Percentage Increase describes the eventual increase in the quantity of any quantity or value. The percentage increase formula is used to compare any value at two specific points that change according to time. The percentage increase formula is calculated as the difference between the final value and the initial value the difference is then divided by the initial value and then multiplied by 100 to get the percentage increase.
In this article, we will discuss percentage increase in detail including the percentage increase formula, how to calculate percentage increase, solved examples, and some practice problems on it.
What is a Percentage Increase?
The percentage increase is defined as the difference between the final value and the initial value, expressed as a percentage. For calculating the percentage increase percentage formula is used and the initial value and the final value are also required.
For the negative value of the percentage increase, we say that there is a percentage decrease of that same magnitude. Now, the percentage increase formula is expressed below.
A percentage Increase is a rise in the value by a certain percentage. That means the value of the item has been increased by the initial value estimated in a certain period of time.
The percentage increase is calculated by using the percentage increase formula. And, the final figure or value is obtained in percent.
Percentage Increase = {(Final Value – Initial Value) / Initial Value} ×100
The percentage increase formula is the way of calculating the increase in value of the item by a certain percentage from its previous value. Percentage increase means the increase in the value of a product, item, or any such thing concerning its 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 increases with the help of a few examples.
The percentage increase formula is derived from these steps:
Step 1: Calculate the difference between the final value and the initial value.
Percentage Increase = Final value – Initial value
Step 2: Dividing the obtained value by the initial value and multiply it by 100, to obtain the number in percent.
Percentage Increase = {(Final Value – Initial Value) / Initial Value} × 100
Percentage increase formula is the method to calculate the increased value in a percent. It is done by dividing the difference between the initial value and the final value of the initial value and multiplying by 100.
Example: In a factory production increases from 600 tons to 900 tons in a year. Find the percentage increase in production.
Solution:
Initial value = 600 tons
Final value = 900 tons
Percentage Increase = [(Final Value – Initial Value)/Initial Value] × 100
= [(900 – 600)/600] × 100
= 50%
Thus, production increased by 50%.
Percentage Increase Between Two Numbers
Percentage increase between two numbers is very useful for solving various problems in mathematics. Percentage increase between two numbers is defined as the increase in a number from a previous number, i.e. if a number is increased to a finite value then its percentage increase is calculated by the following formula:
Percentage Increase between Numbers = (Increase in Number / Original Number) × 100
Percentage Increase vs Percentage Decrease
Some of the common differences between percentage increase and decrease are:
| Aspect |
Percentage Increase |
Percentage Decrease |
| Definition |
An increase in value by a certain percentage |
A decrease in value by a certain percentage |
| Representation |
Positive change |
Negative change |
| Impact on Value |
Value rises |
Value declines |
| Direction on a Graph |
Upward trend |
Downward trend |
| Interpretation |
Indicates growth or improvement |
Indicates decline or deterioration |
| Context |
Generally viewed positively |
Generally viewed negatively |
| Example |
If a product’s price increases by 20%, it is a 20% increase from its original price |
If a product’s price decreases by 15%, it is a 15% decrease from its original price |
| Calculation Formula |
Percentage Increase =(New Value − Original Value)/Original Value × 100 |
Percentage Decrease = (Original Value − New Value)/Original Value × 100 |
Read More: Percentage Decrease
Percentage Increase Calculator
Percentage Increase Calculator is a tool for figuring out how much something has grown in percentage terms. Percentage increase is the ratio, expressed as a percentage, by which a value has grown compared to its original amount.
Check: Percentage Increase Calculator – Free Online Calculator
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Solved Examples on Percentage Increase
Example 1: What is the percentage increase in the rent of a house if in the month of August rent is 3000 rupees and in the month of May rent was 2000?
Solution:
Initial rent = 2000; Increased rent = 3000
Percentage Increase = [(Final Value – Initial Value)/Initial Value] × 100.
= [(3000 – 2000)/200] × 100 = (1000/200) × 100
= (1/2) × 100
= 50%
Thus, Percentage increase in rent is 50%
Example 2: What is the percentage increase from 120 to 200?
Solution:
Given:
Initial value is 120.
Final value is 200.
Percentage Increase = {(Final Value – Initial Value) / Initial Value} × 100
= (200 – 120/120) × 100
= 66.67%
Example 3: What is the percentage increase in the fees of a student from class 9 to class 10 if the fees of class 9 are 1000 and of the class are 1200?
Solution:
Increase in fees = fees of class 10 – fees of class 9
= 1200 – 1000
= 200
Fees of class 9 = 1000
Percentage Increase = (Increase in fees ⁄ fees of class 9) × 100
= (200 ⁄ 1000) × 100
= 20%
Thus, there is a 20% increase in the amount of rent.
Example 4: What is the percent change from 5 to 6?
Solution:
Percentage change is percentage increase as the number rises from 5 to 6.
Step 1: Increase = 6-5 = 1
Step 2: Percentage Increase = 1/5 = 0.2 × 100
= 20%
Thus, from 5 to 6, percentage increase is 20%.
Practice Problems on Percentage Increase
Problem 1: The population of a town increased by 8% over the last year. If the original population was 50,000, what is the new population?
Problem 2: A company’s revenue increased by 15% in the last quarter. If the revenue in the previous quarter was $1,000,000, what is the new revenue?
Problem 3: The price of a product increased by 12% from last year. If the original price was $80, what is the new price?
Problem 4: An investment grew by 6% over the past month. If the original investment was $10,000, what is the new value of the investment?
Summary – Percentage Increase
The concept of percentage increase involves calculating how much a value has grown from its original amount, expressed as a percentage. To find the percentage increase, you subtract the initial value from the final value, divide the result by the initial value, and then multiply by 100. This formula helps determine the extent of increase in terms of percentage. For instance, if factory production rises from 600 to 900 tons, the percentage increase would be 50%. This calculation is crucial for understanding growth or improvement in various contexts, such as business, economics, and everyday scenarios. Conversely, if the result is negative, it indicates a percentage decrease, representing a reduction in value.
FAQs on Percentage Increase
Define percentage increase.
Percentage increase is 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 a percentage increase?
Percentage increase is determined by the formula given by,
Percentage Increase = [(Final Value – Initial Value)/Initial Value] × 100.
In this formula we put the initial and final values into the formula and the percentage increase is calculated.
What is a 20% increase?
A 20% increase refers to a situation where a quantity, value, or amount grows by 20% compared to its original value.
How to calculate the salary increase percentage?
Salary increase percentage is calculated by the given formula:
Percentage Salary Increase = (Increase in Salary / Initial Salary) × 100
How do you calculate a 5% increase?
To calculate a 5% increase, you can multiply the original value by 1.05.
What is the difference between percentage increase and percentage decrease?
Percentage increase is increase in the initial value of any quantity in a specific period of time expressed in percentage. Whereas, the percentage decrease is decrease in the initial value of any quantity in a specific period of time expressed in form of percentage.
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