Efficiency in Physics Formula: How to Calculate It

Efficiency in physics is the ratio of useful output energy (or power) to total input energy (or power), expressed as a percentage. The formula is Efficiency (%) = (Useful output energy ÷ Total input energy) × 100, and it tells you how well a machine or process converts energy into useful work. This calculator applies that formula to any energy or power values you enter, giving you the efficiency percentage instantly.

Formula

The efficiency formula is written as:

η = (E_out / E_in) × 100%

Where:

• η (eta) is the efficiency percentage.
• E_out is the useful energy output, measured in joules (J) or watt-hours (Wh).
• E_in is the total energy input, measured in the same unit as E_out.

For power, the same formula applies: η = (P_out / P_in) × 100%, where P_out and P_in are output and input power in watts (W).

Worked Example

Using the calculator defaults: a machine receives 600 J of energy and converts 450 J into useful work.

1. Write down the formula: η = (E_out / E_in) × 100%
2. Insert the values: η = (450 J / 600 J) × 100%
3. Divide: 450 ÷ 600 = 0.75
4. Multiply by 100: 0.75 × 100 = 75%

The efficiency is 75%. This matches the calculator’s output (rounded to 2 decimals).

When to Use This Formula

Use the efficiency formula whenever you need to compare the useful energy or power delivered by a device to the energy or power supplied to it. Common applications include:

• Electric motors (electrical input vs. mechanical output)
• Light bulbs (electrical input vs. light output)
• Engines (fuel energy input vs. mechanical work output)
• Power plants (fuel or heat input vs. electrical output)
• Batteries (stored energy vs. usable energy during discharge)

In each case, you need two measurements: the total energy or power put in, and the useful energy or power that comes out. The ratio tells you what fraction of the input is actually used for its intended purpose.

How to Read the Result

Efficiency is always a number between 0% and 100% (or sometimes higher for heat pumps, which move more heat than the work input—but that’s a special case). A higher percentage means less energy is wasted. For example:

• 90% efficiency means 90% of the input energy is converted to useful output; 10% is lost (usually as heat or sound).
• 50% efficiency means half the energy is wasted.
• 0% efficiency means no useful output at all (e.g., a brake that converts all kinetic energy to heat).

In real devices, efficiency is always less than 100% because of friction, electrical resistance, or heat losses. The closer to 100%, the more energy-efficient the device.

Common Mistakes and Misconceptions

A frequent error is mixing units—for example, using joules for input and watt-hours for output. Both must be the same unit. Another mistake is confusing efficiency with power: efficiency is a ratio, not a quantity of energy or power.

People also often forget that “useful output” is not the total output. For instance, a light bulb emits heat and light; only the light is “useful” for illumination, so the useful output is the light energy, not the total emitted energy.

Finally, efficiency cannot be calculated from work alone if time is involved—use power instead. The formula works for both energy and power, but you must be consistent.

Limits of the Formula

The simple efficiency formula assumes you can measure both input and output accurately. In practice, measuring “useful” output can be subjective—for a heater, heat is the useful output, but for a refrigerator, heat removal is useful. Also, the formula doesn’t tell you where the losses occur; it only gives the overall ratio. For deeper analysis, engineers use exergy or second-law efficiency, which accounts for the quality of energy.

For heat pumps and refrigerators, the coefficient of performance (COP) is used instead of efficiency because the useful output (heat moved) can exceed the work input. COP = Q_out / W_in, and it can be greater than 1.

Frequently Asked Questions

Can efficiency be over 100%?

No, not for the standard definition. You cannot get more useful energy out than you put in—that would violate the conservation of energy. Heat pumps have COP values above 1, but that’s not efficiency; it’s a different measure because they move heat rather than convert it.

What is the difference between energy efficiency and power efficiency?

Energy efficiency uses total energy (joules) over a period, while power efficiency uses instantaneous power (watts). The formula is the same, but the inputs are different. For example, a motor’s energy efficiency over an hour might be 80%, while its power efficiency at a specific load could be 90%.

How do I calculate efficiency if I only know the power?

You can still use the same formula: divide the useful output power by the total input power and multiply by 100. For example, if a motor draws 1000 W and delivers 850 W of mechanical power, efficiency = (850/1000) × 100 = 85%.

Why do real machines never reach 100% efficiency?

Because of unavoidable losses: friction between moving parts, electrical resistance in wires, heat dissipation, and sound. The second law of thermodynamics states that some energy is always degraded to low-grade heat, so perfect conversion is impossible.

What does a 0% efficiency mean?

It means the device produces no useful output at all. For example, a broken motor that hums but doesn’t turn uses electrical energy but delivers zero mechanical work, so its efficiency is 0%.

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in e_out | Useful output energy | J | 450 | 0
in e_in | Total input energy | J | 600 | 0
out eff | Efficiency | % | (e_out / e_in) * 100 | 2