Efficiency compares useful output with total input

1. Efficiency has no unit because it is a ratio of energies measured in the same unit.
2. It lies between $0$ and $1$, or between $0\%$ and $100\%$.

Calculate efficiency from energy

1. Use:
2. $$\eta =\frac{E_{useful}}{E_{total}}$$
3. $E_{useful}$ and $E_{total}$ are both measured in joules $(J)$.
4. For a percentage, multiply the ratio by $100\%$.

Rearrange for missing energies

1. $$E_{useful}=\eta E_{total}$$
2. $$E_{total}=\frac{E_{useful}}{\eta }$$

Power gives the same ratio

1. When input and output are measured over the same time:
2. $$\eta =\frac{P_{useful}}{P_{total}}$$
3. Use two energies or two powers; never divide energy by power.

Useful output depends on purpose

1. Light is useful for a lamp, kinetic energy is useful for a motor and heating water is useful for a kettle.
2. Other outputs are unwanted for that purpose, even if the same transfer is useful in another device.

Check units and limits

1. Check that useful energy is no greater than total energy.
2. Use $E_{dissipated}=E_{total}-E_{useful}$ when the unwanted transfer is required.