How to Calculate Efficiency: Formula & Examples

Efficiency measures how well a system converts input energy or work into useful output. To calculate it, divide the useful output by the total input and multiply by 100 to get a percentage: Efficiency (%) = (Useful Output / Total Input) × 100. This page’s calculator lets you enter the input and output values (in any consistent units) and instantly returns the efficiency percentage.

Formula

The general efficiency formula is:

Efficiency (η) = (W_out / W_in) × 100%

• η – efficiency (percent, %)
• W_out – useful work or energy output (joules, J)
• W_in – total work or energy input (joules, J)

If you are measuring power instead of energy, the same formula works with watts (W): Efficiency = (Power out / Power in) × 100%. The units of input and output must match (both joules, both watts, both calories, etc.) for the percentage to be meaningful.

Worked Example

Using the calculator’s default values: input = 1000 J, output = 800 J.

1. Write the formula: Efficiency = (Output / Input) × 100%
2. Plug in the numbers: Efficiency = (800 J / 1000 J) × 100%
3. Divide: 800 / 1000 = 0.8
4. Multiply by 100: 0.8 × 100 = 80%

The efficiency is 80%. This means 800 J of the 1000 J input is converted into useful work; the remaining 200 J is lost, typically as heat or friction.

When to Use This Calculation

Efficiency calculations apply to any process that converts one form of energy or work into another. Common examples include:

• Electric motors: electrical energy in, mechanical work out
• Light bulbs: electrical energy in, light (and heat) out
• Engines: chemical energy in fuel, mechanical work out
• Power plants: thermal energy from fuel, electrical energy out
• Batteries: stored chemical energy, electrical energy out
• Human metabolism: food energy in, physical work out

In each case, you need to measure or know the total input and the useful output. The difference is lost energy, usually as heat, sound, or vibration.

How to Read the Result

Efficiency is always a percentage between 0% and 100% (unless you have an impossible perpetual-motion machine). A higher percentage means the system wastes less energy. For example:

• 90% efficiency: 90% of input becomes useful output; 10% is lost.
• 50% efficiency: half the input is wasted.
• 0% efficiency: no useful output at all (all input is lost).

In real systems, 100% efficiency is unattainable because of the second law of thermodynamics – some energy always becomes unusable heat. Even the best industrial motors rarely exceed 95% efficiency.

Common Mistakes and Pitfalls

• Mixing units: If input is in joules and output in calories, you must convert to the same unit first (1 cal = 4.184 J).
• Using power instead of energy: Power (watts) is energy per time. If you have watts, you can still use the formula, but both input and output must be in watts.
• Forgetting to multiply by 100: The formula gives a decimal (e.g., 0.8). Multiply by 100 to get a percentage (80%).
• Ignoring the “useful” part: Only count the output that is actually used for the intended purpose. For a light bulb, the useful output is light, not heat – even though the bulb also produces heat.

Limits of the Formula

The simple efficiency formula assumes you can measure the total input and the useful output. In practice, that can be tricky:

• Heat losses: In engines and power plants, much of the input energy is lost as heat. Measuring that heat requires calorimetry, not just a simple meter.
• Variable loads: Efficiency often changes with operating conditions. A motor might be 90% efficient at full load but only 70% at half load.
• Multiple outputs: Some systems produce more than one useful output (e.g., a combined heat and power plant). You then need a more complex metric like “total efficiency” or “cogeneration efficiency.”

For everyday comparisons, though, the simple formula is usually sufficient and gives a clear, intuitive number.

Efficiency vs. Other Metrics

Efficiency is related to, but distinct from, other performance measures:

• Power factor (electrical): Ratio of real power to apparent power in AC circuits – not the same as efficiency, but often confused with it.
• Specific fuel consumption: Fuel used per unit of work (e.g., g/kWh) – a common way to rate engines, but it’s the inverse of efficiency in some sense.
• COP (coefficient of performance): Used for heat pumps and refrigerators – it can be greater than 1 because it moves heat rather than converting it directly.

When comparing systems, always check which metric is being reported. Efficiency is dimensionless (a percentage), while COP has units of heat moved per work input.

Frequently Asked Questions

What is the formula for efficiency in physics?

The basic formula is Efficiency = (Useful output energy / Total input energy) × 100%. It works for any energy conversion, from a light bulb to a car engine.

Can efficiency be more than 100%?

No, not for a real energy conversion process. That would mean you get more energy out than you put in, which violates the conservation of energy. However, heat pumps and refrigerators have a coefficient of performance (COP) that can exceed 1 – but that’s a different metric, not efficiency.

How do you calculate efficiency of a machine?

Measure the work input (force × distance) and the work output (useful load × distance). Divide output by input and multiply by 100. For example, a pulley that lifts a 100 N load 2 m with 250 J of input work has an efficiency of (200 J / 250 J) × 100 = 80%.

What is the efficiency of a light bulb?

Incandescent bulbs are about 2-5% efficient (most energy becomes heat), while LED bulbs can be 40-60% efficient. To calculate, divide the light output (in lumens, converted to watts of visible light) by the electrical input (in watts).

Why is efficiency always less than 100%?

Because of the second law of thermodynamics, some energy is always lost as heat due to friction, resistance, or other irreversible processes. No real system can perfectly convert all input energy into useful work.

Does efficiency depend on units?

No – as long as input and output use the same unit (joules, calories, watt-hours, etc.), the percentage is the same. The ratio cancels the units. Just be careful not to mix units like joules and calories.

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in input | Input (total energy or work) | J | 1000 | 0
in output | Useful output (energy or work) | J | 800 | 0
out eff | Efficiency | % | (output / input) * 100 | 2