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# Relative Change Calculator

What is relative change?How do you calculate relative change?Example problemsUsing this relative change calculatorFAQs

Our relative change calculator is here to help you calculate the relative change between a variable's initial and final values. It also calculates the percentage of relative change.

In this article, we shall learn what relative change is and apply the relative change formula to some example problems to help you understand this concept better.

If you specifically wish to calculate the relative increase or decrease of a quantity, we recommend our percentage increase calculator or this percentage decrease calculator.

## What is relative change?

Relative change is a quantitative term that measures the change or difference in a variable relative to a reference or initial value. It helps compare two quantities while considering their "size".

The formula for relative change is:

$\text{\small Relative Change}_{(x_i, x_f)} = \frac{x_f - x_i}{|x_i|}$

where:

• $x_i$ — The initial value of a variable; and
• $x_f$ — The final value of the same variable.

As you can see, we calculate the relative change by subtracting the initial value from the final value and then dividing the answer by the absolute value of the initial number. The division by the initial value ensures that:

• The relative change is a unitless number; and
• The relative change between two quantities remains constant irrespective of the units used to measure the quantities.

For example, if the initial value is 4 km and the final value is 6 km, the relative change is $\frac{6-4}{4} = 0.5$. If we use meters instead of kilometers to measure the distance, the initial value would be 4000m, and the final value would be 6000m. Again, the relative change is $\frac{6000-4000}{4000} = 0.5$.

⚠️ Note that the initial or reference value cannot be zero! Relative change is undefined when the initial value is zero.

Multiplying relative change by 100 gives us the relative change percentage:

${\footnotesize \begin{gather*}\rm Relative\\\rm Change\end{gather*}}_{(x_i, x_f)} \% = \frac{x_f - x_i}{|x_i|} \cdot 100$

## How do you calculate relative change?

In order to calculate the relative change between initial xi and final xf values, follow these steps:

1. Subtract the initial value from the final value to get their difference:

Δx = xf − xi

2. Divide this difference by the absolute value of the initial value to get the relative change:

Relative change = Δx/|xi|

3. Multiply this relative change by 100 to get the relative change percentage:

Relative change % = 100 ∙ (Δx/|xi|)

You can verify your result using our relative change calculator.

## Example problems

In this section, we shall consider a couple of examples to understand better how to calculate relative change:

1. If the minimum wage increases from $7/hr to$15/hr, what is the relative change in wages?

• Initial value $x_i = 7$; and
• Final value $x_f = 15$.

Using the relative change formula, we get the following:

\qquad \begin{align*} \text{\small Relative Change}&= \frac{x_f - x_i}{|x_i|}\\[1.5em] &=\frac{15 - 7}{|7|}\\[1.5em] &= 1.1429 \end{align*}

Thus, the relative change is 1.1429 or 114.29%.

1. The theoretical frequency of a vibrating object is 75 Hz. In an experiment, the measured frequency of this vibrating object is 80 Hz. What is the relative error?

The relative error calculation is the same as the relative change percentage calculation:

$\quad {\small\begin{gather*}\rm Relative\\\rm error\ \% \end{gather*} }_{(x_t, x_e)} = 100 \cdot \frac{x_e - x_t}{|x_t|}$

where:

$x_t$ — The theoretical value; and
$x_e$ — The experimental value.

Using this formula, we get the following:

\qquad \begin{align*} {\small\begin{gather*}\rm Relative\\\rm error\ \% \end{gather*} }&= 100 \cdot \frac{(80 - 75)}{|75|}\\[1.5em] &= 6.667 \% \end{align*}

🙋 The relative error is a special case of relative change. You can learn more about the relative error calculation with our relative error calculator!

## Using this relative change calculator

Our relative change calculator is simple to use:

1. Enter the initial or reference value.

2. Enter the final or measured value.

3. Sit back and chill as the tool automatically calculates the relative change and the relative change percentage!

Wish to calculate the relative change of a quantity at different stages as it keeps changing? Our percentage change calculator has got your back!

FAQs

### Why should you use the absolute value of a reference value for relative change?

When calculating relative change, using the absolute value of the reference ensures that the relative change is positive for a relative increase and negative for a relative decrease. Not using the absolute value could give us negative values for the relative increase and vice versa, which would be confusing, to say the least!

### What is the relative change from 75 to 25?

The relative change from 75 to 25 is -0.6667 or -66.67%. To calculate this manually, follow these steps:

1. Subtract the initial value from the final value to get their difference: Δx = 25 − 75 = -50.

2. Divide this difference by the absolute value of the initial value to get the relative change: Relative change = -50/|75| = -0.6667.

3. Multiply this relative change by 100 to get the relative change percentage: Relative change % = 100 × -0.6667 = -66.67%.