Rate of Change Calculator (Formula, Average & Instantaneous)

Find the rate of change (slope) between two points, the average rate of change of a function over an interval, or the instantaneous rate at a point.

Rate of Change Formula

The following formula is used to calculate a rate of change.

Rate of Change = (y₂ - y₁) / (x₂ - x₁)

y₂ = y coordinate of point 2
y₁ = y coordinate of point 1
x₂ = x coordinate of point 2
x₁ = x coordinate of point 1

To calculate the rate of change divide the change in y by the change in x position.

Rate of Change Definition

The rate of change of a line is often referred to as the slope, or rise over run. It's a measure of how quickly a line is changing in the y-direction with every step in the x-direction.

Swapping x and y gives the average change in x with respect to y, provided the change in y is nonzero.

How to calculate a rate of change?

First, determine the coordinate points of point 1.
For this example we will say the first point is (1,2).
Next, determine the coordinate points of point 2.
For this example, we will say the second point is (5,10).
Finally, calculate the rate of change.
Using the formula we find the rate of change to be (10 − 2)/(5 − 1) = 8/4 = 2.

FAQ

What is a rate of change?

An average rate of change is a change in output divided by a nonzero change in input. The input can be time or another quantity.

Is a rate of change a slope?

Yes, a slope is another word for the rate of change of y with respect to x.