Percentage change is a mathematical concept that quantifies the relative increase or decrease in a value, expressed as a percentage of the original amount. It’s calculated using the formula: ((New Value – Original Value) / Original Value) × 100. This versatile tool is crucial for comparing changes across different scales in finance, economics, and various other fields.

Percentage Change Formula

The Formula used to calculate the percentage change:

Percentage Change = ((New Value – Original Value) / Original Value) × 100

Where:

• New Value is the final or current value of the quantity
• Original Value is the initial or starting value of the quantity

This formula gives you a numerical result, which is then described using appropriate percentage change words.

For example:

• If the result is 25%, you might describe this as a “moderate increase”
• If the result is -30%, you might describe this as a “moderate decrease”

The choice of words depends on the magnitude of the change and sometimes on the context of the situation being described.

How to Calculate Percentage Change?

To calculate percentage change, follow these steps:

• Determine the original value and the new value.
• Subtract the original value from the new value to get the difference.
• Divide the difference by the original value.

Multiply the result by 100 to convert it to a percentage.

The formula is:

Percentage Change = ((New Value – Original Value) / Original Value) × 100

Here’s a step-by-step breakdown:

Identify the values:

• Original Value
• New Value

Calculate the difference:

• Difference = New Value – Original Value
• Divide the difference by the original value:
• (New Value – Original Value) / Original Value
• Multiply by 100 to get the percentage:
• ((New Value – Original Value) / Original Value) × 100

Percentage Change Word Problems

Problem 1: The price of a book increased from $20 to $25. What is the percentage change?

Solution:

• Original Value = $20
• New Value = $25

Percentage Change = ((25 – 20) / 20) × 100

= (5 / 20) × 100 = 0.25 × 100 = 25%

The price increased by 25%.

Problem 2: A company’s workforce decreased from 500 to 450 employees. Calculate the percentage change. 

Solution:

• Original Value = 500
• New Value = 450

Percentage Change = ((450 – 500) / 500) × 100

= (-50 / 500) × 100 = -0.1 × 100 = -10%

The workforce decreased by 10%.

Problem 3: A student’s test score improved from 75 to 90. What is the percentage increase?

Solution:

• Original Value = 75
• New Value = 90

Percentage Change = ((90 – 75) / 75) × 100

= (15 / 75) × 100 = 0.2 × 100 = 20%

The test score increased by 20%.

Problem 4: The population of a town grew from 50,000 to 55,000. Calculate the percentage change. 

Solution:

• Original Value = 50,000
• New Value = 55,000

Percentage Change = ((55,000 – 50,000) / 50,000) × 100

= (5,000 / 50,000) × 100 = 0.1 × 100 = 10%

The population increased by 10%.

Problem 5: A car’s value depreciated from $15,000 to $12,000. What is the percentage decrease? 

Solution:

• Original Value = $15,000
• New Value = $12,000

Percentage Change = ((12,000 – 15,000) / 15,000) × 100

= (-3,000 / 15,000) × 100 = -0.2 × 100 = -20%

The car’s value decreased by 20%.

Problem 6: A stock price rose from $50 to $75. Calculate the percentage change. 

Solution:

• Original Value = $50
• New Value = $75

Percentage Change = ((75 – 50) / 50) × 100

= (25 / 50) × 100 = 0.5 × 100 = 50%

The stock price increased by 50%.

Problem 7: The temperature dropped from 25°C to 18°C. What is the percentage change? 

Solution:

• Original Value = 25
• New Value = 18

Percentage Change = ((18 – 25) / 25) × 100

= (-7 / 25) × 100 = -0.28 × 100 = -28%

The temperature decreased by 28%.

Problem 8: A company’s revenue grew from $1 million to $1.5 million. Calculate the percentage increase. 

Solution:

• Original Value = $1,000,000
• New Value = $1,500,000

Percentage Change = ((1,500,000 – 1,000,000) / 1,000,000) × 100

= (500,000 / 1,000,000) × 100 = 0.5 × 100 = 50%

The revenue increased by 50%.

Problem 9: The number of daily users of an app decreased from 10,000 to 8,500. What is the percentage change? 

Solution:

• Original Value = 10,000
• New Value = 8,500

Percentage Change = ((8,500 – 10,000) / 10,000) × 100 = (-1,500 / 10,000) × 100

= -0.15 × 100 = -15%

The number of daily users decreased by 15%.

Problem 10: A athlete’s personal best time improved from 12 seconds to 11.4 seconds. Calculate the percentage change. 

Solution:

• Original Value = 12
• New Value = 11.4

Percentage Change = ((11.4 – 12) / 12) × 100

= (-0.6 / 12) × 100

= -0.05 × 100 = -5%

The athlete’s time decreased by 5%, which is an improvement in performance.

Read More:

• Percentage Increase
• Percentage Decrease
• Ratios and Percentages

Percentage Change Practice Problems

P1. Here are 10 unsolved Problems for you to practice calculating percentage change:

P2. The price of a smartphone decreased from $800 to $720. What is the percentage change?

P3. A company’s annual profit increased from $2 million to $2.6 million. Calculate the percentage change.

P4. The number of students in a school dropped from 1,200 to 1,140. What is the percentage decrease?

P5. An athlete’s weight increased from 70 kg to 73.5 kg during off-season training. Calculate the percentage change.

P6. A country’s GDP grew from $1.2 trillion to $1.38 trillion. What is the percentage increase?

P7. The average daily temperature in a city fell from 28°C to 22°C. Calculate the percentage change.

P8. A car’s fuel efficiency improved from 30 miles per gallon to 34.5 miles per gallon. What is the percentage increase?

P9. The population of endangered species in a national park decreased from 500 to 425. Calculate the percentage change.

P10. A company’s stock price rose from $45 to $58.50 per share. What is the percentage increase?

Frequently Asked Questions

What does a negative percentage change indicate?

A negative percentage change indicates a decrease in value.

If something doubles, what is the percentage increase?

When something doubles, the percentage increase is 100%.

Can percentage change ever be more than 100%?

Yes, percentage increase can exceed 100% if the new value is more than double the original value.

What is the formula for percentage change?

Percentage Change = ((New Value – Original Value) / Original Value) × 100

If the percentage change is 0%, what does it mean?

A 0% change means the value remained the same; there was no increase or decrease.