Four Percentage Calculators
- What is a percent?
- A percent is a number that expresses a ratio in terms of 100.
Percentages and Ratios (and Fractions too)
What does this definition mean in practice?
How do you find percentage? These online percentage calculators are used for calculating:
- percent increase/decrease, and
- percentage of calculations.
A ratio is a relationship between two numbers. If a math class has 12 boys and 15 girls, the ratio of boys to girls is 12:15. (We could also say the ratio of girls to boys is 15:12.) We can also write the ratio of boys to girls as 12/15.
The expression 12/15 is a fraction.
The idea is the same: a ratio represents the same relationship as a fraction; it is simply written in a different form.
That explains what a ratio is. But what does “in terms of 100” mean?
This is the essential point. “In terms of 100” means the following: if the right-hand side of the expression “12:15” (the “15”) became “100,” what number should replace the “12” so the relationship remains equal to the original ratio of 12:15?
The answer is “80.” The ratio 12:15 is the same as 80:100, or 80%. In other words, the class has 80% as many boys as it has girls. Consider which of the percentage calculators below produces this result. If it is not obvious, continue reading.
One clarification first: we did not say the class is 80% boys. That statement would be incorrect. More below…
The Calculator-Calculate Percentage One Value is of Another Value
What percent is 20,000 of 100,000?
Twenty percent - 20%. You can solve this by dividing 20,000 by 100,000 and multiplying by 100 to convert the resulting decimal to a percent, i.e. (20000/100000)*100.
Information
The Calculator-Calculate Total When Percentage Equals a Known Amount
100,000 is 20% of what number?
Five hundred thousand - 500,000. You can solve this problem by dividing 20 by 100 to convert the percentage to a decimal. Then, to find the number 100,000 is 20% of, divide 100,000 by the decimal result, i.e., 100000/(20/100).
The Calculator-Calculate the Value that is a Percentage of a Number
20% of 100,000 is what number?
Twenty thousand - 20,000. You can solve this problem by dividing 20 by 100 to convert the percent to a decimal. Then multiply 100,000 by that decimal to find a percent of, i.e., 100000*(20/100).
The Calculator-Calculate Percentage Decrease
What is the percentage decrease from 100,000 to 80,000?
Twenty percent - 20%. You can solve this problem by subtracting 100000 from 80000. Then divide the result by 100,000 and multiply by 100 to convert to a percentage, i.e., ((80000-100000)/100000)*100.
What is the percentage increase from 80,000 to 100,000?
Twenty-five percent - 25%. You can solve this problem by subtracting 80000 from 100000. Then divide the result by 80,000 and multiply by 100 to convert to a percentage, i.e., ((100000-80000)/80000)*100.
If I want to know what percentage of the class is made up of boys, I would use the same calculator, but the ratio is no longer 12:15. Instead, it is 12:27. Why?
To know the percentage of boys in the class, we must write the ratio as the number of boys to the total number of students. The first ratio (12:15) shows boys relative to girls. The second ratio (12:27) shows boys relative to the entire class.
Percentages Are Normalized Ratios
Why would we convert a ratio such as 12:15 or 12:27 so that the right side becomes 100?
The reason explains why we use percentages.
The purpose of percentages is comparison.
Percentages let us compare relationships that involve different sizes or amounts in a consistent way.
For example, you receive a math test result showing 45 correct answers out of 52 questions. A friend receives a science test result showing 39 correct answers out of 44 questions. Who performed better? Scroll to Percentage Calculator 1 for the answer. This is also the calculator used to convert the 12:15 ratio above to a percentage.
Normalize means to make values comparable. When you convert a ratio to a percentage, you are normalizing that ratio so the results can be compared.
Percentage Calculation Terms and Definitions
- Base
The reference quantity that represents 100%.
Example: In this calculation, 200 is the base, because 10% of 200 equals 20.
- Rate (percent)
The percentage value applied to the base.
Example: In this calculation, the rate is 10%, because 10% of the base 200 equals 20.
- Amount (part)
The known or unknown value that corresponds to a stated percentage of the base and is used to calculate or determine the other percentage values.
Example: In this calculation, the amount is 20, because it equals 10% of the base 200.
- Net amount
An amount that results when a percentage is subtracted from the base, representing the value after a proportional reduction.
Example: Starting from a base of 200, a 10% reduction results in a net amount of 180.
- Gross amount
An amount that results when a percentage is added to the base, representing the value after a proportional increase.
Example: Starting from a base of 200, a 10% increase results in a gross amount of 220.
Percentage Calculator
Calculator 1 converts any ratio to a percentage. It answers the question “What percent is ‘X’ of ‘Y’, that is, ‘X:Y’ or ‘X/Y’?”
First, identify the ratio. Suppose you earn $1,000 per week and $183 is deducted from your pay. To know what percentage of your pay is deducted, use the ratio 183:1000. Enter 183 as “This number” and 1,000 as “is what percent of this number.” The result is 18.3%. In other words, 18.3% is deducted from your pay.
Calculator 1 also works as a fraction to percent calculator. To use it, enter the numerator of the fraction in “This number” and the denominator in “is what percent of this number.” For example, for “27/82,” enter 27 and 82. The percentage is 32.9268%.
Percentage Calculator 1 also functions as a percent to decimal calculator.
Do you see the relationship between percentages, ratios, and fractions?
If not, review the earlier examples before continuing. The remaining sections build on these ideas.
How to Solve Other Percentage Problems
Finding the Total (Reverse Percentage)
When you know the part and the percentage, but need the original amount.
- Example:
You have $2,250 to pay a medical bill, which covers the 20% copay. What is the highest total bill you can afford?
- Solution:
Use the Percentage Base Calculator calculator (Calculator 2). Entering 2,250 and 20% reveals the total bill is $11,250.
Finding the Number (Percentage of a Total)
When you know the total and the percentage, but need the specific number.
- Example:
To get an “A” grade, you need 90% correct answers. If the test has 145 questions, how many must you get right?
- Solution:
Use the Amount/Part Calculator calculator (Calculator 3). Entering 145 and 90% shows you need roughly 131 correct answers.
Calculating Increase and Decrease
When you want to see how much a value has changed.
- Example:
An item drops from $249.95 to $199.95.
- Solution:
Use the Percentage Change calculator (Calculator 4) to see this is a 20% decrease.
Why do “Increase” and “Decrease” percentages differ?
If the price goes back up from $199.95 to $249.95, it is a 25% increase. The percentage changes because your starting number (the base) is different in each scenario.
For more background on percentages, see this Wikipedia article.
Elizabeth Stewart says:
I am wanting to know what is 12% of 58 million dollars…
Karl says:
You need to use calculator #3, if you are asking a question.
Michael says:
I have 150,000 an I wanted split 3 ways.. what is the percentage for each person
Karl says:
To solve the problem requires 2 steps:
1. Find the amount each person gets i.e. 150,000 divided by 3.
2. Then use percentage calculator #1. The result from above calculation is entered as “This number.”