Percentage Difference Calculator: Find Percentage Increase or Decrease

What This Tool Is For

This online tool will allow you to determine the percentage difference between two different figures. At first glance this may seem relatively easy but in reality it will be useful in general situations.

Here are some examples of how the calculating of percentage difference could be beneficial:

• When comparing prices before and after a discount
• When determining how much a reading differs between two readings of the same item
• When comparing how two scores on tests differ from one another, in a percentage based system
• When performing statistical analysis and using a spreadsheet
• When verifying the accuracy of calculations you are completing manually.

Keep in mind that determining the percentage difference is different from calculating the percentage change which is only a one-way action (going from original to current) as percentage difference looks at both items to be considered on the same level and makes no assumptions about one being prior or one being future.

How the Calculator Works

You will first type a number in the first box and then a number in the second box, both being picked up immediately by the calculator, with the workings being done on your behalf, in the background.

The process involved is:

1. The two numbers will be subtracted from each other and then the absolute value of the result will be taken. (Basically will remove the negative sign if one is there).
2. The average of both numbers will then be calculated.
3. The difference of the two numbers is divided by the average of the two numbers.
4. The result multiplied by 100 is then the percentage calculated.

The results of the percentage calculated will be shown as a percentage to two decimal places and will have added lineage indicating whether the second number was a percentage increase or decrease in relationship to the first number entered.

If both numbers entered are 0 or if the average is equal to 0, the calculator will advise that the result is undefined as it is mathematically impossible to divide by; therefore, it cannot calculate the percentage.

The Percentage Difference Formula

$$\text{Diff} \% = \frac{|V_1 – V_2|}{\dfrac{V_1 + V_2}{2}} \times 100$$

Where:

• V₁ is your first number
• V₂ is your second number
• The vertical bars mean absolute value and the result is always positive
• The bottom part is the average of both numbers

Step-by-Step Example

Let’s use V₁ = 50 and V₂ = 75 as the example values.

• Substitute the values into the formula

  $$\text{Diff} \% = \frac{|50 – 75|}{\dfrac{50 + 75}{2}} \times 100$$

• Calculate the absolute difference
  

  $$|50 – 75| = |-25| = 25$$

• Calculate the average
  

  $$\frac{50 + 75}{2} = \frac{125}{2} = 62.5$$

• Divide and multiply by 100
  

  $$\frac{25}{62.5} \times 100 = \mathbf{40.00\%}$$

So the percentage difference between 50 and 75 is 40%.

The summary line states: 75 is 50% greater than 50. This line uses a slightly different method to derive this information than the previous statement. However, the percentage increase is shown (in bold) by using the average in all equations to create one consistent result.

Limitations and Disclaimer

When utilizing this tool, the below are limitations, along with disclaimers: 

• The inputs must both be numbers. Any other type of data (i.e., text, symbols, blank spaces) will not be supported, and no result will be provided for this input configuration.
• If both input values are equal to 0, the output will appear as “undefined.” A simple average of two 0’s is 0; you cannot divide a number by 0.
• The percentage difference calculator and percentage change calculator produce different results. To track how the value of something has changed over some time (older to newer), you need to use the percentage change calculator.
• The answer produced from using this calculator will always be a positive number because absolute value is used in the calculation.
• The output will be rounded to two decimal places; however, if you would like a more accurate calculation for a report or some contract, verify your calculation manually. 

When accuracy is important (reports, contracts, and financial documents), it is strongly recommended that you verify all calculated data. 

When you have two numbers and don’t understand their significance just by looking at them individually, if you look at the two together as percentages then it makes it so much easier to see what’s really going on. With this tool, you will be able to do that math in a second, see how you arrived at your answer, and save or copy it. You can use it for price comparisons, score comparisons, measuring items, etc., so now you have a fast reliable method for getting your answer.