Percentage Calculator
Use this tool to calculate the percentage of a number. Simply enter the total number and the percentage you want to find.
% of =Percentage Calculator in Common Phrases
What is X% of Y?
Find what percentage a number is of another number. Just input the values and click calculate.
% of =X is what % of Y?
Determine the percentage one number represents of another.
is what % of =X is Y% of what?
Find the total number when given a percentage and a part of it.
is % of what? =Percentage Difference Calculator
Compare two numbers to find the percentage difference between them. This helps in comparing values like prices, measurements, or any two quantities.
and =Percentage Change Calculator
Calculates how much a value increases or decreases by a certain percentage. Great for finding price changes, discounts, or growth rates.
to =Understanding Percentages
In mathematics, a percentage is a way to express a number or ratio as a fraction of 100. It is a useful method for representing a dimensionless relationship between two numbers, alongside other methods such as ratios, fractions, and decimals. The percentage symbol “%” is commonly used to denote percentages, but they can also be represented by writing “percent” or “pct” after the number.
Example 1: Calculating the Percentage of Correct Answers
If a student answers 18 out of 20 questions correctly on a test, the ratio of correct answers to total questions is 18/20=9/10=0.9. The value of the ratio is therefore 0.9, and multiplying this by 100 yields:0.9×100=90
In other words, the ratio of 18 correct answers to 20 total questions is equivalent to 90% of the answers being correct.
Example 2: Calculating the Percentage of a Budget Spent
If a person spends 75 out of a 100 budget, the ratio of the amount spent to the total budget is 75/100=3/4=0.75. The value of the ratio is therefore 0.75, and multiplying this by 100 yields:0.75×100=75
In other words, the ratio of 75spenttoa75spenttoa100 budget is equivalent to 75% of the budget being spent.
Example 3: Calculating the Percentage of Votes Received
If a candidate receives 240 votes out of 800 total votes in an election, the ratio of votes received to total votes is 240/800=3/10=0.3. The value of the ratio is therefore 0.3, and multiplying this by 100 yields:0.3×100=30
In other words, the ratio of 240 votes received to 800 total votes is equivalent to 30% of the votes being in favor of the candidate.
Percentage Formula
The percentage formula can be expressed in various forms, but it is fundamentally an algebraic equation involving three values:
P × V1 = V2
Here:
- ( P ) is the percentage,
- ( V1 ) is the initial value being modified, and
- ( V2 ) is the result after applying the percentage.
When solving for ( P ), the formula converts the percentage into its decimal form. To express the result as a percentage, the decimal is multiplied by 100.
Example:
P X 30 = 1.5
P = 1.5/30 = 0.05 X 100 = 5%
When solving manually, the decimal form of the percentage is used, and the result is multiplied by 100 to convert it back to a percentage.
Percentage Difference Formula
The percentage difference between two values is calculated by dividing the absolute difference between the two numbers by their average, then multiplying by 100 to express the result as a percentage.
Percentage Change Formula
Percentage change measures the increase or decrease between two values. It is calculated by finding the absolute difference between the values, dividing it by the original value, and then multiplying by 100 to express the change as a percentage.
Practical Applications
Percentages are widely used in everyday life, such as calculating discounts, interest rates, and statistical data. Understanding how to compute and interpret percentages is essential for making informed decisions in finance, education, and many other fields. Whether you’re calculating a percentage difference, determining a percentage change, or simply converting a ratio to a percentage, the formulas and examples provided above offer a clear guide to mastering this fundamental mathematical concept.