Enter the coordinate points at two different points along a function or line to determine the average rate of change (AROC).

## AROC Formula

The following formula is used to calculate the average rate of change of a function:

AROC = ( fx(x2) – fx(x1) ) / ( X2-X1)

• Where AROC is the average rate of change
• X2 and X1 are coordinate points along the line
• fx(x2) and fx(x1) are the values of the function at those x-coordinates

This formula can be more simply written as:

AROC = (Y2 -Y1) / (X2 – X1)

While this is the same formula as slope, the reason the term AROC is used instead is that it’s used to describe the average rates of changes of non-linear lines while slopes are typically used with linear lines.

## AROC Defintion

What is AROC?

AROC, short for an average rate of change, is a measure of the average rate of change of a function between two points.

## Example Problem

How to calculate AROC?

First, determine the two x coordinate points along the function line. For this example, we will use 3 and 5 respectively.

Next, evaluate the function at those points. For the point located at x=3, the function is equal to 30. For the point located at x=5 the function evaluates to 75.

Finally, calculate the average rate of change using the formula above:

AROC = (Y2 -Y1) / (X2 – X1)

AROC = (75-30) / (5-3)

AROC = 22.5