We use percentages to understand statistics, make partial payments or down payments, and to determine totals when applying discounts at the store. We hear of percentages related to hiring, inflation, economic growth, and COVID-19 rates every day in the news. Whatever the need, being able to calculate percentages correctly helps us make better decisions throughout our lives.
Beyond daily life we also use percentages in professional settings such as determining employee raises, examining reports on progress or income, comparing stats from previous years or to see how the team is performing month to month. Calculating percent change and difference are helpful tools that can be used to show the big picture and make goals to improve performance over time.
In the following article, we will discuss the correct way to calculate the percentage, percentage change, and percentage difference.
What is a percentage?
A percentage or percent is a fraction of a number out of 100. Percentage denotes a piece of a total amount.
For example, 25% represents 25 out of 100, or 25 percent of the total amount. Think of it like a pie: if I give you a quarter of the pie, the percentage I gave you is 25%, and the percentage left is 75%. The two pieces put together make up 100% of the pie.
As seen above, percentages are taken “out of 100” or an amount “for every 100.”
For example, you could say either “it rained 10 days out of every 100 days” or you could say “it rained 10% of the time.”
You can also portray a percentage as a decimal.
For example, 14% could also be written as 0.14, which you can find by dividing the percentage by 100, in this case 14 divided by 100.
Otherwise, a percent is often depicted by using a percent sign or “%.”
Retailers for instance might use a sign that says, “Sale! 60% OFF” meaning deduct 60% of the total price tag.
How to calculate the percentage?
Although there are different ways to get a final calculation in the form of a percentage, the following formula is one straightforward way to figure out percentages.
1. Define the whole or total amount for what you are calculating
For example, if you want to calculate the percentage of how many days it snowed in a year, you would use the number of days in the year, 365 (unless it’s a Leap Year), as the whole amount.
2. Find the amount representing the part of the whole and divide it by the total amount
Using the previous example, let’s say that it snowed 40 days out of the 365 days of a given year. We would divide 40 by 365, which equals 0.109.
3. Multiply the value from step two by 100
Continuing with the previous example, you would multiply 0.109 by 100, which equals 10.9. After rounding, this translates to 11%. So, in a given year, it snowed 11% of the time.
Percentages are useful in comparing trends, such as snowfall per year in this example.
Problems involving in Calculating Percentage
Problems involving percentages might not always be presented as the part and the whole now what is the percentage. Some problems can be worded differently and confusing to the reader. Here are three types of percentage problems you might encounter that could potentially frustrate you.
- Calculate the partial amount
- Calculate the percentage
- Calculate the whole amount
1. Calculate the partial amount
The following question is an example of a problem that would require you to use a percentage calculation to determine the ending number: “What is 50% of 25?” Here the problem is asking for the smaller number that is a piece of the whole number. So 25 is the whole amount, and 50 is the percentage, and we want to find the part of 25 that is 50% of the whole.
Since we already have the whole number and percentage we would move to the second step listed in the previous section, “find the amount representing the part of the whole and divide it by the total amount.” However, you’ll notice you already have the percentage, so instead of dividing you will want to multiply the percentage by the whole number. For this equation, you would multiply 50% in its decimal form of 0.5, by 25. This gives you an answer of 12.5, so you could answer this problem with “12.5 is 50% of 25.”
2. Finding the percentage
Sometimes word problems are posed in a way to make the problem solver think differently. It may be something as simple as wording it differently or including or excluding words that help us know which number is the whole and which is the part. A tricky way of asking for a percentage calculation might be “What percent of 50 is 20?” In this case the whole number is 50 and the part is 20. We know that we must divide the part by the whole to reach the percentage. So, using this example, you would divide 20 by 50. This equation would give you 0.4. Multiply 0.4 by 100 to get 40, or 40%. Thus, 20 is equal to 40% of 50.
3. Calculating the whole number
Another way to pose a question using a percentage is to ask to find the whole number. For example : “60% of what is 3?” This is typically a more difficult equation to mentally comprehend, however if you use the previously mentioned formula you can calculate the answer. For this type of percentage problem, you would want to divide the whole number by the percentage given. Using the example of “60% of what is 3?”, you would divide 3 by 60% or 0.6. This would give you 5, which means that 3 is 60% of 5.
How to calculate percentage change
A percentage change is simply a value that represents the proportion of change over time. This can be comprehended as the difference between the new value and the old value divided by the old value. The percentage change formula can be applied to any number that is being measured over time, for example, the percentage increase or decrease in sales from this week compared to last week.
You can solve a percentage change by dividing the difference between the old value and the new value by the original value and then multiplying it by 100. The formula for solving a percentage change is the following:
For a percentage increase:
[(New Value – Old Value)/Old Value] x 100
For a percentage decrease:
[(Old Value – New Value)/Old Value] x 100
Take this price percentage increase for example:
A speaker set cost $100 last year but now costs $175. To determine the percentage increase of the speaker set, subtract the old price from the new price: 175 – 100 = 75. Next, divide this by the old price: 75 divided by 100 equals 0.75. You will then multiply this number by 100: 0.75 x 100 = 75, or 75%. So, the speaker set has increased in price by 75% over the past year.
A price percentage decrease is as follows: A microwave cost $100 last year but now costs only $85. To determine the percentage decrease, you would first need to subtract the new price from the old price: 100 – 85 = 15. You will then divide this number by the old price: 15 divided by 100 equals 0.15. You would then multiply this by 100: 0.15 x 100 = 15. or 15%. This means the microwave costs 15% less than it did last year.
Calculate Percentage Difference
Sometimes you will be comparing two different items, not the same item over time but two that are related to each other to see what the percent difference is. Some examples of this might be determining the percent difference between two people’s heights, or how many sales were made between two separate associates in the same month. In these examples, we can’t pick an old value as the reference number or “whole number” so we need the average between the two values. This will help us determine the percent difference between the heights or number of sales.
The following is the formula used to calculate a percentage difference:
|V1 – V2|/ [(V1 + V2)/2] × 100
In this formula, we see the difference between the two values divided by the average of the two values and finally multiplied by 100 to find the percentage difference.
One way of using this formula to determine the percent difference between the number of sales between two associates.
For example, One associate made 25 sales last week and another made 30 sales. To determine the percentage difference, you would first subtract the low value from the high value: 30 – 25 = 5. You would then determine the average number of sales among the two associates (25 + 30 / 2 = 27.5). Next divide 5 by 27.5 = 0.18. Then multiply 0.18 by 100 = 18. This means that there is an 18% difference in sales between both associates.
Calculating the percent difference, in this case, is more telling than just saying one associate did 5 more sales than the other. If the numbers were higher, for example ten times higher, 250 sales and 300 sales, we would still have an 18% difference if we do the math, but the whole number difference is 50 sales. Having a percent difference gives us a better understanding of what the normal distribution of sales might look like among most associates. If the percentage difference is over a certain threshold a manager might consider reassignment of team members to better suit the company’s needs.
