How to Calculate a Rate of Change

Calculates the change and the rate of change from the original value as (new − original) ÷ original × 100 (%). A decrease gives a negative rate.

Explanation

This measures how much a value has grown or shrunk, expressed as a percentage of where it started. Divide the change by the original value and multiply by 100.

r = \dfrac{b - a}{a} \times 100

$a$ is the original value, $b$ is the new value and $r$ is the rate of change in per cent. The change itself is $b - a$ : positive when the value has risen, negative when it has fallen.

Example

Going from 200 to 250, the change is $250 - 200 = 50$ and the rate is $\dfrac{50}{200} \times 100 = 25$ . The value has risen by 25%.

Notes

Always divide by the original value, never by the new one. The base you pick decides the answer.

A rise and a fall of the same percentage do not cancel out. Starting from 200, a 25% rise reaches 250, and a 25% fall from there gives $250 \times 0.75 = 187.5$ , below where you began.

Per cent and percentage points are different units. If approval climbs from 40% to 50%, that is a gain of 10 percentage points, but a rate of change of 25%.

An original value of 0 offers no base to grow from, so no rate can be worked out.