Percentage Change Formula

Last Updated : 10 Jan, 2024

Mathematics with its spread fields to cover every method of calculation under its different branches. The branches of mathematics as arithmetic, geometry, algebra, exponential, etc have their own methods and formulas for the means of calculation.

The percentage is also one of the branches of mathematical calculation methods which expresses the numbers in the fraction of 100. The percentage is about the study of ratios. It is mathematically symbolized by the sign ‘%’. It does not have any unit of measurement for its expression.

Percentage change formula

Percentage change can be understood as a derived value obtained by the course of increase or decrease in the initially estimated value of something. The derived value obtained after the calculation is determined as the value of percentage change.

Generally, two different forms of percentage change are studied viz. percentage increase and percentage decrease.

The percentage increase is the derived number in which the new value obtained is increased than that of the initial value by a certain percent.
The percentage decrease is the derived number in which the new value obtained is decreased than that of the initial value by a certain percent.

Percentage increase and percentage increase formula

The percentage increase is the rise in the value of an item with a certain percentage. The final value is found to be bigger than the initial value of the particular item. The percentage increase value is calculated with the help of the percentage increase formula.

In the percentage increase formula, the increased value is determined by dividing the difference of the values by the initial value and multiplying by 100. The final solution or figure is given in the form of a percent (%).

Mathematically the formula for percentage increase is represented as

Percentage Increase = $\frac{Final value - Initial value}{Initial value}$ ×100

Calculating percentage increase

For calculating the percentage increase using the percentage increase formula following steps are followed:

Step 1: Find the difference between the final value and the initial value.

=> Final value – initial value

Step 2: Divide the differential value with the initial value.

=> Final value – Initial value/ initial value

Step 3: Multiply the product of previous steps by 100 to get the value in percentage.

=> Percentage Increase = $\frac{Final value - Initial value}{Initial value}$ ×100

Percentage decrease and percentage decrease formula

The percentage decrease is the drop in the value of an item with a certain percentage. the final value is lower than the estimated initial value. The percentage decrease value is calculated with the help of the percentage decrease formula.

In the percentage decrease formula, the decreased value is determined by dividing the difference of the values by the initial value and multiplying by 100. The calculated value is given in the form of a percent (%).

Mathematically the formula for percentage decrease is represented as

Percentage Decrease = $\frac{Initial\ value - Final\ Value}{Initial\ value}$ × 100

Calculating percentage decrease

For calculating the percentage decrease using the percentage decrease formula following steps are followed:

Step 1: Find the difference between the final value and the initial value.

=> Final value – initial value

Step 2: Divide the differential value with the initial value.

=> Final value – Initial value/ initial value

Step 3: Multiply the product of previous steps by 100 to get the value in percentage.

=> Percentage Decrease = $\frac{Final value - Initial value}{Initial value}$ × 100

Sample Problems

Question 1: What is the percentage change from 14000 to 16000?

Solution:

Given:

The initial value is 14000

The final value is 16000

As the final value is greater than the initial value percentage has increased.

We have,

Percentage increase = $\frac{Final value - Initial value}{Initial value}$ ×100

=> (16000 – 14000/14000) × 100

=> 14.28%

Question 2: What is the percentage change from 4000 to 5000?

Solution:

Given:

The initial value is 4000

The final value is 5000

As the final value is greater than the initial value percentage has increased.

We have,

Percentage increase = $\frac{Final value - Initial value}{Initial value}$ × 100

=> (5000 – 4000/4000) × 100

=> 25%

Question 3: What is the percentage change from 300 to 500?

Solution:

Given

The initial value is 300

The final value is 500

As the final value is greater than the initial value percentage has increased.

Percentage increase = $\frac{Final value - Initial value}{Initial value}$ × 100

=> (500 – 300/300) × 100

=> 66.67%

Question 4: What is the percentage change from 50 to 25?

Solution:

Given:

The initial value is 50.

The final value is 25.

As the initial value is greater than the final value percentage has decreased.

Percentage Decrease = $\frac{Initial value - Final Value}{Initial value}$ × 100

=> (50 – 25/50) × 100

=> 50%

Question 5: What is the percentage change from 150 to 100?

Solution:

Given:

The initial value is 150.

The final value is 100.

As the initial value is greater than the final value percentage has decreased.

Percentage Decrease = $\frac{Initial value - Final Value}{Initial value}$ × 100

=> (150 – 100/150) × 100

=> 33.3%

Question 6: What is the percentage change from 3500 to 2500?

Solution:

Given:

The initial value is 3500.

The final value is 2500.

As the initial value is greater than the final value percentage has decreased.

We have,

Percentage Decrease = $\frac{Initial value - Final Value}{Initial value}$ × 100

=> (3500 – 2500/3500) × 100

=> 28.5%

Question 7: What is the percentage change from 120 to 200?

Solution:

Given:

The initial value is 120.

The final value is 200.

As the initial value is greater than the final value percentage has decreased.

Percentage Decrease = $\frac{Initial value - Final Value}{Initial value}$ × 100

=> (200 – 120/200) × 100

=> 40%