This average rate of change calculator finds the secant slope between two function points and displays both coordinate differences.
Math
Average Rate of Change Calculator
Find the secant slope between two points on a function.
Calculator
About this calculator
Formula notes
average rate of change = [f(x2) - f(x1)] / (x2 - x1), provided x2 is not equal to x1.
Worked examples
- Example: points (1, 3) and (5, 11) give change in x = 4, change in f(x) = 8, and average rate = 2.
- For f(x) values 4 and 31 at x values -2 and 7, the changes are 27 and 9, so the average rate of change is 3.
How to use it
- Enter the first x and function value.
- Enter a different second x and its function value.
- Interpret the signed result as output change per input unit.
Frequently asked questions
Why can the two x values not be equal?
Equal x values make the denominator zero, so a finite secant slope is not defined.
Is this an instantaneous derivative?
No. It is the average slope across an interval; a derivative describes a limiting slope at one point.
Limits and interpretation
- Only the two entered endpoints are used, so the result does not reveal curvature, turning points, discontinuities, or behavior between those points.
- The output carries units of function value per x unit; interpreting it as a percentage or physical rate requires compatible meanings and units.