |
In the percentage-change formula, the vertical bars around the starting value mean its absolute value. For the positive values normally used in prices, quantities, and measurements, this gives the familiar formula of dividing the change by the original value.
How to Use the Percentage Calculator
- Choose the tab that matches the question you are trying to answer.
- Enter the two values you already know in the labeled fields.
- Read the answer, formula, and short explanation in the result panel.
The result updates automatically. You can also select one of the example buttons to see how each calculation works. Decimals, negative values, and percentages greater than 100 are accepted when the calculation allows them.
Percentage Examples
Example 1: What is 25% of 200?
Convert 25% to a decimal by dividing it by 100, then multiply by 200:
Therefore, 25% of 200 is 50.
Example 2: 45 is what percent of 180?
Divide the part by the whole, then multiply by 100:
This means 45 is 25% of 180.
Example 3: 42 is 35% of what number?
Divide the known part by 35, then multiply by 100:
Therefore, 42 is 35% of 120.
Example 4: What is the percentage change from 80 to 100?
First find the change, which is 20. Then compare it with the starting value:
The value increased by 25%.
Understanding Percentage Increase and Decrease
A positive percentage change means the value increased. A negative result means it decreased. The calculator describes the direction in words, so a result of −20% is shown as a 20% decrease.
Percentage increases and decreases are based on the starting value. This is why increasing a value by 25% and then decreasing the new value by 25% does not return to the original amount.
| Step | Calculation | Result |
|---|---|---|
| Start | — | 100 |
| Increase by 25% | 100 × 1.25 | 125 |
| Decrease by 25% | 125 × 0.75 | 93.75 |
Percentage change is undefined when the starting value is zero because the formula would require division by zero. In that situation, it is clearer to report the numerical change instead.
Percentage Change vs. Percentage Points
Percentage points describe the direct difference between two percentages. Percentage change describes how large that difference is compared with the starting percentage.
For example, if an interest rate rises from 20% to 25%, it increased by 5 percentage points. Relative to the original 20%, however, the percentage increase is 25%.
Common Mistakes to Avoid
- Using the wrong whole: in “A is what percent of B?”, B is the whole and belongs in the denominator.
- Forgetting to divide by 100: 25% is 0.25 when used in multiplication, not 25.
- Using the final value as the base: percentage change is normally compared with the starting value.
- Rounding too early: keep the full value during the calculation and round only the final answer.
- Confusing related calculations: percentage change, percentage difference, and percent error answer different questions.
Frequently Asked Questions
How do I calculate a percentage of a number?
Divide the percentage by 100 and multiply by the number. For example, 15% of 80 is 0.15 × 80, which equals 12.
How do I find what percentage one number is of another?
Divide the part by the whole and multiply by 100. If 18 students out of a class of 24 passed, then 18 ÷ 24 × 100 = 75%.
Can a percentage be greater than 100%?
Yes. A percentage greater than 100% means the amount is larger than the reference whole. For example, 150% of 40 is 60.
Can a percentage be negative?
It can in calculations where negative values are meaningful. A negative percentage change usually indicates a decrease, although the calculator presents the magnitude as a positive percentage and labels it as a decrease.
What is the difference between percentage change and percentage difference?
Percentage change compares a new value with a starting value, so the order matters. Percentage difference compares two values using their average as the reference, so it is useful when neither value is the starting or accepted value.
Is percentage change the same as percent error?
No. Percentage change measures movement from a starting value to a final value. Percent error compares an experimental or measured value with a known or accepted reference value.
How many decimal places should I use?
It depends on the situation. Whole percentages are often enough for a quick estimate, while financial, scientific, or statistical work may need two or more decimal places. Avoid rounding until the final step.
Quick Summary
A percentage expresses a value in relation to 100. The main step is to identify which value is the part, which is the whole, and whether you are measuring an amount or a change. Choose the matching calculator tab, enter the two known values, and the missing value will be calculated automatically.
Related Percentage Calculators
Use a more specific calculator when your question needs a particular percentage calculation:
- Target Percentage Calculator
- Percentage Breakdown Calculator — compare several categories as shares of one total and check the unallocated amount.
- Percentage Increase Calculator — find how much a value increased as a percentage.
- Percentage Decrease Calculator — find how much a value decreased as a percentage.
- Percentage Change Calculator — measure the percentage change from an old value to a new value.
- Reverse Percentage Calculator — work backward from a percentage result to find the original value.
- Percent Off Calculator — calculate a discount, sale price, and amount saved.
- Percentage Difference Calculator — compare two values when neither is treated as the original value.
- Percent Error Calculator — compare a measured value with an accepted value.
- Percentage Point Calculator — find the percentage-point difference between two percentages.
- Fraction Percent Calculator — convert a fraction to a percentage or a percentage to a fraction.