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You find here several easy percentage calculators with examples. You can use our easy percent calculators to compute percentages.
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Calculation of percentages (theory and examples)
We explain how percentages are calculated and give some examples.
1. Introductory example
Let's look at an example with different ways of describing a ratio:
20 out of 80 British people believe the sun revolves around the earth.
5 out of 20 British diplomats are women.
25 out of 100 British households are single-person households.
Comparing these ratios might be a bit complicated, but if we write them in terms of percentages, they are equivalent: 25%, which is 25 out of 100.
This example shows the practicality of the widespread use of percentages, which is why we need to be able to understand and calculate percentages.
2. Definition and calculation of percentages
Percentage is a way of referring to a ratio by referring to the number 100. To calculate a percentage, we identify the total number by 100%.
The percentage n % means n individuals out of 100.
50% is half of the total (50 out of 100).
25% is a quarter of the total (25 out of 100).
20% is one-fifth of the total (20 out of 100).
We calculate the ratio of blonde students in a class of 80 students, of which 12 are blonde.
Since there are 12 blonde students out of a total of 80 students, the ratio of blonde students is: R = 12 / 80
Note that in the denominator we write the total number of students and in the numerator the number of blonde students.
Since we want to write the ratio relative to 100, we write 100 in the numerator:
R = x /100
Since the ratio must be equal, we set both expressions equal to calculate
12 / 80 = x / 100
We solve the first-degree equation (the 100 in the denominator passes multiplicatively to the other side): 12 / 80 = x /100 → x = 12 * 100 / 80 → x = 15
So we find that 15 out of 100 students are blonde, so 15% of the students are blonde.
3. Rule of three
The higher a ratio is, the higher the percentage is. This means that the percentage is directly proportional to the ratio. Therefore, we can calculate the percentage by applying a simple rule of three.
Recall the above example: in a class of 80 students, 12 are blonde. We calculate the percentage of blonde students by applying a rule of three (using a table):
|12||12 * 100 / 80 = 15%|
A few more examples
60% of 900 = ???
(900/100) x 60 = 540
First we check how much is one percent: we divide 900 by 100. We get 9.
Then we multiply one percent by 60 (60% = 60 per hundred = 60 percent) so 9 x 60 = 540.
90 = ??? % of 125
90 x (100/125) = 72 %
First we calculate how much is one unit: we divide 125 by 100.
Then we multiply one unit by 90 because we want to know how much is 90 units.
In this way we calculate the percentage.
What is the % change from 150 to 190?
(190-150) x (100/150) = 26.66 %
150 represents 100%. So the percent of one unit is represented by 100/150.
190-150 is 40. So 40 units present 40 x (100/150) = 26.66 %
In this way we calculate the percentage increase or decrease.
What are percentages?
One percent is one hundredth. We use a % to indicate it. So 5 percent is the same as 5%, 0.05, 5/100 or five hundredths. It is that simple!
That is nice, but we usually do not only use percentages. Sometimes we want to show the ratio between 2 numbers. For example: what is 40% of 20? That's 40 hundredths of 20, so if we share 20 cookies in 100 equal pieces (good luck with that!), 40 of those pieces are our 40% of 20 cookies. Let's count: 40/100 * 20 = 8. A little trick does apply here: if you want to divide by a hundred, just move the comma two places to the left. In our calculation, 40/100 * 20 we could also do so: (40 * 20) / 100 (it is the same). 40 * 20 is 800. Move the comma in 800 2 places to the left and you get 8.00. Enter these values at the top of the page, 40 and 20. Then you get "40% of 20 is 8".
In another case you want to indicate, for example, how many percent a number has descended or increased. For example, if you have 10 apples and you eat 2 of them ... Then you have lost 20% apples. Why? Because 8 is 80% of 10. All apples were 100%, now we still have 80%, so the number of apples has descended by 20% (because 100 - 80 = 20). Use our percent increase tool for this.
The term percent comes from the Latin per center (per hundred) and is indicated by the sign "%" , or simply "pct" or "percent". In mathematics, a percentage is a number in the fraction of 100.
American people say percent, British people prefer to use per cent.
Percentages for solutions
A percent does not always have to indicate a few hundredths of the whole. This way, solutions are also shown in percentages. A physiological salt solution is, for example, referred to as a solution of 0.9% kitchen salt. This 0.9% means that the solution contains 0.9 grams of salt per 100 mL (= 100 grams). The percentage here therefore refers to the weight.
The volume percentage often states the addition: "vol", then we get for example: 14% vol or 14 vol%.
A percentage point, also written as %-point, is used to indicate the absolute difference between values expressed as a percentage.
A percent is therefore a hundredth part, while a percentage point is a unit of account that expresses the change of a percentage.
If the interest on your savings account rises from 2% to 3%, you can express this as "an increase of 50% of the old interest rate", or as "an increase of 1 percentage point" (which is 1% of the whole). An "increase of 1%" is not clear, because it could indicate an increase of 1% of 2 (0.02) which brings the total to 2.02% instead of 3%.
1 per mille is 1 thousandth part, the word per mille also means "per thousand". A per mille is noted as ‰, such as the percent (%) but with 3 "zeros" instead of 2. Here, 1 per mille = 0.1%.
For more information on percents click here: Wikipedia