What is average rate of change?
The change in function values divided by the change in input over an interval.
Average Rate of Change Calculator
Find the average rate of change of a function on [a, b], or from two output values.
Choose a mode
Use x², quadratic coefficients, or enter y₁ and y₂ directly.
About this calculator
How to use Average Rate of Change Calculator, plus the formulas and logic behind the results.
Tool description
Average rate of change is the slope of the secant line joining (a, f(a)) and (b, f(b)).
How to use
- Select f(x)=x², quadratic, or direct y-values.
- Enter the interval endpoints (and coefficients or y-values).
- Select Calculate to view the average rate of change.
- Compare with the instantaneous rate f′(x) when relevant.
Formulas & reference
ARC = (f(b) − f(a)) / (b − a)Direct: (y₂ − y₁) / (x₂ − x₁)
ARC tips
- Units are “output units per input unit”
- Same idea as slope of a secant
- Instantaneous rate is the limit as b → a
- Direct mode needs y₁ and y₂
Calculation logic
Evaluates f at the endpoints (or uses given y-values) and divides by the change in x.
Requires b ≠ a. Educational tool for precalculus and calculus I.
Average Rate of Change Calculator FAQ
Common questions about this calculator and how to use the results.
How is it different from a derivative?
The derivative is the instantaneous rate; ARC is the average over an interval.
Can a equal b?
No—division by zero is undefined.
What does direct mode do?
It uses your y₁ and y₂ without evaluating a formula.
Is f(x)=x² common?
Yes—it is a frequent textbook example on [a, b].
Can values be negative?
Yes—negative ARC means the function decreased on average.