Efficiency calculator with working

• Efficiency: a motor is supplied with 200 J and does 150 J of useful work. $150 \div 200 \times 100 = 75\%$.
• Useful power: a 60 W bulb is 15% efficient. Useful light output $= 15 \div 100 \times 60 = 9$ W; the other 51 W heats the surroundings.
• Total input: a 40% efficient engine gives 2,000 J of useful energy. Total input $= 2000 \div 0.40 = 5000$ J.

Efficiency can be written as a decimal (0.75) or a percentage (75%). Exam questions say which they want; the calculator gives a percentage, and you can divide by 100 for the decimal. An efficiency above 1 (or 100%) is impossible, so if you get one, the useful and total values are probably the wrong way round.

Wasted energy = total input − useful output. In the motor example, $200 - 150 = 50$ J is dissipated, mostly as heat from friction and electrical resistance. On a Sankey diagram, the width of each arrow shows the amount of energy, so the useful arrow's share of the input arrow is the efficiency.

Reduce unwanted energy transfers: lubricate moving parts to cut friction, insulate buildings (thicker walls, cavity insulation, double glazing), and use streamlined shapes to reduce air resistance. LED bulbs are more efficient than filament bulbs because less of their energy is wasted as heat.

• Putting the total on top: always useful ÷ total.
• Mixing joules and watts in the same calculation.
• Forgetting to multiply by 100 when a percentage is asked for.

Practise with our efficiency questions, and use the power calculator if you need power first.

• Read the question for "useful": in a kettle the useful output is heating the water, but in a light bulb, heat is wasted.
• Show the division and the × 100 as separate steps.
• If the question gives a Sankey diagram, read the useful and total values off the arrows before calculating.
• An answer above 100% always means the two values are the wrong way round.