## What Is the Relative Change Formula?

**The relative change formula is used to compare the change between two quantities in comparison with the initial value.** Relative change helps us understand the extent by which the original value has changed. It is a ratio that describes the size of the absolute change in comparison to the initial value.

Suppose that an initial value A changes to a new value B, then we define the absolute change as

**Absolute change **$=$** Final Value **$-$** Initial Value**

The absolute change is the actual numerical change (the value showing the actual increase or decrease in the original value). It has a unit.

**Relative change takes into account the initial value you started with. It helps you compare the change with respect to the original value.**

Divide the absolute change by the initial value to get the relative change formula.

**Relative change** $= \frac{Final \;Value \;-\; Initial \;Value}{Initial \;Value} = \frac{Absolute\; change}{Initial \;Value}$

Note that the “relative change” expressed as a percentage makes it easier to interpret and understand. Thus, it is always convenient to express relative change as a percentage. Relative change is expressed as a percentage by multiplying the relative change by 100.

The relative change as a percentage can be written as

**Relative Change as a Percent **$= \frac{Final \;Value \;-\; Initial \;Value}{Initial \;Value} \times 100 = \frac{Absolute\; change}{Initial \;Value} \times 100$

where

“Final Value” is the new value after the change.

“Initial Value” is the old value or the value before the change.

The above formula is preferred for calculating the relative change.

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## How to Calculate Using the Relative Change Formula

The relative change is a percentage that represents the difference between the two values. If the value is positive, it means there is an increase. If the value comes out to be negative, it indicates a decrease.

Let us understand the steps for calculating relative change with the help of an example.

**Example: The price of a toy went from **$\$50$** to **$\$75$**. What is the relative change?**

**Step 1: **Note down the initial value and the final value.

Initial value $= \$50$

Final value $= \$75$

**Step 2: **Find the absolute change.

Here, the absolute change $=$ Final value $-$ Initial Value $= \$75 \;-\; \$50 = \$25$

**Step 3: **Divide the absolute change by the initial value and multiply the ratio by 100.

Relative Change (C) $= \frac{(Final \;Value \;-\; Initial\; Value)}{Initial\; Value} \times 100$

Relative Change (C) $= \frac{(75 \;-\; 50)}{50} \times 100 = 50\%$

Here, we can say that there is a $50\%$ rise in the initial price of the toy.

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## Facts on Relative Change Formula

- When a quantity doubles in value, its relative change $= 1 = \frac{1}{100} = 100\%$.
- The absolute change and relative change are positive if the new value is greater than the original or initial value.
- The absolute and relative change are negative if the new value is less than the initial value.

## Conclusion

In this article, we learned about the relative change formula, how to express it as a percentage, and examples. Let’s move ahead and solve a few examples and practice problems on the formula for relative change.

## Solved Examples on Relative Change Formula

**1. Bella invested **$\$12,000$** in a certain scheme and it increased to **$\$13,000$** in one year. Determine the relative change as a percentage.**

**Solution:**

Initial investment $= \$12,000$

Final Value $= \$13,000$

We can use the formula for relative change

Relative Change as a percentage $= \frac{(Final \;Value \;-\; Initial \;Value)}{Initial\; Value} \times 100$

$= \frac{(13,000 \;-\; 12,000)}{12,000} \times 100$

$= (\frac{1,000}{12,000} \times 100)$

$≈ 8.33\%$

Therefore, the invested amount increased by $8.33\%$ approximately.

**2. A restaurant served 80 guests on Monday and 60 guests on Tuesday. Find the percentage of relative change. What does it tell you?**

**Solution:**

Initial Value $= 80$

Final Value $= 60$

Relative change $= \frac{(Final \;Value \;-\; Initial \;Value)}{Initial \;Value}$

Relative change $= \frac{(60 \;-\; 80)}{80}$

Relative change $= \frac{-\;20}{80}$

Relative change $= \;-\;0.25$

Now, relative change percentage $= \frac{(Final \;Value \;-\; Initial \;Value)}{Initial \;Value} \times 100 =\;-25\%$

Therefore, the restaurant observed a 25% decrease in the number of guests.

**3. The total revenue of a company in the previous year is **$\$500,000$**. The latest revenue for the present year is **$\$600,000$**. What will be the change in the revenue of the company?**

**Solution:**

Initial Value or previous year’s revenue $= \$500,000$

Final Value or current year’s revenue $= \$600,000$

Relative Change (C) $= \left(\frac{(Final\; Value \;-\; Initial \;Value)}{Initial\; Value} \times 100\right)\%$

Relative Change (C) $= \left(\frac{(600,000 \;-\; 500,000)}{500,000} \times 100\right)\%$

$= (\frac{100,000}{500,000} \times 100)\%$

$= 20\%$

Therefore, $20\%$ is the relative change representing a percentage increase in the company’s revenue.

**4. A town’s population grew by **$20\%$** in ten years. What was the town’s original population if the current population is 24,000?**

**Solution:**

Change percentage in population growth (Relative Change Percentage) $= 20\%$

Current Population (Final value) $= 24,000$

Using the formula, we get

$20 = \frac{(24,000 \;-\; Initial \;Value)}{Initial\; Value} \times 100$

$\frac{20}{100} = \frac{(24,000 \;-\; Initial \;Value)}{Initial \;Value}$

$0.2 = \frac{(24,000 \;-\; Initial \;Value)}{Initial \;Value}$

$0.2 \times Initial \;Value = 24,000 \;-\; Initial \;Value$

$1.2 \times Initial \;Value = 24,000$

$Initial \;Value = 20,000$

Therefore, the town’s original population was 20,000.

## Practice Problems on Relative Change Formula

## Relative Change Formula: Definition, Facts, Examples, FAQs

### The price of an item went from $\$50$ to $\$70$. Find relative change.

Relative Change $= \frac{70 \;-\; 50}{50} = 0.4$

### The speed of a car went from 25 mph to 35 mph in a minute. What is the relative change as a percentage?

Relative Change Percentage $= \frac{(35 \;-\; 25)}{25} \times 100 = 40\%$

Relative Change Percentage $ = \frac{10}{25} \times 100 = 40\%$

### The price of a smartphone changed from $\$400$ to $\$500$ in one year. What is the absolute change?

Absolute Change $=$ (New Value $-$ Old Value) $= \$400\;-\;\$500 = \$100$

### A company’s revenue doubled in one year. Find the relative change and its percentage.

Let original revenue $= R$

Revenue after one year $= 2R$

Relative change $= \frac{2R \;-\; R}{R} = \frac{R}{R} = 1$

Relative change percentage $= 100\%$

### A house’s worth increased by $25\%$ in the last 12 months. What was the original price if the current market value is $\$250,000$?

Use the relative change formula to solve for the initial value.

Relative Change (C) $= \left(\frac{(Final \;Value \;-\; Initial\; Value)}{Initial\; Value} \times 100\right)\%$

$25\% = \frac{(\$250,000 \;-\; Initial\; Value)}{Initial \;Value} \times 100$

Initial Value $= \$200,000$

## Frequently Asked Questions about Relative Change Formula

**What does a positive or negative relative change indicate?**

A positive relative change means there is an increase or growth in the initial value, while a negative relative change indicates a decrease or decline.

The relative change formula is frequently used to assess the size of changes and contrast diverse data sets in various fields, including business, economics, statistics, and finance.

**What is absolute change?**

Absolute change is the difference between two values without taking the direction of the change into account. Regardless of whether there is a rise or a drop, it shows the size of the difference between the final and initial values.

**Why do we use the relative change formula?**

Relative change formula is used to compare the difference between two quantities to the initial value. If you are comparing values over time (possibly to indicate growth or decline), you need to use the relative change formula.

**What is the difference between absolute value and relative value?**

The key difference is that relative value measures the change or difference relative to a reference point as a percentage, while absolute value measures the numerical difference without taking the reference point or direction into account. While relative value concentrates on the ratio or relative change, absolute value concentrates on the magnitude.