What Is a Percentage?
A percentage is a way of expressing a number as a part of 100. The word percentage comes from the idea of "per hundred."
The percentage symbol is %. For example, 25% means 25 out of every 100.
What Is a Percentage Calculator?
A percentage calculator is an online tool that performs common percentage calculations quickly. It can be useful for schoolwork, shopping, finance, statistics and everyday comparisons.
Different percentage questions require different formulas, so the first step is identifying what you are trying to calculate.
How to Calculate a Percentage of a Number
To calculate a percentage of a number, convert the percentage to a decimal and multiply it by the number.
Example: 20% of 150
How to Find What Percentage One Number Is of Another
Sometimes you already have two numbers and want to know what percentage one represents of the other.
Example: 30 out of 150
How to Calculate Percentage Increase
Percentage increase measures how much a value has increased compared with its original value.
Example: Increase From 100 to 125
How to Calculate Percentage Decrease
Percentage decrease measures how much a value has fallen compared with its original value.
Example: Decrease From 200 to 150
How to Calculate Percentage Change
Percentage change compares the difference between two values relative to a chosen reference value.
The sign of the result can indicate whether the value increased or decreased.
Percentage Discounts
Percentages are commonly used for discounts.
If an item costs $200 and the discount is 15%, first calculate the discount amount.
Percentages and Tax Calculations
Percentage calculations can also be used to estimate a tax amount when a known percentage rate applies.
The exact tax rules and rates depend on the relevant jurisdiction and type of transaction.
Percentage Profit and Loss
Percentages are also used to express profit or loss relative to a cost or other reference amount.
Profit Percentage = (Profit ÷ Cost Price) × 100
The correct reference value matters. A percentage based on cost is not necessarily the same as a percentage based on selling price.
Finding the Original Number From a Percentage
Sometimes you know the result after a percentage has been applied and want to find the original value.
Example
Suppose a price after a 20% discount is $80. The original price can be found by recognizing that $80 represents 80% of the original price.
Percentage vs Percentage Points
These two terms are not always interchangeable.
If an interest rate changes from 5% to 7%, the change is 2 percentage points. The relative percentage increase is different.
Converting Percentages to Decimals
To convert a percentage to a decimal, divide it by 100.
25% = 0.25
75% = 0.75
100% = 1.00
Converting Decimals to Percentages
To convert a decimal to a percentage, multiply it by 100 and add the percentage symbol.
0.50 × 100 = 50%
0.85 × 100 = 85%
Common Percentage Calculation Mistakes
- Using the wrong original or reference value.
- Forgetting to divide a percentage by 100.
- Confusing percentage change with percentage points.
- Using the new value instead of the original value as the denominator when calculating percentage change.
- Rounding too early in a multi-step calculation.
- Mixing percentage and decimal formats.
Why the Reference Value Matters
The denominator in a percentage calculation determines what the result is measured against.
For example, if a price rises from $50 to $60, the increase is $10. Relative to the original $50, the percentage increase is 20%.
Using $60 as the denominator would produce a different number and would answer a different mathematical question.
How to Use a Percentage Calculator
- Identify the type of percentage calculation.
- Enter the required number or values.
- Check which value is the original or reference value.
- Select the calculate option.
- Review the result and make sure it answers the question you intended to ask.
Everyday Uses of Percentage Calculations
- Shopping discounts.
- Tax estimates.
- Exam scores.
- Business growth.
- Price increases and decreases.
- Financial comparisons.
- Statistics and reports.
Try the Percentage Calculator
After understanding the different percentage formulas, you can use the calculator to quickly solve common percentage problems.
