We often have to calculate the percentage, be it for some maths exercises, to issue an invoice or to follow the change of price … and we try to answer the question: X is what percent of Y? In this article we discuss calculating percentages and give some practical examples. It’s easy, so let’s start.
Formula: (X/Y) × 100 copy
Excel and google Spreed sheets formula
What Is a Percentage?
One percent is one hundredth. To indicate this, we use the sign x %”. So, 5 percent equals 5%, 0.05, 5/100. It's that easy! This is all very well, but most of the time we don't just use percentages.
Sometimes we want to represent the ratio between 2 numbers. For example: what is 40% of 20, or 40 hundredths of 20? If you divide 20 cookies into 100 identical pieces, then 40 of those pieces represent 40% of those 20 cookies.
Let's do the math: 40/100 * 20 = 8.
A little trick for the calculation: if you want to divide by one hundred, just move the decimal to the left two digits.
For our calculation (40/100 * 20), we could have done as follows: (40 * 20) / 100 (which amounts to the same). 40 * 20 = 800. By moving the decimal to the left 2 digits, we get 8.00. In another case, for example, you want to calculate the percentage decrease or increase of a number. If you have 10 apples and you eat 2, you will have 20% less apples, because 8 is 80% of 10. All apples together were 100%. Since we still have 80%, the number of apples has decreased by 20% (because 100 - 80 = 20).
Examples of Calculating Percentages
Example 1: VAT on prices of goods
A company fixes the net selling price of a product at 83.19 $. Consumers must pay an additional 21% VAT to the company at the time of purchase. What is 21% of 83.19? Our calculator gives a result of 17.4699, rounded to 17.47.
The gross price for the end user is therefore 83.19 + 17.47 = 100.07 $. To obtain this result, the calculator performs the following steps: 83.19 x 0.21 (corresponding to 21% as a decimal number) = 17.4699 or 83.19 x 21/100 (corresponding to 21% as a fraction) = 17.4699.
Example 2: How much has profit increased?
A starting entrepreneur made a profit of 6000 $ in the first financial year. This entrepreneur foresees a profit of 9,000 $ for the current year. Since he wants to know with what percentage his profits will have increased, he uses the percentage calculator to calculate the percentage corresponding to an increase from 6000 to 9000 $.
The entrepreneur learns that his profits have increased by 50%. However, if his new company did not develop well in the second year and his profit fell from 6,000 euros to 4,500 $, the percentage calculation will show that the company recorded a loss of 25%.
Calculating a Percentage Difference
To increase or decrease an amount by 1% means to increase or decrease this amount by a certain proportion. The percentages are calculated on a basis of 100, which is why we speak of percent.
(There are also some other bases of calculation, such as a base of 60 for an hour or a base of 24 for a day.)
To increase or decrease an amount by 1%, you must define: V1: the starting value, i.e., the basic amount that we want to increase or decrease; V2: the final value, i.e., the new amount after the increase or decrease. The formula we use to calculate the percentage of increase or decrease is: Difference (in%) = ((V2 - V1) / V1) x 100
Example of a Percentage Difference Calculation
Last month, the laptop you wanted to buy cost $ 400. Today, you find the price displayed at the store is 320 $. Compared to last month, the price of the computer has therefore changed by:
Difference (in%) = ((V2 - V1) / V1) x 100 = ((320 - 400) / 400) x 100 = (- 80/400) x 100 = - 20%