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Average rate of change calculator

Compute the average rate of change of a function on an interval: [f(b) − f(a)] / (b − a), the slope of the secant line between (a, f(a)) and (b, f(b)). Type any function of x, set the endpoints a and b, and see f(a), f(b) and the average rate instantly.

Related tools

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Instantaneous rate of change calculatorCompute the instantaneous rate of change f′(x₀) — the derivative of a function evaluated at a single point, and the slope of the tangent line there. Type any function of x and a point x₀; the tool differentiates symbolically, evaluates f′(x₀), and gives the tangent-line equation.Percentage change calculatorFind the percentage increase or decrease between two numbers.Percentage point change calculatorFind the difference in percentage points between two percentages, and the relative change.Average (mean) calculatorCompute the mean, sum and count of a list of numbers.Average Deviation Calculator (mean absolute deviation)The average absolute deviation from the mean AND from the median — the median is the point that minimises it, which is worth seeing. Every |x − centre| is listed, and the standard deviation sits beside it for contrast: squaring makes SD react hard to a single outlier while the average deviation barely moves. The outlier preset is built to show exactly that.Weighted average calculatorCompute a weighted average from a list of values and their weights.Antilog Calculator (inverse logarithm)The antilogarithm undoes the logarithm: antilog_b(y) = bʸ, so log_b(bʸ) = y. Pick base 10, e, 2 or your own, enter the exponent, and the result comes back with the inverse relationship spelled out and the round trip checked. Bases of zero or less, and base 1, are rejected with the reason.Wronskian calculatorThe Wronskian of a set of functions — the determinant built from them and their successive derivatives — is the classic test for linear independence in differential equations. Enter your functions and a point; it differentiates each symbolically, builds the matrix and evaluates the determinant.

Open Average rate of change calculator and you get an answer straight away, with no account to create. It covers a, f(a — adjust any of them and the result follows immediately.

How to use it

  1. Open the tool — no signup or install needed.
  2. Enter your input or adjust the available options.
  3. Get your result instantly, then copy or download it.

Frequently asked questions

What is Average rate of change calculator?

Compute the average rate of change of a function on an interval: [f(b) − f(a)] / (b − a), the slope of the secant line between (a, f(a)) and (b, f(b)). Type any function of x, set the endpoints a and b, and see f(a), f(b) and the average rate instantly.

What does a concrete case look like?

f(x) = x², [1, 3] → (9 − 1) / (3 − 1) = 4 — the tool shows every step in between, not just the final figure.

What does it take into account?

It factors in a, f(a. Change any of them and the output follows immediately.

When would I actually use this?

Checking a derivative or an integral you worked out by hand, finding where a function turns, and getting a numeric answer when no closed form exists.

What is the most common mistake?

Integrating across a discontinuity as if it were not there. A numeric method will happily return a finite value for an integral that diverges — check the domain before trusting the number.

How is Average rate of change calculator different from Instantaneous rate of change calculator?

They sit next to each other but answer different questions: Instantaneous rate of change calculator is the one to open when you need it to compute the instantaneous rate of change f′(x₀) — the derivative of a function evaluated at a single point, and the slope of the tangent line there. Type any function of x and a point x₀; the tool differentiates symbolically, evaluates f′(x₀), and gives the tangent-line equation. Pick whichever matches what you're starting from — both are free.

Is there a tool for the next step?

Percentage change calculator is the closest one after this: Find the percentage increase or decrease between two numbers.

What else is worth having open alongside it?

Percentage point change calculator and Average (mean) calculator — they come up in the same task often enough to be worth a second tab.

Where do the figures come from?

Symbolic results are exact; numeric ones come from adaptive quadrature or a standard step method, and the tool reports which. Where both are available, compare them — a large gap means the problem is ill-conditioned.

Further reading

All guides →
How-toPercentage Change: Increase and DecreaseSubtract old from new, divide by the old value, times 100. Here's the formula, why increases and decreases aren't symmetric, and where it's used.ExplainerPercentage Difference vs. Percentage Change vs. Percentage ErrorThree percentages that look alike but answer different questions. Learn the formula for each, when to use it, and why they give different numbers.How-toHow to Calculate a Weighted AverageA weighted average gives some values more influence than others. Learn the Σ(w·x) / Σw formula with grade and portfolio examples you can follow step by step.How-toHow to Calculate a Percentage: 4 Methods with ExamplesA clear guide to percentages: find X% of a number, work out what percent one number is of another, and add or subtract a percentage — with worked examples.ExplainerMean, Median and Mode: What's the Difference?Mean, median and mode all describe the 'middle' of your data — but answer different questions. Here's what each means, with examples and when to use which.ExplainerGeometric vs Arithmetic Mean: Which to UseThe arithmetic mean adds and divides; the geometric mean multiplies and takes a root. Learn which fits growth rates, ratios, and averages.