About the Average Rate of Change Calculator
Find the average rate of change of a function between x = a and x = b — the slope of the secant line.
Also known as: rate of change, secant slope, average rate, slope between two points on a curve.
How to use this calculator
- Enter f(x), a, b.
- The result updates instantly as you type — press Calculate (or Enter) at any time.
- Open “Step-by-step” to see how the answer was worked out.
- Use Copy result or Share to save the answer or send a link with your inputs.
Formula
ARC = (f(b) − f(a)) / (b − a)
Worked example
Using the values pre-filled in the calculator above:
- f(x): x^2 + 3x
- a = 1
- b = 4
the calculator returns:
- Average rate of change: 8
- f(a): 4
- f(b): 28
Working
(f(4) − f(1)) ÷ (4 − 1) = (28 − 4) ÷ 3 = 8