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Efficiency Equation GCSE Physics: Formula & Worked Examples

Updated · Standard formula, shown below

Efficiency (decimal) 0.40
Efficiency (%)
40.0 %
Result
Total input energy
100 J
You entered
Useful output energy
40 J
You entered

Efficiency Equation GCSE Physics: Formula & Worked Examples

The efficiency equation in GCSE Physics is efficiency = useful output energy (or power) ÷ total input energy (or power), usually written as a decimal or multiplied by 100 to give a percentage. You will use two versions: one for energy transfers (Eout/Ein) and one for power transfers (Pout/Pin). This page explains both formulas, how to apply them in exams, and the common pitfalls that cost marks.

Formula

The efficiency equation is one of the few in GCSE Physics that has two interchangeable forms. Both give the same ratio, but you choose based on the information in the question.

  • Energy version: efficiency = useful output energy ÷ total input energy
  • Power version: efficiency = useful output power ÷ total input power

In symbols: η = Eout / Ein or η = Pout / Pin, where η (the Greek letter eta) is efficiency, E is energy in joules (J), and P is power in watts (W).

Because energy and power are related (power = energy ÷ time), the time cancels out when you divide output by input, so both formulas give the same numerical result for the same device.

Worked Example

Using the calculator defaults: an appliance receives 100 J of energy and converts 40 J into useful output. What is its efficiency?

  1. Write the formula: efficiency = Eout ÷ Ein
  2. Substitute the numbers: efficiency = 40 J ÷ 100 J = 0.4
  3. Convert to a percentage: 0.4 × 100 = 40%

The calculator shows efficiency as 0.40 (decimal) and 40.0% (percentage). Both are correct answers in an exam, but always check what the question asks for – if it says “give your answer as a percentage,” you must multiply by 100.

When to Use Each Version

GCSE questions often give you energy values (in joules) or power values (in watts). The rule is simple:

  • If the question mentions energy, work done, or heat – use the energy version (Eout/Ein).
  • If the question mentions power, watts, or “per second” – use the power version (Pout/Pin).

For example, a light bulb might be rated at 60 W input power and produce 3 W of light. Its efficiency is 3 W ÷ 60 W = 0.05 = 5%. The remaining 57 W is wasted as heat.

Common Mistakes and How to Avoid Them

Most marks are lost on units and on misidentifying “useful” output. Here are the frequent traps:

  • Mixing up energy and power: Don’t divide joules by watts. Always use the same quantity type in the numerator and denominator.
  • Forgetting to multiply by 100: If the question asks for a percentage, a decimal answer loses a mark. Read the command word carefully.
  • Calling all output “useful”: In a filament lamp, light is useful but heat is wasted. In a heater, heat is useful and light is wasted. Identify the intended output from the device’s purpose.
  • Rounding too early: Keep at least three significant figures until the final step, then round to the precision asked (usually 2 decimal places for decimals, or whole percentages).

Real-World Context and Efficiency Values

No real device is 100% efficient because some energy is always transferred to the surroundings, usually as heat or sound. Typical GCSE examples include:

  • LED light bulbs: about 40–50% efficient (light output vs electrical input)
  • Filament bulbs: about 5% efficient
  • Electric motors: 70–90% efficient
  • Human body: about 25% efficient when converting chemical energy to movement

These figures are illustrative, not exact, but they show why efficiency matters: improving efficiency reduces energy waste, fuel use, and running costs. In physics exams, you are often asked to suggest ways to improve efficiency, such as adding insulation, using lubricants, or switching to LED bulbs.

Limitations of the Equation

The efficiency equation is a simple ratio and has three important limitations you should know for exams:

  • It doesn’t tell you how much energy is wasted. You can calculate wasted energy as input minus useful output, but the equation alone doesn’t show where the waste goes.
  • It assumes you can measure “useful” output. In reality, defining what counts as useful can be subjective – a car engine’s useful output is kinetic energy, but heat from the engine is not entirely useless in winter.
  • It doesn’t account for time. Two devices can have the same efficiency but very different power ratings. Efficiency is a ratio, not a measure of performance.

Frequently Asked Questions

What is the efficiency equation for GCSE Physics?

The core equation is efficiency = useful output energy ÷ total input energy, or efficiency = useful output power ÷ total input power. Both are given on the GCSE Physics equation sheet, so you don’t need to memorise them, but you must know which to use.

How do I calculate efficiency as a percentage?

First calculate the decimal efficiency (useful output ÷ total input). Then multiply by 100. For example, 0.4 becomes 40%. If the question asks for a percentage, always include the % sign.

What is the difference between energy and power in the efficiency equation?

Energy is the total amount of work done (measured in joules). Power is the rate of energy transfer (joules per second, or watts). The efficiency ratio is the same whether you use energy or power, because time cancels out – but you must not mix them in the same fraction.

Why can’t efficiency be greater than 1 (or 100%)?

Because of the conservation of energy. You cannot get more useful energy out than you put in. Some energy is always wasted, usually as heat, sound, or light. An efficiency greater than 1 would mean energy is created, which violates the law of conservation of energy.

What does “useful output” mean in an exam question?

It is the energy or power that the device is designed to produce. For a speaker, it’s sound; for a motor, it’s kinetic energy; for a heater, it’s heat. Any other energy transfer is wasted. Read the question carefully – sometimes it tells you exactly which output is useful.

How do I find wasted energy from the efficiency equation?

Subtract the useful output from the total input: wasted energy = total input energy – useful output energy. For example, if 100 J goes in and 40 J is useful, then 60 J is wasted. You can also calculate the percentage wasted as (wasted ÷ total input) × 100.

Related

Formula used
in e_in | Total input energy | J | 100 | 0
in e_out | Useful output energy | J | 40 | 0
out eff | Efficiency (decimal) | - | e_out / e_in | 2
out eff_pct | Efficiency (%) | % | (e_out / e_in) * 100 | 1

Each line is one input (in, sel, list) or one result (out: label, unit, formula, decimals). How the calculators work

Method: the standard formula for this calculation, rounded as each result states. See how the calculators work or report an error.