# Definition:Rate of Change

## Definition

The rate of change of a physical quantity is its (first) derivative with respect to an independent variable which is usually, but not exclusively, time.

Loosely speaking, it means how fast something changes, with a wider scope than change in physical displacement.

### Time

When the independent variable of a rate of change is time, it is commonplace to take that fact for granted, and refer merely to its rate of change.

### Rate of Increase

A rate of increase is a rate of change measured in a strictly positive direction.

### Rate of Decrease

A rate of decrease is a rate of change measured in a strictly negative direction.

Hence a negative rate of decrease is a rate of increase.

### Dimension

Let a physical quantity $P$ have dimension $\mathsf D$.

Then the rate of change of $P$ with respect to time has dimension $\mathsf {D T}^{-1}$.

## Also see

• Results about rate of change can be found here.