# Percentage Difference Calculator

V1
V2
Percent Difference  =  85.7143%
GENERATE WORK

## Percentage Difference - work with steps

Input Data :
V_1 = 100
V_2 = 250

Objective :
Find the percent difference between two values.

Formula

\text{% difference} = \frac{| V_1 - V_2 |}{((V_1 + V_2))/2 } \times 100

Solution :
% difference = \frac{| 100 - 250 |}{((100 + 250))/2 } \times 100

 = \frac{|-150|}{((350)/2) } \times 100

 = \frac{150}{175} \times 100

= 0.8571\times100

= 85.7143%

Percentage difference between two values 100 and 250 is 85.7143%

Percentage difference calculator uses two values, $Y_1$ and $Y_2$, either both positive or both negative real numbers, and calculate the percent difference between these numbers. It is an online mathematical tool requires two real numbers and finds the percentage difference between two real numbers in order to determine how close they are, relative to average (arithmetic mean) of these numbers.
It is necessary to follow the next steps:

• Enter two real numbers $Y_1$ and $Y_2$ in the box. These numbers need to be either both positive or both negative;
• Press the "GENERATE WORK" button to make the computation;
• Percent difference calculator will give the percentage difference between two numbers, relative to arithmetic mean of these numbers.
Input: Two real numbers. Note that these numbers need to be of the same sign;
Output: The result is a percent value, i.e. a positive real number and $\%$ after the number.

Percent Difference Formula:
The percent difference between two numbers $Y_1$ and $Y_2$ is given by the formula
$${\rm{percent\;difference}}=\Big|\frac{Y_2-Y_1}{\frac{Y_1+Y_2}{2}}\Big|\times 100\%$$

## What is Percent Difference?

The percent difference between two real numbers is percent that determines how close they are relative to average of these numbers. There are other formulas for the percent difference. For instance, the percent difference between two numbers $Y_1$ and $Y_2$ can also be calculated in the following ways:

$${\rm{percent\;difference}}=\Big|\frac{Y_2-Y_1}{{\rm min}\{Y_2,Y_1\}}\Big|\times 100\%$$
and
$${\rm{percent\;difference}}=\Big|\frac{Y_2-Y_1}{{\rm max}\{Y_2,Y_1\}}\Big|\times 100\%$$
The previous formulas require dividing by the minimum of the two numbers or the maximum of the two numbers, but we use dividing the difference between the two numbers by the average of these numbers. Thus, to find the percent difference between two numbers $Y_1$ and $Y_2$, we use the following formula
$${\rm{percent\;difference}}=\Big|\frac{Y_2-Y_1}{\frac{Y_1+Y_2}{2}}\Big|\times 100\%$$
In some cases, if one number is much greater than the other, the percent difference may not provide an acceptable result for the problem. For example, if $Y_1=1$ and $Y_2=2000$, the percent difference is $199.8001\%$. But, if we replace the second value $Y_2=2000$ by $Y_2=20,000,000$, the percent difference is still about $200\%$. This is because for the following reason: If both numbers have the same sign, then $$|Y_2-Y_1|<|Y_1+Y_2|$$ So,
$$\frac{|Y_2-Y_1|}{|Y_1+Y_2|} <1\Rightarrow \Big|\frac{Y_2-Y_1}{\frac{Y_1+Y_2}{2}}\Big|\times 100\% <200 \%$$
Hence, the percent difference is always less than $200\%$.

### How to Calculate Percent Difference?

A percent difference between two numbers $Y_1$ and $Y_2$ is the absolute value of the difference between two numbers, divided by the average of these numbers, and multiplied by $100\%$. This means,

$${\rm{percent\;difference}}=\Big|\frac{Y_2-Y_1}{\frac{Y_1+Y_2}{2}}\Big|\times 100\%$$
The percentage difference work with steps shows the complete step-by-step calculation for finding the difference between two numbers $Y_1$ and $Y_2$ with $Y_1=100$ and $Y_2=250$. For any other combinations of values of $Y_1$ and $Y_2$, just supply values and click on the "GENERATE WORK" button. The grade school students may use this percentage difference calculator to generate the work, calculate the percentage difference between any two numbers, verify the results or do their homework problems efficiently.

### Applications or Use of Percent Difference

The percent difference is useful in comparing number values that are relatively close to one another. In some experiments, results are compared, in order to derive prediction. This comparison uses a different type of analysis, percent difference or percent error. When we compare two experimental quantities, $Y_1$ and $Y_2$, neither of which can be considered the correct value, instead of these values we will use the percent difference.

### Percent Difference Practice Problems

Pracrice Problem 1: Find the percentage difference between $3$ and $17$.

Pracrice Problem 2: Two groups of mathematicians are participating in the mathematical congress. A group of geometers has $235$ people, while the group of statisticians has $218$ people. Find the percent difference in the number of these groups.

The percentage difference calculator, formula, example calculation (work with steps), real world problems and practice problems would be very useful for grade school students (K-12 education) to learn how to find how much percent difference between two numbers or quantities. This concept can be useful in manufacturing, economics, statistics, etc.