Scientific reading
Write the ratio
For an appropriately defined interval and output, efficiency η=E_useful/E_input, or η%=100×E_useful/E_input. Provided energies refer to the same comparable input/output account, equivalent mean power ratio η=P_useful/P_input follows because the time cancels. In this simplified model, 0≤η≤1. If a calculation exceeds 100% on this basis, reconsider the inputs, stored energy, definition of useful output or instrument measurements.
A useful distinction
Two devices may share the same useful energy and time while differing in efficiency because one demands more input. Conversely, two devices may have identical efficiency but different input energies and powers. Efficiency answers 'what fraction was useful?', whereas power answers 'how fast did this particular transfer occur?' No single number answers both questions.
Solve the balance with decimals
If E_input=400 J and η=75%, E_useful=0.75×400=300 J and E_other=100 J. With t=5 s, P_in=80 W and P_useful=60 W. A second device at η=60% with the same input and interval has useful energy 240 J and useful power 48 W. These outputs are synthetic and do not characterize real products.
Respect the steady-run assumption
This equation accounts for an input energy budget separated into outputs with no net change of stored energy in the device. If a battery, spring or capacitor is charging/discharging internally, changes to stored energy require an additional ledger term. Our model deliberately excludes those complexities but asks students to name them.