Percentage change is a measure of the relative difference between two values. The formula for calculating percentage change is:

Percentage change = (difference / original value) *** 100**, where

- Difference = New value - Original value.
- Original value is the starting point.
- Proportion of change = Difference / Original value.
- Percentage change = Proportion *
**100.**

Imagine you have **10 candies** and you get 5 more, so now you have **10 + 5 = 15** candies.

- Difference = New value
**(15)**- Original value**(10) = 15 - 10 = 5.** - Original value is
**10 candies.** - Proportion of change = Difference
**(5)**/ Original value**(10) = 0.5.** - Percentage change = Proportion
**(0.5) * 100 = 50%.**

So, the increase in the number of candies is **50%.**

Percentage change is useful in a variety of contexts, including:

**Personal finance:**To track the change in the value of investments over time, such as stocks or bonds.**Business:**To track sales growth over time, or to compare market share of different products.**Economics:**To track changes in macroeconomic indicators such as inflation or unemployment rates over time.

Here are some examples example problems that involve calculating percentage change:

**Example 1 - **An item that was originally priced at **$100** is now on sale for **$80**. What is the percentage decrease in price?

**Answer:** The difference is **$100 - $80 = $20**, and the percentage change is

** ($20 / $100) * 100 = 20%.**

**Example 2 - **A stock was originally priced at **$50** per share, and now it is priced at **$60** per share. What is the percentage increase in price?

**Answer: **The difference is **$60 - $50 = $10**, and the percentage change is **($10 / $50) * 100 = 20%.**

**Example 3 - **A product was originally produced in **100 units**, and now it is produced in **120 units**. What is the percentage increase in production?

**Answer: **The difference is **120 - 100 = 20**, and the percentage change is **(20 / 100) * 100 = 20%.**

**What you will learn from this article - **

- Understanding Percentage Change Formula
- Calculating Percentage Change: Detailed Examples
- Overcoming Common Challenges in Percentage Change Calculation
- Applying Percentage Change in Various Scenarios

The percentage change formula is used to calculate the difference between two values as a percentage of the original value.

This can be useful when comparing data over time or when comparing different items. To calculate the percentage change, you first need to subtract the original value from the new value. Then, you divide that difference by the original value and multiply by 100 to get the percentage change.

The formula for percentage change is as follows:

*% Change = (New Value - Original Value) / Original Value x 100*

For example, if the price of a stock was **$50** and it has now increased to **$60**, the percentage change would be: % Change = **(60 - 50) / 50 x 100 = 20%**. This means that the stock has increased by **20%** in value.

It's important to note that the percentage change can be positive or negative. A positive percentage change indicates an increase in value, while a negative percentage change indicates a decrease in value.

It's also important to note that the percentage change can be used to compare different items or data sets. For example, if you wanted to compare the growth of two companies, you could calculate the percentage change in their revenue over the past year.

The percentage change formula is a way to express the difference between two values as a percentage of the original value, it can be positive or negative and it is used to compare different items or data sets over time.

**Calculating the percentage change in the value of a stock**

Let's assume the original value of the stock is **$50** and the new value is **$60**. The difference between the new value and the original value is **$60-$50 = $10.**

To find the percentage change, divide the difference by the original value and multiply by 100: **($10/$50) x 100 = 20%**. The stock has increased by **20%** in value. Calculating the percentage change in the price of a product:

**Calculating the percentage change in the Price of the Product **

Let's assume the original price of the product is **$100** and the new price is **$90**. The difference between the new price and the original price is **$90-$100 = -$10**.

To find the percentage change, divide the difference by the original price and multiply by 100: **(-$10/$100) x 100 = -10%**. The price of the product has decreased by 10%

**Calculating the percentage change in the number of customers**

Let's assume the original number of customers is 100 and the new number is **120.** The difference between the new number and the original number is **120-100 = 20.** To find the percentage change, divide the difference by the original number and multiply by 100: **(20/100) x 100 = 20%**. The number of customers has increased by **20%**

**Calculating the percentage change in the height of a building**

Let's assume the original height of the building is **100** meters and the new height is 90 meters. The difference between the new height and the original height is **90-100 = -10**. To find the percentage change, divide the difference by the original height and multiply by **100: (-10/100) x 100 = -10%.** The height of the building has decreased by **10%**.

**Calculating the percentage change in the weight of a package** Let's assume the original weight of the package is **5 kilograms** and the new weight is **5.5 kilograms**. The difference between the new weight and the original weight is **5.5-5 = 0.5.** To find the percentage change, divide the difference by the original weight and multiply by **100: (0.5/5) x 100 = 10%.** The weight of the package has increased by **10%**.

It is important to know whether a percentage change is an increase or a decrease and what the sign of the percentage change represents. A positive percentage change represents an increase and a negative percentage change represents a decrease.

**Example:**

The price of a product increased from **$100** to **$120**. What is the percentage change in the price of the product?

**Solution:**

- The difference between the new price (
**$120**) and the original price ($100) is**$120-$100 = $20.** - To calculate the percentage change, divide the difference
**($20)**by the original price**($100)**and multiply by**100: ($20/$100) x 100 = 20%.**

**-: The price of the product has increased by 20%.**

The base value, which is the original value, can greatly affect the calculation of percentage change. A small change in a large base value will result in a smaller percentage change than the same change in a small base value.

**Example**:

The value of a stock increased from **$50 to $60** and then decreased to **$55**. What is the percentage change in the value of the stock?

**Solution**:

The stock increased from **$50 to $60**, resulting in a change of **$10.**

- The stock then decreased from
**$60 to $55**, resulting in a change of**-$5.** - To calculate the percentage change, divide the change by the original value and multiply by
**100** - For the first change:
**($10/$50) x 100 = 20%**. This means the stock increased by**20%.** - For the second change:
**($5/$60) x 100 = -8.33%.**

**-: This means the stock decreased by 8.33%.**

Before calculating the percentage change, it is important to make sure the units of the original value and the new value are the same. For example, if the original value is in dollars and the new value is in euros, the values should be converted to the same unit.

**Example**:

The height of a building increased from **100 meters to 120 feet**. What is the percentage change in the height of the building?

**Solution:** First, the units should be converted to the same unit, in this case, meters. **120 feet** is equivalent to **36.58 meters**.

The difference between the new height and the original height is **36.58-100 = -63.42**. To find the percentage change, divide the difference by the original height and multiply by **100**: ** (-63.42/100) x 100 = -63.42%. **The height of the building has decreased by

Percent is often confused with percentage points. For example, a change from **10% to 20% is a 100%** increase, not a **10% increase**.

**Example: **

The interest rate increased from **10% to 20%.** What is the percentage change in the interest rate?

**Solution: **

- The difference between the new interest rate (
**20%**) and the original interest rate**(10%) is 20%-10% = 10**percentage points. - To calculate the percentage change, divide the difference (
) by the original interest rate (**10 percentage points****10%**) and multiply by**100: (10/10) x 100 = 100%.**

**-: The interest rate increased by 100%.**

The result of the calculation of percentage change should be multiplied by **100** to convert the decimal to a percentage.

**Example:**

The price of a product increased from **$100 to $110**. What is the percentage change in the price of the product?

**Solution**

The difference between the new price and the original price is **$110-$100 = $10.** To find the percentage change, divide the difference by the original price and multiply by **100 **** ($10/$100) x 100 = 10%. **The price of the product has increased by

**Not considering the time interval**

Percentage change is usually calculated over a specific time interval, such as a year or a quarter. It is important to make sure the time interval is clear and consistent when calculating percentage change.

**Example:**

The number of customers increased from **100 to 120** in one year. What is the average annual percentage change in the number of customers?

**Solution:**

The difference between the new number and the original number is **120-100 = 20**. To find the average annual percentage change, divide the difference by the original number and the time interval and multiply by **100**

*(20/100) x 100/1 = 20%.*

The average annual percentage change in the number of customers is **20%**.

**Rounding errors**

Rounding can introduce errors into the calculation of percentage change. It is important to carry out intermediate calculations to sufficient precision before rounding the final result.

**Example:**

The value of a stock increased from **$100 to $110** and then decreased to **$105**. What is the percentage change in the value of the stock?

**Solution:**

- The stock increased from
**$100 to $110**, resulting in a change of**$10**. - The stock then decreased from
**$110 to $105**, resulting in a change of**-$5**. - To calculate the percentage change, divide the change by the original value and multiply by
**100**: - For the first change:
**($10/$100) x 100 = 10%**. This means the stock increased by**10%**. - For the second change:
**($5/$110) x 100 = -4.54%.**

-: **This means the stock decreased by 4.54%.**

**Q1. What is the percentage change in the value of a bond over a year?**

**Example:** A bond increased from **$100 to $105** over a year.

The percentage change in the value of the bond is **(105-100)/100 x 100 = 5%.**

**Q2. What is the percentage change in the value of a mutual fund over a year?**

**Example: **A mutual fund increased from **$50 to $55** over a year. The percentage change in the value of the mutual fund is **(55-50)/50 x 100 = 10%.**

**Q3. What is the percentage change in the value of a real estate property over a year?**

**Example:** A real estate property increased from **$200,000 to $220,000** over a year. The percentage change in the value of the property is **(220,000-200,000)/200,000 x 100 = 10%.**

**What is the percentage change in the Gross Domestic Product (GDP) over a year?**

**Example: **The GDP increased from **$20 trillion to $21 trillion** over a year. The percentage change in the GDP is **(21-20)/20 x 100 = 5%.**

**What is the percentage change in the unemployment rate over a year?**

**Example**: The unemployment rate decreased from **8% to 7%** over a year. The percentage change in the unemployment rate is **(8-7)/8 x 100 = 12.5%.**

**What is the percentage change in the inflation rate over a year?**

**Example: **The inflation rate increased from **2% to 3%** over a year. The percentage change in the inflation rate is **(3-2)/2 x 100 = 50%**.

**What is the percentage change in the operating expenses of a company over a quarter?**

**Example:** The operating expenses of a company decreased from **$500,000 to $450,000** over a quarter. The percentage change in the operating expenses is **(500,000-450,000)/500,000 x 100 = 10%.**

**What is the percentage change in the profit margin of a company over a quarter?**

**Example:** The profit margin of a company increased from **8% to 9%** over a quarter. The percentage change in the profit margin is **(9-8)/8 x 100 = 12.5%.**

**What is the percentage change in the return on investment (ROI) of a company over a year?**

**Example: **The ROI of a company increased from **10%** to **12%** over a year. The percentage change in the ROI is **(12-10)/10 x 100 = 20%.**

**What is the percentage change in the total assets of a company over a year?**

**Example: **The total assets of a company increased from **$100 million** to **$120 million** over a year.

The percentage change in the total assets is **(120-100)/100 x 100 = 20%.**

**What is the percentage change in the total liabilities of a company over a year?**

**Example: **The total liabilities of a company decreased from $50 million to **$45 million** over a year.

The percentage change in the total liabilities is **(50-45)/50 x 100 = 10%**

**What is the percentage change in the shareholders' equity of a company over a year?**

**Example**: The shareholders' equity of a company increased from **$60 million** to **$65 million** over a year.

The percentage change in the shareholders' equity is** (65-60)/60 x 100 = 8.33%.**

A. The original perimeter of the rectangle was 40 units. One side was increased from **20 units** to **20 units + 20% of 20 units = 24 units**. The other side was decreased from **20 units** to **20 units** - **10% of 20 units** = **18 units**. The new perimeter is **24 units + 18 units = 42 units**. The percentage change in the perimeter is **(42-40)/40 x 100 = 5%**.

A. The original price of a commodity was **$100**. Its supply decreased by **10%** and its demand increased by **20%**. The new price is **$100 + 20% of $100 - 10% of $100 = $108**. The percentage change in the price is **(108-100)/100 x 100 = 8%**.

A. The original revenue of a company was **$1000**. Its expenses decreased by **10%** and its sales increased by **20%**. The new revenue is **$1000 + 20% of $1000 - 10% of $1000 = $1080**. The percentage change in the revenue is **(1080-1000)/1000 x 100 = 8%.**

A. The original profit of a company was **$100**. Its revenue decreased by **10%** and its expenses increased by **20%**. The new profit is **$100 - 10% of $100 + 20% of $100 = $98**. The percentage change in the profit is **(98-100)/100 x 100 = -2%**.

A. The original mean of a set of data was **50**. One value was added to the set, increasing the mean to **55**, and another value was removed from the set, decreasing the mean to **45**. The percentage change in the mean is **(45-50)/50 x 100 = -10%**.

A. The original market share of a company was **30%**. Its competitors increased their market share by **10%** and the company launched a new product. The new market share is **30% + 10% - 10% = 30%**. The percentage change in the market share is **(30-30)/30 x 100 = 0%**.

A. The original exam scores of a student was **50**. Their scores increased in one subject to **60** and decreased in another subject to **40**. The new exam scores is **(60+40)/2 = 50. **The percentage change in the exam scores is **(50-50)/50 x 100 = 0%**.

A. The percentage increase in height is **(6-5)/5 x 100 = 20%.**

A. The percentage decrease in weight is **(200-180)/200 x 100 = 10%.**

A. The percentage increase in price is **(22-20)/20 x 100 = 10%**.

A. The percentage decrease in price is **(100-90)/100 x 100 = 10%**

A. The percentage score of the student is **80/100 x 100 = 80%**.

A. The percentage increase in sales is **(120,000-100,000)/100,000 x 100 = 20%**.

A. The percentage decrease in fuel efficiency is **(20-18)/20 x 100 = 10%**.

A. The percentage decrease in dividend yield is **(4-3)/4 x 100 = 25%.**

A. The percentage increase in savings is **(1200-1000)/1000 x 100 = 20%**

Q18. A company's profits increase from **$500,000** to **$600,000**. What is the percentage increase in profits?

A. The percentage increase in profits is **(600,000-500,000)/500,000 x 100 = 20%.**