Percentage Change Formula | Decrease, Yield, Increase

Percentage Formula

In simple terms, percent means per hundred. Whenever you have to express the number between one and zero then percentage formula is needed. Usually, the percentage is defined as the fraction of 100. The symbol for percentage is “%” and the major application of percentage is to compare or find the ratios. Here, we have given percentage formula in mathematics –

The Percentage Formula is given as,

\[\ Percentage = \frac{Value}{Total\:Value}\times 100\]

Percentage Change Formula

Whenever we find the difference between two numbers then it would be either greater or less than earlier. To compare any two values or to find the differences, we need a percentage change formula. They are named as the percentage increase or percentage decrease in mathematics. Let us discuss on each of the concepts in the next sections deeply.

Percentage change formula is

\[\ Percentage\;Change=\frac{Old\;Value-New\;Value}{Old\;Value}\times 100% \]

Percentage Decrease Formula

To find the percentage decrease, you first need to note down the numbers you are comparing. First, find the difference i.e. Decrease Value = Original number – New number. Now you have to divide the decreased value with original value and multiply the same with 100. If your final output is a negative number then this would be percent increase otherwise percent decrease. With the same technique, this is possible to calculate the percentage differences of multiple numbers.

The Percentage Decrease Formula is given as,

\[\ Percentage\;Decrease = \frac{Decrease\;in\;value}{Original\; value} \times 100 \]

Percentage Increase Formula

To find the percentage decrease, you first need to note down the numbers you are comparing. First, find the difference i.e. Increase Value = New number Original number. Now you have to divide the Increase value with original value and multiply the same with 100. If your final output is a negative number then this would be a percent decrease otherwise percent increase. The Percentage Increase Formula in mathematics is given is given as,

The Percentage Increase Formula is given as,

\[\large Percentage\;Increase=\frac{Increased\;Value}{Original\;Value}\times 100\]

Note down, the final value could be positive, negative or zero. For zero value, it means there is no change in percent at all.

Percentage Yield Formula

Every time when we are experimenting, the final value would be a little different from your predictions. In case of chemistry, this difference is popular with the name percentage yield. Take an example of the online recipe where actual ingredients with proper quantity are given. Also, it will give you a perfect idea of servings. But, the quantity may be off or extra in most of the cases. There are different reasons for the same like wrong cup measures, food spoilage, or different stove etc.

\[\ Percentage\; Yield = \frac{actual\;yield}{theoretical\;yield} \times 100\;% \]

The same concept is applicable when we do perform experiments in Chemistry lab to make a Compound. However, the experiment should be performed in ideal conditions only. Still, most of the times, there are experimental errors most of the times and your predictions would be slightly different from the actual one.

Here, is given a quick formula to calculate the percentage yield in mathematics and chemistry. When you apply this formula, make sure that actual yield value and theoretical yield values are in the same units otherwise there would be a definite error in the final value.


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