Percentage Calculator
Calculate percentages, find what percentage one number is of another, and work out percentage increases, decreases, and differences with clear step-by-step results.
Percentage Calculator
Choose the type of percentage calculation, enter your values, and get an instant result with the formula and calculation steps shown clearly.
Calculate Percentage
Select the calculation that matches the question you want to answer.
Calculation Result
Step-by-Step Calculation
What Is a Percentage?
A percentage expresses a quantity as a part of 100. The word percent means “per hundred,” so 25% represents 25 parts out of 100, or 0.25 as a decimal.
Percentages are used to describe proportions, compare values, measure changes, and communicate rates. They appear in shopping discounts, interest rates, grades, statistics, business reports, salary changes, and many everyday calculations.
How to Use This Percentage Calculator
- Select the type of percentage calculation.
- Enter the requested numbers in the input fields.
- Click Calculate to see the result.
- Review the formula and step-by-step calculation.
- Use Reset to start a new calculation.
The calculator is designed to show not only the answer but also how the answer was obtained, making it useful for checking calculations and learning the underlying method.
Percentage Formulas
The formula depends on the question being asked.
Result = (X ÷ 100) × Y
Find what percentage X is of Y
Percentage = (X ÷ Y) × 100
Percentage increase or decrease
Percentage Change = ((New Value − Original Value) ÷ Original Value) × 100
Percentage difference
Percentage Difference = |A − B| ÷ ((A + B) ÷ 2) × 100Although these formulas all involve percentages, they answer different questions. Choosing the correct formula is important because the reference value changes depending on the calculation.
Percentage Calculator Examples
Example 1: What is 20% of 150?
Convert 20% to a decimal and multiply it by 150.
20% of 150 = (20 ÷ 100) × 150 = 30Therefore, 20% of 150 is 30.
Example 2: 30 is what percentage of 150?
(30 ÷ 150) × 100 = 20%Therefore, 30 is 20% of 150.
Example 3: Increase from 150 to 180
((180 − 150) ÷ 150) × 100 = 20%The value increased by 20% relative to the original value.
Example 4: Decrease from 200 to 160
((160 − 200) ÷ 200) × 100 = −20%The negative result indicates a 20% decrease.
Percentage Increase and Decrease
Percentage change compares a new value with an original value. The original value is the reference point, which is why it appears in the denominator.
A positive result means the value increased, while a negative result means the value decreased. If the original and new values are identical, the percentage change is zero.
Percentage Difference vs. Percentage Change
Percentage change and percentage difference are not interchangeable. Percentage change is appropriate when there is a defined starting or original value, such as a price changing from one amount to another.
Percentage difference is a symmetric comparison. It uses the average of the two values as the reference, so swapping the two numbers produces the same result.
Percentage Difference = |A − B| ÷ ((A + B) ÷ 2) × 100Where Are Percentages Used?
- Shopping: discounts, markups, sales prices, and price changes.
- Finance: interest rates, returns, fees, and investment performance.
- Education: marks, grades, scores, and completion rates.
- Business: growth, margins, conversion rates, and performance metrics.
- Statistics: survey proportions, rates, and population comparisons.
- Everyday life: changes in weight, quantities, time, distance, and other measurements.
Common Percentage Mistakes
Using the wrong reference value
For percentage change, divide by the original value. Using the new value as the denominator answers a different question.
Confusing “X% of Y” with “X is what percentage of Y”
For example, 20% of 150 is 30, while 30 is 20% of 150. The statements are related, but they start with different questions.
Confusing percentage points with percentages
If a rate moves from 20% to 25%, it increases by 5 percentage points. Relative to the original 20%, that is a 25% increase.
Understanding Your Result
A percentage should be interpreted together with the numbers used to calculate it. The same percentage can represent very different absolute amounts depending on the starting quantity.
For example, a 10% increase on 100 is 10, while a 10% increase on 10,000 is 1,000. Percentage describes the relative size of a change; it does not replace the underlying numerical values.
Frequently Asked Questions
How do I calculate a percentage?
For X% of Y, divide X by 100 and multiply by Y. For example, 20% of 150 is 30.
How do I find what percentage one number is of another?
Divide the first number by the second and multiply by 100. For example, 30 ÷ 150 × 100 = 20%.
How do I calculate percentage increase?
Subtract the original value from the new value, divide by the original value, and multiply by 100.
Can a percentage be greater than 100%?
Yes. A percentage can exceed 100% when the quantity being described is greater than the reference amount.
Can percentage change be negative?
Yes. A negative percentage change means the new value is lower than the original value.
What is 25% as a decimal?
25% equals 0.25 because 25 ÷ 100 = 0.25.
What is the difference between percentage change and percentage difference?
Percentage change uses the original value as the reference, while percentage difference uses the average of the two values.
Can I use this calculator for discounts?
Yes. You can calculate the discount amount by finding the percentage of the original price, then subtract it from the original price to determine the discounted amount.
Percentage Calculator Disclaimer
This calculator is provided for general informational and educational purposes. Results are based on the values entered and the selected mathematical formula. Always check important calculations independently when accuracy is critical.