Percentage Calculator
Use our free percentage calculator to quickly calculate percentages, percentage change, and percent increase. Understand the math behind it. Try it now!
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Purpose
Percentages represent a proportion of a whole expressed as a fraction of 100. They're used everywhere: calculating discounts, understanding interest rates, tracking sales growth, and analyzing grades. This percentage calculator handles multiple calculation types including finding a percentage of a value, calculating what percent one number is of another, and determining percentage change between two values.
How to use
To use the percentage calculator, follow these steps:
- Identify the Calculation Type: Determine which type of percentage calculation you need to perform (e.g., percentage of a value, percentage change, percent increase).
- Enter the Values: Input the relevant values into the designated fields. For example, to calculate the percentage of a value, enter the total value and the part you want to express as a percentage.
- Select the Calculation Option: Choose the appropriate calculation option from the available dropdown menu or radio buttons.
- Click Calculate: Press the "Calculate" button to initiate the calculation.
- View the Results: The calculated percentage will be displayed in the designated output field.
Examples
Example 1: Calculating a Discount
A store offers 25% off an $80 item. Select "Percent Of" mode, enter 25 and 80. Result: $20 discount, so final price is $60.
Example 2: Finding Percentage Change
Your investment grew from $100 to $125. Select "Percent Change" mode, enter 100 (old) and 125 (new). Result: 25% increase.
How it works
The percentage calculator utilizes several fundamental formulas, depending on the specific calculation being performed. Here are some of the most common:
Percentage of a Value: To find what percentage a value (X) is of another value (Y), the formula is:
Percentage = (X / Y) * 100- For example, if X = 20 and Y = 100, then Percentage = (20 / 100) * 100 = 20%. This means 20 is 20% of 100.
Percentage Change: To calculate the percentage change between an old value (Old) and a new value (New), the formula is:
Percentage Change = ((New - Old) / Old) * 100- A positive percentage change indicates an increase, while a negative percentage change indicates a decrease. For example, if Old = 50 and New = 60, then Percentage Change = ((60 - 50) / 50) * 100 = 20%. This represents a 20% increase.
Percent Increase: The formula for percent increase is the same as percentage change when the new value is greater than the old value:
Percent Increase = ((New - Old) / Old) * 100- For example, if Old = 100 and New = 120, then Percent Increase = ((120 - 100) / 100) * 100 = 20%. This means the value increased by 20%.
These formulas are fundamental to understanding and calculating percentages in various contexts.
FAQ
What is a percentage?
A percentage expresses a number as a fraction of 100, denoted by the % sign. For example, 50% means 50 out of 100, or half of the total. Percentages make it easy to compare proportions across different values.
How do I calculate the percentage of a number?
Multiply the number by the percentage and divide by 100. For example, 25% of 80 = (25 × 80) / 100 = 20. Alternatively, convert the percentage to a decimal (25% = 0.25) and multiply: 0.25 × 80 = 20.
What is percentage change?
Percentage change measures how much a value increased or decreased relative to its original amount. Formula: ((New - Old) / Old) × 100. For example, if a price went from $50 to $60, the percentage change is ((60-50)/50) × 100 = 20% increase.
What's the difference between percentage and percentage points?
A percentage point is the arithmetic difference between two percentages. If interest rates rise from 5% to 7%, that's a 2 percentage point increase. But as a percentage change, it's a 40% increase ((7-5)/5 × 100). This distinction matters in finance and statistics.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100. For example, to find what percent 15 is of 60: (15 / 60) × 100 = 25%. So 15 is 25% of 60.