# Calculate Percentage Difference

## How To Calculate Percentage Difference

Percentages are used to express how large or small one quantity is relative to another quantity. The first quantity usually represents a part of, or a change in, the second quantity. For example, an increase of \$0.15 on a price of \$2.50 is an increase by a fraction of 0.15/2.50 = 0.06. Expressed as a percentage, this is therefore a 6% increase. While percentage values are often between 0 and 100 there is no restriction and one may, for example, refer to 111% or −35% in complex calculation of percentage.

Examples:

A shop keeper sells and earns profit that is expressed proportionate to purchase price like:

Example 1:

Item A:

Purchase price = \$100

Sale Price = \$125

Profit = \$25

Profit percentage = 25%

Example 2:

Item B:

Purchase price = \$100

Sale Price = \$95

Profit = \$-5

Profit percentage = -5% (Loss)

Example 3:

Item C:

Purchase price = \$100

Sale Price = \$250

Profit = \$150

Profit percentage = 150%

Examples how to calculate percentage difference

If you want find the different between percent Z and percent Y you should

(Z-Y)/Z x100.

Example 1:

We want to know the  percentage difference between \$30 and \$80

30 minus 80 divided 30 multiplied by 100

(30\$-80\$) / 30 x 100 or 1.666666666666667 x 100 = 1.666666666666667%

Example 2:

Example 2:

We want to know the  percentage difference between 75% and 125%

125% minus 75% divided 75% multiplied by 100

(125-75) / 75 x 100 or  0.6666666666666667 x 100 = 66.66666666666667%

To calculate percentage is not only a mathematical trick, we must understand its application in our day to day routine. While discussing percentage we often come across increase or decrease in percentage. This especially stands prominent while carrying out analysis to reach out logical conclusion. Sometimes due to inconsistent usage, it is not always clear from the context what a percentage is relative to. When speaking of a “10% rise” or a “10% fall” in a quantity, the usual interpretation is that this is relative to the initial value of that quantity which is called percentage difference. For example, if an item is initially priced at \$200 and the price rises 10% (an increase of \$20), the new price will be \$220. Note that this final price is 110% of the initial price (100% + 10% = 110%). Generally percentages of one kind of quantity can be simply added or difference between them calculated give fairly accurate result, however altering basic type of quantities can lead to error.

### Some other examples of how to calculate percentage difference:

• An increase of 100% in a quantity means that the final amount is 200% of the initial amount (100% of initial + 100% of increase = 200% of initial); in other words, the quantity has doubled.
• An increase of 800% means the final amount is 9 times the original (100% + 800% = 900% = 9 times as large).
• A decrease of 60% means the final amount is 40% of the original (100% − 60% = 40%).
• A decrease of 100% means the final amount iszero (100% − 100% = 0%).

Another illustration given below will mark the percentage difference:

An industrialist announces 15% increase in weekly wages of its employees drawing \$200 per week. After a month he owner withdraws the privilege publishes sad news of decreasing 15% weekly wages for same employees. What weekly salary will employees be drawing in both cases ?

Solution:

Weekly salary = \$200

Increase (15%)= \$200/100*15=\$30

Increased salary=\$200+\$30=\$230

An employee would be entitled to draw \$230 per week with increase of 15%.

Now see the decrease:

New weekly salary = \$230

Decrease (15%)=\$230/100*15=\$34.5

Revised salary=\$230-\$34.5=\$195.5

An employee would be entitled to draw \$195.5 per week with decrease of 15%.

From this example we can understand behavior of percentage calculation with reference to change in quantity i.e. increase and decrease.

In general, a change of X percent in a quantity results in a final amount that is  100+X  percent of the original amount (equivalently, 1+ 0.01 X times the original amount). This goes a bit farther and takes jumps towards understanding in terms of economics.

You ca easy calculate percentage difference with our percentage different calculator.