A Percentage Change Calculator (% change calculator) will numerically quantify the change from one unit to another and show us the change as an increase or decrease.
These type of calculator are mostly used when we are presented with an “initial” and “final” value. A change declared as an increase in the amount when the change is positive and decrease in amount when the resultant value is negative of the percentage value.
When you use the percent change calculator the order of the numbers plays an important role. You have a starting and ending value or an "initial number" and a "final number." Whilst you are comparing 2 numbers you might want to use the percent difference formula and calculation
Percentage difference is basically given by: the absolute value of the change in the value, which is then divided by the average of the 2 numbers, all then multiplied by 100. We then put the percent sign, %, to declare the % difference.
Percentage Difference= |V1−V2|[(V1+V2)2]×100
For example:
What is the percentage difference between 4 and 6?
Let V1 = 5 and V2 = 7 and plug numbers into our formula
|V1−V2|[(V1+V2)2]×100|V1−V2|[(V1+V2)2]×100
=|5−7|[(5+7)2]×100
=|−2|[122]×100
=26×100=26×100
=0.333×100=33.33%difference
We can notice that if V1 = 7 and V2 = 5 we would still have a difference of 33.33% because here we are calculating a difference between two numbers and not the change from one number to another, percentage change
Example
Monica weighed 62 kg as of before the holidays. She is now 8% thinner than she was before.
How much does Monica weigh now?
62 – 8% * 62
= 62 – 4.96
= 57.04 kg
Note: Initial value – rate of decrease = final value
A decrease shown in percentage is in fact decrease which has been expressed in the form of percentage , quantity over time.
Verbal conditions such as "decrease", ", "lowering", "reduction "fall" can help one identify that here calculation of a rate of decrease has to be done.
Calculating the final value
Vf = Vi * q
Example
A smartphone costs $300.
due to the decrease in the demand, the manufacturer decides to lowers the price by 25%.
How much does the smartphone cost now?
Vf = 300 * (1 - 25/100)
= 300 * (1 - 0.25)
= 300 * 0.75
= 225
Before availing the discount, the Smartphone cost $300.
Calculating the percent change
q = 1 - Vi / Vf
Example
As given above, the Smartphone manufacturer lowers the price from $300 to $225.
What is the percentage by which the price has decreased?
q=1-225/300
=1-0.75
=0.25
There is 25% decrease from the initial price.
Particular characteristics of the percent of change
Percentage increase and decrease of the same percentage
Rather than how the popular belief goes, if the starting value increases by p % and then decreases by the same percentage, the resultant is not the starting value. This also applies when there is a decrease of p% and then an increase of the same percentage.
Example
The price of a book costing $50 increases by 10%
Vf=50⋅(1+10/100)
=50⋅(1+0,1)
=50*⋅1,1
=55
The increase of the price now has led to , the book now costing $55. We lower its price by 10%.
Vf−=55⋅(1-10/100)
=55⋅(1-0,1)
=55*⋅0,9
=49,5
The book now costs $49.5 rather than $50 as some might have expected.
Disclaimer
While every effort has been done in developing this calculator, we are not accountable for any incidental or consequential damages arising from
the use of the calculator tools on our web site. These tools serve to visitors as a free calculator tool. Please use at your own risk.
The calculations provided are just a guide. You are advised to speak to a professional financial advisor before taking any financial decision.
