Percentage Increase
Percentage increase describes the eventual increase in the quantity in percent form. The percentage increase formula is used to compare the growth in a quantity from the initial value to its final value, over a period of time. Mathematically, this formula is represented as the difference between the final value and the initial value which is divided by the initial value and then multiplied by 100.
In this article, we will explore the concept of percentage increase and its formula. Let us learn more about the percentage increase formula in this article with the help of a few solved examples for a better understanding of the concept.
What is Percentage Increase?
Percentage increase is the difference between the final value and the initial value, expressed in the form of a percentage. To calculate the percentage we need to have the initial value and the increased (new) value. In other words, we can say that percentage increase is a measure of percent change which gives the extent to which a quantity gains magnitude, intensity, or value. If the percentage increase is a negative value, then we can say that there is a percentage decrease of the same magnitude. Let us now explore the percentage increase formula.
Percentage Increase Formula
Following the concept of percentage increase, the percentage increase formula is derived and expressed as: Percentage Increase = [(Final Value - Initial Value)/Initial Value] × 100. It should be noted that since the percentage has to be a positive quantity, we take the absolute value of the initial value. If the percentage increase is a negative value, then it is a percentage decrease. The percentage increase is the relative change in the quantity with respect to its initial value. If the percentage change is positive, then it is the percentage increase and if the percentage change is negative, it is a percentage decrease.
How to Calculate Percentage Increase?
We know that percentage increase is expressed as the difference between the final value and the initial value which is divided by the initial value and then multiplied by 100. Let us understand how to calculate percentage increase with the help of a few examples.
Example 1: The production of sugar in a firm increases from 400 tons to 700 tons after a year. Find the percentage increase in the production of sugar.
Solution: Initial value = 400 tons; Final value = 700 tons
Percentage Increase = [Final Value - Initial Value)/Initial Value] × 100
= [(700 - 400)/400] × 100 = 75%
Therefore, sugar production increased by 75%. In other words, the percentage increase in the production of sugar was 75%.
Example 2: The height of a tree increased from 10 ft to 15 ft after a year. Find the percentage increase in its height.
Solution: The initial height of the tree = 10 ft.; the final height of the tree = 15 ft.
Using the percentage increase formula,
Percentage Increase = [(Final Value - Initial Value)/Initial Value] × 100.
= [(15 - 10)/10)] × 100 = (5 /10) × 100
= 50%
Therefore, the percentage increase in the height of the tree = 50%.
Find Percentage Increase
The percentage increase formula helps in comparing how much a value has increased over time. This formula has many real-life applications like comparing the profit of a business after every year, the percentage increase in the salary of a person, the percentage increase in the production of goods, and many more. It gives us an idea about how much a quantity has increased compared to the initial value because it allows us to determine the relative scale of the increase. It shows that the percent increase between two given values is the difference between the final value and the initial value, which is expressed as a percentage of the initial value. Let us understand this with an example. Consider the profit earned by two businessmen for 2 years.
| Businessmen | Profit in 2020 | Profit in 2021 |
|---|---|---|
| Mark | $10,000 | $15,000 |
| Robert | $30,000 | $35,000 |
We can see that the profit of both businessmen increased by $5,000 in the second year. Increase in profit for Mark's business = 15000 - 10000 = $5000; Increase in profit for Robert's business = 35000 - 30000 = $5000
Does this mean that they are growing at the same rate? No, because the growth has to be compared with the initial value. We use the percentage increase formula for this. Let us calculate the percentage increase for both of them separately using the percentage increase formula: Percentage Increase = [(Final Value - Initial Value)/Initial Value] × 100.
Percentage increase of profit in Mark's business = [(15000 - 10000) / 10000] × 100 = (5000/10000) × 100 = 50%
Percentage increase of profit in Robert's business = [(35000 - 30000 / 30000) × 100 = (5000/30000) × 100 = 16.67%
It means that Mark earned more profit than Robert. It can also be expressed as the percentage increase of Mark is more than the percentage increase of Robert.
Percentage Increase Between Two Numbers
As we discussed the concept of percentage increase, let us understand how to find the increase between two numbers in percent form. We find an increase in the original number and divide it by the original number multiplied by 100 to find the percentage increase between two numbers. Mathematically, we can write the formula for the same as,
Percentage Increase Between Numbers = Increase in Number ÷ Original Number × 100
Important Notes on Percentage Increase
- The percentage increase is the difference between the final value and the initial value, expressed in the form of a percentage.
- The percentage increase formula is derived and expressed as Percentage Increase = [(Final Value - Initial Value)/Initial Value] × 100
- If the percentage change is positive, then it is the percentage increase and if the percentage change is negative, it is a percentage decrease.
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FAQs on Percentage Increase
What is Percentage Increase in Math?
Percentage increase is the difference between the final value and the initial value, expressed in the form of a percentage. In other words, it is the difference between the final value and the initial value which is divided by the initial value and then multiplied by 100.
What is the Percentage Increase Formula?
The percentage increase formula is used to compare the growth in a quantity from the initial value to its final value, over a period of time. We know that percentage increase is the difference between the final value and the initial value, expressed in the form of a percentage. Mathematically, the formula is expressed as: Percentage Increase = [(Final Value - Initial Value)/Initial Value] × 100.
How to Calculate Percentage Increase?
The percentage increase can be determined using its formula given by, Percentage Increase = [(Final Value - Initial Value)/Initial Value] × 100. We can substitute the initial and final values into the formula to find the percentage increase.
How to Calculate Percentage Increase Between Two Numbers?
To calculate the percentage increase between two numbers, we use the formula, Percentage Increase = [(Final Value - Initial Value)/Initial Value] × 100. For example, the height of an apple tree increases from 15 ft to 18 ft in a year. In order to find the percentage increase in the height of the tree, we can use the given formula and substitute the values as: Final value = 18, initial value = 15. After substituting the values in the formula, we get, [(18 - 15)/15] × 100 = (3/15) × 100 = 20%. Therefore, the percentage increase in the height of the apple tree is 20%.
How to Calculate Percentage Increase in Salary?
In order to calculate the percentage increase in the salary of a person, we use the percentage increase formula, Percentage Increase = [(Final Value - Initial Value)/Initial Value] × 100. For example, the salary of a person increases from $700 to $1050 after a year. Here, the initial value = 700, the final value = 1050. Substituting the values in the formula, Percentage Increase = [(1050 - 700)/700] × 100 = (350/700) × 100 = 50%. Therefore, the percentage increase in the salary of the person is 50%.
What is the Percentage Increase from 20 to 25?
In the given question, the percentage increase can be calculated with the help of the percentage increase formula, Percentage Increase = [(Final Value - Initial Value)/Initial Value] × 100. Here, the initial value is 20 and the final value is 25. Substituting the values in the formula, Percentage Increase = [(25 - 20)/20] × 100 = (5/20) × 100 = 25%.
What is the Difference Between Percentage Increase and Percentage Decrease?
Percentage increase is the increase in the initial value of a quantity over a period of time in percent form. On the other hand, the percentage decrease gives the decrease in the initial value over a period of time in percent form.