# Percentage Increase Formula

The percentage increase formula is used to compare the growth in a quantity from the initial to its final value, over a period of time, expressed in percentage. The percentage increase formula expresses the growth of a value in percentage which shows the increased value from the initial value. Let us learn more about the percentage increase formula and solve a few examples.

## What is Percentage Increase Formula?

The percentage increase formula helps in determining the difference between the increased value from the initial value. The percentage increase formula is the ratio of the increase in the quantity to its initial value multiplied by 100 and it is expressed in percentage. if there is an extreme increase in the value, the percentage will also increase accordingly. Since the percentage has to be a positive quantity, we take the absolute value of the initial value. i.e.

**Percentage increase = Quantity Increase / Initial value x 100**

For example, consider the following two businesses.

Initial Investment | Final Valuation of the Business | |
---|---|---|

Business-1 |
$10,000 | $15,000 |

Business-2 |
$30,000 | $35,000 |

We can see that both businesses increased by $5,000. 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.

Increase in business-1 = 15000 - 10000 = $5000

Increase in business-2 = 35000 - 30000 = $5000

Let us calculate the percentage increase in each of business-1 and business-2.

Percentage increase in business-1 = (5000 / |10000| ) * 100 = 50%

Percentage increase in business-2 = (5000 / |30000| ) * 100 = 16.67%

It means that the business-1 is growing more rapidly.

## Percentage Increase Formula

To calculate the percentage increase formula, we require two basic steps.

- Step 1: Calculate the difference between the two terms i.e. Increase = New Number - Original Number
- Step 2: By using the percentage increase formula, calculate the value by dividing the increased value by the original number and multiply it with 100

## Examples Using Percentage Increase Formula

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

**Solution: **

The initial value of the car = $15.

The final value of the car = $20.

The increase in the value = 20 - 15 = $5.

Using the percentage increase formula,

Percentage increase = (Increase in the height / | Initial value of the height | ) × 100

= (5 / |15|) × 100

= (5 / 15) × 100

= 33.33%

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

**Example 2: The height of a tower was increased from 30 ft to 50 ft. Find the percentage increase in the height of the tower.**

**Solution:**

The initial height of the tower = 30 ft.

The final height of the tower = 50 ft.

The increase in the height = 50 - 30 = 20 ft.

Using the percentage increase formula,

Percentage increase = (Increase in the height / | Initial value of the height | ) × 100

= (20 / |30|) × 100

= (20 / 30) × 100

= 66.67%

Therefore, the percentage increase in the height of the tower = 66.67%.

**Example 3: 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 final rent = $250

The increase in rent = 250 - 200 = $50

Using the percentage increase formula,

Percentage increase = (Increase in the height / | Initial value of the height | ) × 100

= (50/ |200|) × 100

= (50/200) × 100

= 25%

Therefore, the percentage increase in the rent is 25%

## FAQs on Percentage Increase Formula

### What is Percentage Increase Formula?

The percentage increase formula helps in determining the difference between the increased value from the initial value. The percentage increase formula is the ratio of the increase in the quantity to its initial value multiplied by 100 and it is expressed in percentage. The percentage has to always be positive, hence the absolute value of the initial value is taken into consideration.

### What is the Formula to Calculate the Percentage Increase Formula?

The formula to calculate the percentage increase is expressed in percentage and it is the ratio of the increase in values to the absolute value of the initial value. The formula is:

Percentage increase = Quantity Increase / Initial value x 100

Where, the initial value is denoted as |initial value| keeping the absolute value in mind.

### What are the Two main Steps to Calculate the Percentage Increase Formula?

The two main and basic steps required to calculate the percentage increase is:

- Step 1: Calculate the difference between the two terms i.e. Increase = New Number - Original Number
- Step 2: By using the percentage increase formula, calculate the value by dividing the increased value by the original number and multiply it with 100

### Using the Percentage Increase Formula, find the Increase in the Percentage of a Box of Berry's Starting from $20 a box to $35 a box.

Initial price = $20

Final price = $35

Increase Price = $35 - $20 = $15

Using the percentage increase formula,

Percentage increase = Quantity Increase / Initial value x 100

= (15/ |20|) × 100

= (15/20) × 100

= 75%

Therefore, the percentage increase of a box of berry's is 75%