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186 LearnersLast updated on 30 September 2025
Percentage Change
The way of expressing a number or ratio as a fraction of 100 is percentage. Percentage change is the change in the value, either increasing or decreasing. In real life, we use it to calculate the loss and profit, analyze population growth, salary increment, and so on.
What is Percentage Change?
Percentage change represents the change between the final and initial value, expressed as a fraction of 100. It is the difference between the new value and the old value divided by the old value multiplied by 100.
That is, percentage change = ((Final value - Initial value) / Initial value) × 100
The percentage change can both increase or decrease. The percentage increase is the change in percentage where the final value is greater than the initial value. The percentage decrease is the change in percentage where the final value is lesser than the initial value.
Methods to Calculate the Percentage Change
There are different methods to find the percentage change. A few of them have been discussed here.
Finding the Percentage Change Using Formula
To find the percentage change, we use the formula:
Percentage change = ((Final value - Initial value) / Initial value) × 100
For instance, the price of a jacket has increased from 50 to 65. What is the percentage increase?
To find the percentage increase, we use the formula,
Final value = 65
Initial value = 50
Percentage increase = ((Final Value – Initial Value) / Initial Value) × 100
= (15/50) × 100 = 30%
Formula for Percentage Increase:
To find the percentage increase, the formula used is:
Percentage increase = ((Final Value – Initial Value) / Initial Value) × 100
Formula for Percentage Decrease:
To find the percentage decrease, the formula used is:
Percentage decrease = ((Old Value – New Value) / Old Value) × 100
Tips and Tricks For Percentage Change
These tips and tricks help students learn and remember percentage change effectively. Here are a few pointers to master percentage change.
- Memorize the formula: The best way to calculate the percentage change is by memorizing the formula. That is, percentage change = ((Final value - Initial value) / Initial value) × 100
- Identify the initial and final value: When working on percentage change, it's important to identify the initial and final value to get the accurate report.
Common Mistakes and How to Avoid Them in Percentage Change
When calculating the percentage change, students might make few errors. In this section, we will learn a few common mistakes and ways to avoid them.
Mistake 1
Confusion with the formula
When calculating percentage change, students may use an incorrect formula. To avoid this mistake, memorize the formulas properly and understand the reason behind using each and every formula.
Mistake 2
Confusion with the base value
When calculating the percentage change, getting confused with the base value is common among students. A common mistake is using the final value instead of the initial value as the base. Always remember that the base value is the initial value and not the final value.
Mistake 3
Forgetting to multiply the result by 100
Not multiplying the result by 100 will lead to an incorrect answer. So students should not forget to multiply the decimal with 100 to get the correct answer.
Mistake 4
Misidentifying the percentage change in word problems
When working on word problems, students get confused with the increase and decrease of the percentage change. They should read the questions carefully to avoid this mistake.
Mistake 5
Not including the percentage symbol (%) in the final answer
When writing the final answer, it is important to include the percentage symbol (%). Without the symbol, the answer would be incomplete.
Percentage Change Examples
Problem 1
A jacket was originally priced at $80, but the store increased the price to $100. What is the percentage increase?
The percentage increase is 25%
Explanation
To find the percentage increase, we use the formula,
percentage change = ((Final value - Initial value) / Initial value) × 100
Here, final value = 100
Initial value = 80
So, the percentage increase = (20/80) × 100 = 25%
Problem 2
A student scored 60 marks in a test. After studying harder, they scored 75 marks in the next test. What was the percentage increase?
The percentage increase is 25%
Explanation
To find the percentage increase, we use the formula,
percentage change = ((Final value - Initial value) / Initial value) × 100
Here, initial value = 60
Final value = 75
Hence, percentage change = (15/60) × 100 = 25%
Problem 3
A car was worth $20,000 last year, but its value dropped to $15,000. What is the percentage decrease?
The percentage decrease is 25%
Explanation
We use the formula, percentage change = ((Old Value – New Value) / Old Value) × 100
Here, the old value = 20000
New value = 15000
percentage change = ((20,000 – 15,000) / 20,000) × 100 = 25%
Problem 4
A laptop was originally $1,200, but it is now on sale for $900. What is the percentage decrease?
The percentage decrease is 25%
Explanation
We use the formula, percentage change = ((Old Value – New Value) / Old Value) × 100
Here, the old value = 1200
New value = 900
percentage change = (300/1200) × 100 = 25%
Problem 5
A tenant’s rent increased from $800 per month to $880. What is the percentage increase?
The percentage increase is 10%
Explanation
We use the formula, percentage change = ((Final value - Initial value) / Initial value) × 100
Here, the initial value = 800
New value = 880
Percentage change = (80/800) × 100 = 10%
FAQs on Percentage Change
1.What is percentage change?
2.How do you calculate percentage change?
3.Where is percentage change used in real life?
4.Is the percentage change always positive?
5.Does percentage change work the same for large and small numbers?
6.What is the percentage change from 80 to 120?
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Dr. Sarita Ghanshyam Tiwari
About the Author
Dr. Sarita Tiwari is a passionate educator specializing in Commercial Math, Vedic Math, and Abacus, with a mission to make numbers magical for young learners. With 8+ years of teaching experience and a Ph.D. in Business Economics, she blends academic rigo
Fun Fact
: She believes math is like music—once you understand the rhythm, everything just flows!
