Average Rate of Change Calculator
Calculate the average rate of change of a function between two points — enter a, f(a), b and f(b) to get (f(b) − f(a)) ÷ (b − a), the slope of the secant line.
How to find the average rate of change
The average rate of change of a function over an interval is how much the output changes per unit of input, on average. You divide the change in the function value by the change in x between two points a and b. If you have a function rather than two values, evaluate it at a and b first, then enter those as f(a) and f(b).
average rate of change = (f(b) − f(a)) ÷ (b − a)
For example, from a = 1 with f(a) = 3 to b = 4 with f(b) = 12: (12 − 3) ÷ (4 − 1) = 9 ÷ 3 = 3. Geometrically this is the slope of the secant line joining the two points on the curve. It differs from the instantaneous rate of change (the derivative), which is the slope of the tangent at a single point.
Looking for a plain number average? Try the average calculator for mean, median and mode.
Frequently asked questions
How do you calculate the average rate of change?
Divide the change in the function value by the change in x: (f(b) − f(a)) ÷ (b − a). For example, from a = 1, f(a) = 3 to b = 4, f(b) = 12: (12 − 3) ÷ (4 − 1) = 9 ÷ 3 = 3.
What is the average rate of change?
It is how much a function changes on average over an interval — the total change in output divided by the change in input. Graphically it is the slope of the straight (secant) line joining the two points on the curve.
Is average rate of change the same as slope?
Over an interval, yes — the average rate of change equals the slope of the secant line between the two points. It differs from the instantaneous rate of change (the derivative), which is the slope of the tangent at a single point.