Work and energy describe how much energy is transferred. Power describes how quickly that transfer occurs.

Over a time interval $\Delta t$, the average power is

$$\bar P=\frac{\Delta W}{\Delta t}.$$

More generally, the same idea applies to any energy transfer:

$$\bar P=\frac{\Delta E}{\Delta t}.$$

Units

The SI unit of power is the watt:

$$1,\mathrm W=1,\mathrm{J/s}.$$

A machine transferring $1000,\mathrm J$ in $2,\mathrm s$ has average power

$$500,\mathrm W.$$

Energy and power are different

Two machines can perform the same amount of work but have different powers if one performs it more quickly.

Likewise, a high-power device does not necessarily transfer more total energy; it transfers energy at a higher rate while it operates.

Variable power

If the transfer rate changes during the process, different time intervals can have different average powers. Instantaneous power refines the same idea by considering increasingly short time intervals once differential calculus is available.

The central concept is always energy transferred per unit time.