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To calculate the rate of change, you divide the change in one quantity by the corresponding amount of change in another quantity. Change is represented as the Greek letter delta (Δ), so the basic formula for rate of change is:
Exactly how you calculate Δy and Δx will depend on the application.
Slope
In algebra, the average rate of change formula is the same as the slope formula, or “rise over run”:
Δy/Δx = (y2 – y1)/(x2 – x1)
Where the rate of change equals the average change of a function between ordered pairs (two points): [x1, y1] and [x2, y2].
Calculus
In calculus, the rate of change refers to how a function changes between two data points. The formula is:
Δ = (f(b) – f(a))/ b – a
Where the rate of change is equal to the average change in a function between [a, f(a)] and [b, f(b)].
The instantaneous rate of change, or derivative, is equal to the change in a function at one point [f(x), x]:
Or
Where x is the independent variable, y is the dependent variable and d represents delta (Δ) or change.
Acceleration
The average rate of change of velocity is known as acceleration, and you can calculate it using this formula:
Where a is acceleration, v1 is ending velocity, v0 is starting velocity, and t is time.
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