Watt

The watt ($\mathrm{W}$) is the derived SI unit for Power.

Power is energy transfer per unit time:

$$P=\frac{E}{t}$$

So one watt means one Joule transferred every Second:

$$1\mathrm{W}=1\mathrm{J}{\mathrm{s}}^{-1}$$

Using base units:

$$1\mathrm{W}=1\mathrm{kg}{\mathrm{m}}^2{\mathrm{s}}^{-3}$$

That extra ${\mathrm{s}}^{-1}$ compared with the Joule is the whole point: watts measure rate. A $100\mathrm{W}$ bulb transfers $100\mathrm{J}$ of energy each second. Run it for $60\mathrm{s}$ and it uses:

$$E=Pt=100\mathrm{W}\times 60\mathrm{s}=6000\mathrm{J}$$

Electrical power is often written:

$$P=IV$$

so

$$1\mathrm{W}=1\mathrm{A}\mathrm{V}$$

This is consistent with $\mathrm{V}=\mathrm{J}{\mathrm{C}}^{-1}$ and $\mathrm{A}=\mathrm{C}{\mathrm{s}}^{-1}$:

$$\mathrm{A}\mathrm{V}=\frac{\mathrm{C}}{\mathrm{s}}\frac{\mathrm{J}}{\mathrm{C}}=\frac{\mathrm{J}}{\mathrm{s}}$$

Common mistake: a watt is not an amount of energy. It is how quickly energy is being transferred or converted.

Quick check: energy bills use kilowatt-hours because they multiply power by time. $1\mathrm{kWh}=3.6\times 10^6\mathrm{J}$.

Quick check

Power is energy transfer per time:

$$1\mathrm{W}=1\mathrm{J}{\mathrm{s}}^{-1}.$$

In circuits, the same unit appears as

$$P=IV,$$

because ampere times volt gives

$$\mathrm{C}{\mathrm{s}}^{-1}imes\mathrm{J}{\mathrm{C}}^{-1}=\mathrm{J}{\mathrm{s}}^{-1}.$$

Common use

Watts are useful whenever the time-rate matters: motors, heaters, lamps, solar panels, computer power draw, and mechanical engines. Same total energy over a shorter time means higher power.