# 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. 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. Let us learn more about the percentage increase formula in this article.

## What is Percentage Increase Formula?

Before learning more about the percentage increase formula, let us understand what percentage increase means. 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. Following this concept, 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.

## 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 an example.

**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, the 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%.

## Use of the Percentage Increase Formula

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, or the percentage increase in the salary of a person, or 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.

## Examples Using Percentage Increase Formula

**Example 1: The price of Ken's toy car increased from $15 to $20. Find the percentage increase in the price using the percentage increase formula.**

**Solution: **

The initial value of the car = $15; the final value of the car = $20.

Using the percentage increase formula, Percentage increase = [(Final Value - Initial Value)/Initial Value] × 100.

= [(20 - 15) /15] × 100 = (5 /15) × 100

= (5 / 15) × 100

= 33.33%

Therefore, the percentage increase in the price of the toy car = 33.33%.

**Example 2: What is the percentage increase in the rent of a house if in the month of November it was $200 and in the month of March it was $250?**

**Solution:**

The initial rent = $200; the increased rent = $250

Using the percentage increase formula, Percentage Increase = [(Final Value - Initial Value)/Initial Value] × 100.

= [(250 - 200)/200] × 100 = (50/200) × 100

= (50/200) × 100

= 25%

Therefore, the percentage increase in the rent is 25%.

## FAQs on Percentage Increase Formula

### 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.

### 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.

### 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%.

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