Efficiency Physics: How to Calculate It

Efficiency in physics measures how well a system converts input energy into useful output energy. You calculate it by dividing the useful output energy (or power) by the total input energy (or power), then multiplying by 100 to get a percentage. The formula is Efficiency (%) = (Useful Output Energy ÷ Total Input Energy) × 100.

Formula

The efficiency equation is written as:

η = (E_out / E_in) × 100%

Where:

• η (eta) is the efficiency, expressed as a percentage.
• E_out is the useful energy output, measured in joules (J).
• E_in is the total energy input, also in joules (J).

The same structure works for power (watts): η = (P_out / P_in) × 100%. Because time cancels out, energy and power give identical results.

Worked Example

Using the calculator defaults: input energy = 1000 J, useful output energy = 450 J.

1. Write the formula: η = (E_out / E_in) × 100%
2. Plug in the numbers: η = (450 / 1000) × 100%
3. Divide: 450 ÷ 1000 = 0.45
4. Multiply by 100: 0.45 × 100 = 45%

The calculator shows 45.0% efficiency, with 550 J lost to heat, sound, or friction.

Why Efficiency Matters

Efficiency tells you how much of the energy you pay for actually does the job. A light bulb with 10% efficiency converts only a tenth of its electrical input into visible light; the rest becomes heat. An electric motor at 90% efficiency wastes only 10% as heat. Engineers use this number to compare designs, choose components, and estimate operating costs. In thermodynamics, efficiency also sets the theoretical ceiling for engines: the Carnot limit depends on the temperature difference between the hot and cold reservoirs, so no real engine can reach 100%.

Common Mistakes and Unit Pitfalls

• Mixing energy and power: You can divide joules by joules or watts by watts, but never joules by watts. Convert to consistent units first.
• Forgetting the × 100: The ratio alone (0.45) is not a percentage. Multiply by 100 unless you are using the decimal form.
• Using total output instead of useful output: Efficiency only counts the output you actually want. Waste heat is not useful, even though it is energy.
• Rounding too early: Round only the final answer, not intermediate steps, to avoid small errors.
• Confusing efficiency with power factor: In electrical systems, power factor (cos φ) is a different concept. Efficiency compares output to input power, while power factor relates real to apparent power.

Real-World Examples

Here are typical efficiency values for common devices (approximate, vary by model and conditions):

• LED light bulb: 20–40% (visible light output vs. electrical input)
• Incandescent bulb: 2–5%
• Electric motor: 70–95%
• Gasoline engine: 20–30%
• Diesel engine: 30–40%
• Solar panel: 15–22%
• Human body (cycling): ~20–25%

These numbers show why engineers prioritize efficiency: a small percentage gain in a large system can save significant energy and money over time.

How to Measure Input and Output

To calculate efficiency, you need both values. In practice:

• Electrical input: Measure voltage and current, then multiply: P = V × I. For AC, include the power factor if needed.
• Mechanical output: Measure force and velocity, or torque and angular speed: P = F × v or P = τ × ω.
• Thermal systems: Use the heat added and the work extracted. For heat pumps and refrigerators, the coefficient of performance (COP) is used instead of efficiency, and it can exceed 100%.

If you cannot measure output directly, you can often calculate it from the useful effect (e.g., lifting a known mass a known height) and the time taken.

Limits of the Formula

The simple efficiency formula assumes you can identify all energy inputs and outputs. In real systems, energy can leave in unexpected forms: vibration, noise, electromagnetic radiation, or chemical changes. The formula also does not tell you why efficiency is low, only that it is. To improve efficiency, you need a detailed energy audit. Additionally, efficiency is not constant; it often changes with load, temperature, and speed. A motor may be 90% efficient at full load but only 60% at 20% load. Always note the operating conditions when quoting an efficiency figure.

Frequently Asked Questions

Can efficiency be greater than 100%?

No, for a normal energy-conversion process, efficiency cannot exceed 100% because that would violate conservation of energy. However, devices like heat pumps and refrigerators use a different metric called coefficient of performance (COP), which can be greater than 1 because they move heat rather than convert it directly.

What is the difference between energy efficiency and power efficiency?

They are numerically the same if the time period is the same. Energy is power multiplied by time, so the time cancels in the ratio. For example, a device that uses 100 W and outputs 40 W has 40% efficiency whether you measure over one second or one hour.

How do I calculate efficiency if I only know the input and the losses?

Subtract the losses from the input to get the useful output: E_out = E_in − E_lost. Then use the standard formula. For instance, if you put in 500 J and lose 150 J as heat, useful output is 350 J, so efficiency = (350 / 500) × 100 = 70%.

Why do engines have low efficiency compared to electric motors?

Internal combustion engines are limited by the Carnot cycle and real-world losses like friction, heat to the exhaust, and incomplete fuel combustion. Electric motors avoid combustion and have fewer moving parts, so they convert a much larger share of electrical input into mechanical work.

Does efficiency affect the cost of running a device?

Yes. A device with higher efficiency uses less input energy for the same useful output, so it costs less to run for the same result. However, higher-efficiency devices often have a higher purchase price, so the payback period depends on usage hours and energy prices.

What is the efficiency of a human body?

For mechanical work like cycling or lifting, the human body is roughly 20–25% efficient. Most of the food energy is released as heat, which is why you get warm during exercise. This is not a fixed number; it varies with fitness, activity, and diet.

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• Multiply Fractions GCSE: Step-by-Step Guide

in e_in | Input energy | J | 1000 | 0
in e_out | Useful output energy | J | 450 | 0
out eff | Efficiency | % | (e_out / e_in) * 100 | 1
out loss | Lost energy | J | e_in - e_out | 0
out ratio | Output/input ratio | - | e_out / e_in | 3