How to Use the Percentage Calculator
This percentage calculator allows you to find a percentage of a number, determine what percentage one number is of another, and calculate percentage change (increases or decreases). It also provides a step-by-step solution showing how the answer is obtained.
To use the calculator:
- Select the calculation you want to perform from the three available options.
- Enter the values in the corresponding input fields.
- Click Calculate.
The calculator instantly returns the answer and provides a clear, step-by-step solution showing exactly how the value was obtained. You can also use the Copy button to copy the answer and solution or click Reset All to clear the calculator.
Example: How to Find 18.5% of 160 Using the Calculator
To find 18.5% of 160 using the calculator:
- Select the first option, What is X% of Y?
- Enter 18.5 in the percentage field and 160 in the number field.
- Click Calculate
The calculator returns 29.6 and shows how the answer was calculated.
What Is a Percentage?
A percentage is a number or ratio expressed as a fraction of 100. The word percent means per hundred, and percentages are represented using the percentage symbol (%).
For example, 25% means 25 out of every 100. This can also be expressed as a fraction or decimal. That is, 25% = 25/100
= 0.25
Similarly, 50% means 50 out of 100, which is equivalent to 0.5 or one-half.
Percentages are commonly used to express how much one quantity represents relative to another. For instance, examination scores are often expressed as percentages so that students who take tests with different total marks can be compared on the same scale.
Percentage of a Number Formula
To find a given percentage of a number, use the following formula:
Percentage Amount = (Percentage ÷ 100) × Number
Where:
- Percentage is the percentage you want to find, such as 15%.
- Number is the total amount or quantity.
- Percentage Amount is the resulting value.
The formula works by converting the percentage into a decimal and multiplying it by the given number.
How to Find a Percentage of a Number by Hand
To calculate a percentage of a number manually, follow these steps:
- Identify the percentage and the number.
- Divide the percentage by 100 to convert it into a decimal.
- Multiply the decimal by the given number to obtain the percentage amount.
Example 1
What Is 15% of 240?
Solution
To find 15% of 240 manually, follow these steps:
Step 1: Identify the given values.
From the question, we know that:
- Percentage = 15%
- Number = 240
Step 2: Convert the percentage to a decimal.
To convert 15% into a decimal, we divide 15 by 100. Thus, 15 ÷ 100 = 0.15
Step 3: Multiply the decimal by the given number.
The required percentage is: Percentage amount = 0.15 × 240
= 36
Therefore, 15% of 240 is 36.
You can quickly verify this result using the first option of the above percentage calculator.
Formula for Finding What Percentage One Number Is of Another
To find what percentage one number is of another, we use the formula:
Percentage = (Part ÷ Whole) × 100%
Where:
- Part is the amount whose percentage you want to determine.
- Whole is the total or reference amount.
- Percentage is the part expressed as a percentage of the whole.
Note. The whole should not be zero because division by zero is undefined.
This formula is commonly used to calculate examination scores, survey percentages, and the proportion of a total represented by a particular quantity.
How to Find What Percent One Number Is of Another by Hand
To calculate what percentage one number is of another manually, follow these steps:
- Identify the part and the whole.
- Divide the part by the whole.
- Multiply the result by 100 to express it as a percentage.
Example 2
Suppose a student answers 45 questions correctly out of 180 questions in an examination. What percentage of the questions did the student answer correctly?
Solution
This question requires us to determine what percentage 45 is of 180. To do that manually, follow these steps:
Step 1: Identify the given values.
From the question:
- Part = 45
- Whole = 180
Step 2: Divide the part by the whole.
Dividing 45 by 180, we get:
45 ÷ 180 = 0.25
Step 3: Multiply the result in Step 2 by 100
Therefore, the required percentage is: Percentage = 0.25 × 100%
= 25%
Therefore, 45 is 25% of 180. This implies that the student answered 25% of the examination questions correctly.
You can also find this percentage using the second calculation in the calculator above.
Percentage Change Formula
Percentage change measures how much a value has increased or decreased relative to its original value.
For example, you may want to calculate the percentage increase in the price of an item, the percentage decrease in sales, or the percentage change in a student’s examination score.
The percentage change formula used by this calculator is:
Percentage Change = [(New Value − Original Value) ÷ |Original Value|] × 100%
Where:
- Original Value is the starting value.
- New Value is the final value.
- |Original Value| represents the absolute value of the original number.
For positive original values, the formula gives the same result as dividing by the original value directly.
A positive result indicates an increase, while a negative result indicates a decrease. If the result is zero, there has been no change.
Note that percentage change is undefined when the original value is zero.
How to Find Percentage Change by Hand
To calculate the percentage increase or decrease between two values manually, follow these steps:
- Identify the original value and the new value.
- Subtract the original value from the new value to find the difference.
- Divide the difference by the absolute value of the original value.
- Multiply the result by 100 to express the change as a percentage.
Example 3: Calculate the Percentage Increase from 150 to 180
Suppose the price of a product increases from $150 to $180. Calculate the percentage increase.
Solution
To find the percentage increase from $150 to $180, follow these steps:
Step 1: Identify the given values.
From the question:
- Original Value = $150
- New Value = $180
Step 2: Find the difference between the two values.
Subtract the original price from the new price:
Difference = 180 − 150
= 30
Therefore, the price increased by $30.
Step 3: Divide the difference by the original value.
Since the original value is positive:
30 ÷ 150 = 0.20
Step 4: Convert the result to a percentage.
Using the percentage change formula:
Percentage Change = [(180 − 150) ÷ 150] × 100%
= (30 ÷ 150) × 100%
= 0.20 × 100%
= 20%
Therefore, the price increased by 20%, from $150 to $180.
Example 4: Calculate the Percentage Decrease from 150 to 120
Suppose the price of the same product decreases from $150 to $120. Find the percentage decrease.
Solution
From the question:
- Original Value = $150
- New Value = $120
Using the percentage change formula:
Percentage Change = [(120 − 150) ÷ 150] × 100%
= (−30 ÷ 150) × 100%
= −0.20 × 100%
= −20%
Therefore, the price decreased by 20%, from $150 to $120.
Notice that the result is negative because the new value is smaller than the original value.
For more calculations involving increases and decreases between two values, you can use the Percentage Change Calculator.
Common Uses of Percentages
Percentages are widely used in mathematics, education, business, statistics, and everyday activities.
Some common applications include:
- Examination scores: Calculating the percentage of marks obtained out of the total possible marks.
- Shopping discounts: Finding the discount amount when a product is sold at a reduced price.
- Sales tax: Determining the amount of tax charged as a percentage of a product’s price.
- Tips: Calculating the amount to leave as a tip based on a percentage of a bill.
- Business performance: Measuring changes in sales, revenue, or expenses over time.
- Statistics: Expressing the number of observations belonging to a particular category as a percentage of the total.
For example, suppose a store offers a 20% discount on an item originally priced at $150.
The discount amount is:
Discount = (20 ÷ 100) × 150
= 0.20 × 150
= $30
Subtracting the discount from the original price gives:
Sale Price = $150 − $30
= $120
Therefore, a 20% discount saves you $30, reducing the price of the item from $150 to $120.
How to Calculate Percentages in Excel
Microsoft Excel allows you to calculate percentages using simple arithmetic formulas.
Suppose you want to find 20% of 150. Enter 20 in cell A2 and 150 in cell B2.
You can calculate the percentage amount using:
=A2/100*B2
Excel will return 30.
However, if A2 contains 20% as an actual percentage value, you can simply use:
=A2*B2
To find what percentage 30 is of 150, enter 30 in cell A2 and 150 in cell B2, then use:
=A2/B2
Format the result cell as a percentage. Excel will display 20%.
Note: When you format a decimal result as a percentage in Excel, you do not need to multiply it by 100 again.
Frequently Asked Questions
What is a percentage calculator?
A percentage calculator is an online math tool used to find a percentage of a number, determine what percentage one number is of another, or calculate percentage increases and decreases. This calculator also provides a clear step-by-step solution.
How do you calculate a percentage?
To calculate what percentage one number is of another, divide the part by the whole and multiply by 100. For example, 30 out of 120 is (30 ÷ 120) × 100% = 25%.
What is 20% of 150?
20% of 150 is 30. To calculate this, divide 20 by 100 and multiply by 150.
20% of 150 = (20 ÷ 100) × 150 = 30.
What is 15% of 200?
15% of 200 is 30. Dividing 15 by 100 gives 0.15, and multiplying 0.15 by 200 gives 30.
How do I calculate a percentage without a calculator?
To find a percentage of a number without a calculator, divide the percentage by 100 and multiply the result by the number. Alternatively, you can use familiar percentages. For example, 10% of 200 is 20, so 20% of 200 is 40.
Can a percentage be greater than 100%?
Yes. A percentage can exceed 100% when the quantity being compared is greater than the reference value. For example, 150 is 150% of 100.
Can I use decimal numbers in the percentage calculator?
Yes. The calculator supports both whole numbers and decimals. For example, 12.5% of 80 is 10.
What is the difference between percentage change and percentage difference?
Percentage change compares a new value with an original value and measures how much it has increased or decreased. Percentage difference, on the other hand, compares two values without treating either as the original value. These calculations use different formulas and may give different results.
What is the difference between a percentage and a percentile?
A percentage expresses a quantity as a fraction of 100, while a percentile describes the position of a value relative to other observations in a dataset.
For example, scoring 80% on an examination does not necessarily mean a student is at the 80th percentile. You can use the Percentile Calculator to calculate percentiles and percentile ranks.
