## Percentage Difference calculator - Calculate the difference in percetage between two values.

#### Percentage Difference Calculator

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Difference in Percentage: | 0 |

### What are percentage and percentage difference?

A percentage is a fraction with the denominator as 100. When we express some fraction as a percentage, we express how many parts of the 100, the fraction denotes. In other words, a percentage indicates the quantity of something in terms of 100. The word ‘percent’ essentially means ‘per hundred’. The symbol for percentage is %. For example, the ratio 15/16 as a percentage is 93.75%.

The simplest way of expressing a fraction (or ratio) as a percentage is A/B = P × 100, where ‘A’ is the numerator of the fraction, ‘B’ is the denominator and ‘P’ is the percentage. In a percentage calculation, the denominator denotes the total value of a quantity, and the numerator denotes some part of the total value. The percentage simply expresses this ratio in terms of 100.

The percentage difference can be calculated for two non-identical numbers. Consider 15 and 19. We need to find the percentage difference between these two numbers. The difference between 15 and 19 is 4. Now, we need to express this 4 in the form of a percentage. We need to divide this 4 by some number to obtain a percentage value. In the case of percentage difference, we carry out the division by the number which is the average of the two given numbers. In other words, we divide 4 by 17, which is the average of 15 and 19. After performing long division, we multiply this by 100 to obtain the percentage.

### Percentage difference formula

If A = first value, B = second value, then the formula for percentage difference (P) is

$$ Percentage \; difference, \;P \; = {{|First value − second value|}\over{({{first value + second value}\over2})}} * 100 $$

$$ or, \; P = {{|A-B|}\over{({{A+B}\over2})}}*100 $$

It should be noted that the percentage difference is not the same as percentage change. The percentage difference simply compares two numbers, whereas the percentage change indicates the increase or decrease of a value over some period of time.

### Calculating percentage difference

To find the percentage difference between two numbers, consider A = 25 and B = 37.

1) The first step is to find the absolute value of the difference between the two numbers.

|A − B| = |25 − 37| = |−12| = 12

2) Next, we find the average of the two numbers. $$ ({{A+B}\over2}) = ({{25+37}\over2}) = {62\over2} = 31 $$

3) Now we divide the difference of the two numbers by the average. $$ {{|A-B|}\over{({{A+B}\over2})}} = {12\over31} = 0.3871 ≈ 0.39 $$

4) Finally, multiply the result of this division by 100 to obtain the percentage. $$ 0.39 × 100 = 39\% $$

5) Hence, the percentage difference of 25 and 32 is approximately 39%.

Note that, if the values of A and B were swapped, the percentage difference would still be the same, because, in the very first step, we consider the absolute value of the difference between the two numbers. Now consider, A = 37 and B = 25. Then,

$$ {{|37-25|}\over{({{37+25}\over2})}}*100 = {{|12|}\over{({62\over2})}} = {12\over31}*100 = 0.3871 × 100 \\ P ≈ 39\% $$

### Percentage difference and percentage change

The percentage difference is a non-directional comparison between any two given numbers. However, it can be easily confused with percentage change (that is, percentage increase or percentage decrease). Percentage growth is used to show the increase in a value by comparing the initial value and final value over some time. Percentage decrease shows the decrease in a value over a period of time by comparing the initial and final values.

$$ Percentage \; growth = {{Final \; value − initial \; value}\over{|initial \; value|}} * 100 $$

$$ Percentage \; decrease = {{initial \; value − final \; value}\over{|initial \; value|}} * 100 $$

The formula varies slightly in these two cases. Moreover, we do not consider the absolute value of the difference between the two numbers.

Percentage difference, on the other hand, is used when both the values mean the same thing. Here, one value is not older than the other value, and there is no change in the values over a period of time.

$$ Percentage \; difference = {{|First \; value − second \; value|} \over ({{first \; value + second \; value}\over2})} * 100 $$

In this formula, unlike the case of percentage growth or percentage decrease, we consider the absolute value of the difference between the two numbers. So, the position of the two values in the formula does not matter. However, a change in the position of the values in the case of percentage growth (or percentage decrease, would give a completely different interpretation altogether. A negative percentage growth essentially means a decrease in the value over some time, whereas a negative percentage growth indicates an increase in the value.

### Areas of application

We use percentages in various walks of life. When we need to compare two values, there are several measurements which can be used. Percentage difference is primarily used when the values that we are comparing are related or they mean the same thing. It is frequently used in finance and in businesses. For example, a business might need to compare the number of employees this year versus the number of employees last year. This can be done using the percentage difference. However, if the business wants to compare the old number of employees with the new number of employees, to either find an increase or decrease in the number of employees, the formula to be used would be that of percentage growth (or percentage decrease). Consider another real-life example below.

__Question:__ Jesse’s Shoes had 150 customers yesterday and 180 customers today. Moreover, today, Jesse’s Shoes had 180 customers whereas James’ Shoes had 160 customers. How would we use the percentage difference and percentage change in these two situations?

__Answer:__ First, we consider the number of customers in Jesse’s Shoes store yesterday and today. The old number of customers = 150, and new number of customers = 180. Therefore, we would need to calculate the percentage growth.

$$ Percentage \; growth = {{Final \; value − initial \; value}\over{|initial \; value|}} * 100 \\ = {{180-150}\over {|150|}}*100 \\ = {30\over150}*100 \\ = {1\over5}*100 = 20\% $$

In the next case, we compare the number of customers between the two stores today. There is no old or new value involved here. Both the numbers mean the same.

$$ Percentage \; difference = {{|First \; value − second \; value|} \over ({{first \; value + second \; value}\over2})} * 100 \\ = {{|180-160|}\over{({{180+160}\over2})}}*100 \\ = {{|20|}\over {({340\over2})}}*100 \\ = {20\over170}*100 \\ = 0.11764 × 100 \\ = 11.764 \% ≈ 12 \% $$