​Average Rate of Change Calculator

The variation in y-value by variation in x-value for both distinct points on the graph is known as the average change rate for the function.

In simple words, The average rate of change is the change in the rate of a quantity divided by the total time. Or, The change in rate per year is known as the rate of change because it narrates how output volume changes relative to the alteration in input volume. If you use the required first and last input-output volumes data, you can easily find the Average rate of change.


Formula of ​Average Rate of Change Calculator

To find the average rate of change, we divide the output rate variation by the variation in the input rate.

Average rate of change = change in output / change in input

In mathematical form it is written as follows:

Average rate of change => AROC = Δy/Δx
AROC = (y2 - y1)/(x2 - x1)
AROC = [f(x2) - f(x1)]/x2 - x1
  • The change in value is demonstrated by the Greek letter  Delta (∆).

  • So the ratio is read by delta y over delta x.

  • ∆f Symbolize ∆y, changing the function doesn’t mean it changed the value of the output function.


To know about the cap rate, you can use our Cap Rate Calculator.


Suppose we run a petroleum agency and want to calculate the average rate of change in the petrol price from 2010 to 2013. Using the date below in the table will figure out the solution.

y 2007 2008 2009 2010 2011 2012 2013 2014
C (y) 2.31 2.62 2.84 3.30 2.41 2.85 3.20 3.68


From the graph, we can see that in 2010 the price was $3.30, whereas, in 2013, the price is increased by $3.20.

Using the formula of the average rate of change,

Δy/Δx = (y2 - y1)/(x2 - x1)

Putting values in the formula:

AROC  = (3.20 - 3.30) / (2013 - 2010)
AROC = (-0.10) / (3)
AROC = -0.033 / year

The decrease of -0.033/year is known as a negative change or a negative increase. When output decreases as input increases, this rate of change is known as negative change.

How to use ​Average Rate of Change Calculator?

The steps to use ​the average rate of change calculator are as follows:

Step 1: Enter the value of x1 in the first required input.

Step 2: Enter the value of f(x1) in the second required input.

Step 3: Enter the value of x2 in the third required input.

Step 4: Enter the value of f(x2) in the fourth required input.

Step 5: The calculator will automatically display an answer on the screen.

Calculator use

Using the Average rate of change calculator, you can find the solution without doing any self-calculations. Just enter the input and output values. After that, our algorithm will find the optimum solution for you.