Rate Of Change Calculator

Work out rate of change instantly with clear inputs, formula shown and shareable results.

About Rate Of Change Calculator

The average rate of change is the change in the output divided by the change in the input — the gradient of the straight line joining the two points, Δy/Δx.

Formula

Average rate of change

rate = (y₂ − y₁) / (x₂ − x₁)

Worked example

With the default values below, Rate Of Change Calculator returns Average rate of change of 8.00000000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Starting value: 120
Ending value: 168
Starting time or x: 2
Ending time or x: 8

Results

Average rate of change: 8.00000000
Total change in y: 48.000000
Percentage change: 40.0000 %
Interval width: 6.000000

Step by step

1Values used
2Average rate of change
3Average rate of change= 8.00000000
4Total change in y= 48.000000
5Percentage change= 40.0000 %
6Interval width= 6.000000

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

From 120 at x = 2 to 168 at x = 8?

Δy = 48 over Δx = 6, so the rate is 8 per unit, a 40% increase overall.

How does this differ from an instantaneous rate?

This is the mean gradient across the whole interval; the instantaneous rate is the derivative at a single point.