Percentage of a Percentage Calculator
The percentage of a percentage calculator can multiply one percentage by another to get the cumulative value. It can then apply these two percentages (one at a time) to some value, to show the percentages' individual and combined effect.
In this article, we will discuss some examples of a percentage of a percentage (like what is 30% of 80%), and why the idea of "a percent of a percent" matters.
If you liked our calculator and want to learn more, for example, how to calculate percent error, check our other calculators on percentages.
Calculate percentage of a number
Indeed, we all know how to determine the percentage of a number. Don't worry if you don't — we will make a brief recap before we dive any further into discovering the world of percentage of a percentage.
To understand how to calculate the percentage of a number, let's work through an example. You've just scored 83 out of 125 in your geography exam, and you're interested in your score in terms of a percentage.
The formula to determine the percentage of a number is:
Percentage = (Number / Total) × 100
So, the number for which you want to determine the percentage is the numerator, and the number for which you want to determine the percentage out of is the denominator. Then, you multiply the answer by 100.
Therefore, your test score as a percentage is:
% = (obtained marks / total) × 100
= (83 / 125) × 100
= 0.664 × 100
We do have a percentage calculator that will help you find the percentages of numbers.
How to use the percentage of percentage calculator
A tool to determine the percent of a percent is sure to come in handy occasionally. So, it only makes sense to learn how to calculate a percentage of a percentage using our effective tool.
There are two sections in the tool. The first section calculates the percentage of a percentage given:
- The first percentage; and
- The second percentage.
And before you can say "percentage", you have your answer: the cumulative percentage.
The second section allows you to apply the previous inputs to an actual number. Here, you have to input the original value. The result comprises the number after applying the first percentage and the final number after applying the second percentage.
Example of percentage of percentage, 40% of 90%
Let's walk through a working example of a percentage of a percentage. Suppose the first percentage is
40% and the second is
90%. The calculator will compute:
= (1st % × 2nd % ) × 100
= (40/100) × (90/100) × 100
= (0.4) × (0.9) × 100
= 0.36 × 100
Let's apply this process to real numbers. Suppose the original number is
10. We apply the first percentage:
10 × 0.4 = 4
And then the second:
4 × 0.9 = 3.6
This is the final value you get after calculating 40% of 90% of 10.
You might want to check out our multiplication calculator if you require help multiplying decimals or fractions.
Percent of a percent
No knowledge in this world is purposeless. And yes, that implies determining the percent of a percent has its own significance, like in scenarios where the relative proportion or contribution of one percentage within another is needed in the fields of finance, economics, business, and statistics.
Following are some situations where knowing how to calculate the percentage of a percentage is significant:
Tax calculations: You'll need to calculate the tax on a certain percentage of an amount.
Cost markup: This includes calculating the percentage markup on a product.
Contribution to a whole: This includes determining the contribution of a specific category as a percentage of a total.
What are percentages?
A percentage is a concept we use to describe a number or ratio expressed as a fraction of 100. It is often used because it is easier for us to think of a percentage of a certain size than the associated decimal number. We often express a percentage using the sign '%' or the abbreviations 'pct.', 'pct' and 'pc'. A percentage is a dimensionless number and has no unit.
How can I find the percentage of a percentage?
Finding the percentage of percentage may seem confusing, but just follow these steps:
- Divide each percentage by 100 to convert to decimal form, e.g.:
80%/100 = 0.8 and 45%/100 = 0.45.
- Multiply the decimals together:
0.8 × 0.45 = 0.36.
- Multiply by 100 if you want to return back to a percentage:
0.36 × 100 = 36%.
Can a percentage of a percentage exceed 100?
Yes, because either or both of the percentages can have high values. As an example, for 150% and 80% the cumulative percentage will be 120%. In a mathematical sense, the percentage can be over 100% if you compare them with each other. However, when talking about a percentage of something concrete, you can't get more than 100% of something.
What is the final value of 160 if the cumulative percentage is 8.75%?
The final value of 160 will be 14. Assume that first percentage is 25% and second is 35%, and then:
- Calculate the percentage of a percentage: (0.25)(0.35) = 0.0875 = 8.75%.
- Find a value of 160 after 1st percentage: 160 × 0.25 = 40.
- Multiply 40 by 0.35 to get the final value of 14.
- Or calculate 160 × 0.0875 = 14.
What is 30% of 80%?
30% of 80% is 24%.
Figuring it out is fairly simple. Divide both percentages by 100 to determine their fractions. Afterward, multiply the fractions and finally multiply the answer by 100. You have your answer.
30% of 80%
= (30/100 × 80/100) × 100
= (0.3 × 0.8) × 100
= (0.24) × 100