Efficiency Formula

The efficiency formula = useful output/total input x 100\% measures how much of the input energy is converted to useful work.

The Formula

\eta = \frac{\text{useful output}}{\text{total input}} \times 100\%

When to use: What fraction of the energy you put in actually goes where you want it to go, rather than being wasted as heat.

Quick Example

A car engine: only ~25% of fuel energy becomes motion; the rest becomes heat.

Notation

\eta

(eta) is the efficiency as a fraction or percentage,

E_{\text{useful}}

is useful output energy in joules,

E_{\text{total}}

is total input energy,

T_H

and

T_C

are the hot and cold reservoir temperatures in kelvin.

What This Formula Means

The ratio of useful output energy (or power) to total input energy, expressed as a percentage — always less than 100% due to energy losses.

What fraction of the energy you put in actually goes where you want it to go, rather than being wasted as heat.

Formal View

Efficiency is defined as

\eta = \frac{E_{\text{useful}}}{E_{\text{total}}} = \frac{P_{\text{useful}}}{P_{\text{total}}}

, where

0 \leq \eta \leq 1

(or

0\% \leq \eta \leq 100\%

). The Carnot efficiency sets the theoretical maximum for heat engines:

\eta_{\text{Carnot}} = 1 - T_C / T_H

Worked Examples

Example 1

easy

A machine uses

500 \text{ J}

of input energy and produces

350 \text{ J}

of useful output. What is its efficiency?

Answer

\eta = 70\%

First step

Use the efficiency formula:

\eta = \frac{\text{useful output}}{\text{total input}} \times 100\%

Full solution

2
Substitute the given values: $\eta = \frac{350}{500} \times 100\%$ .
3
$\eta = 70\%$

Efficiency measures how well a machine converts input energy into useful output. No real machine is 100% efficient because some energy is always lost to heat, sound, or friction.

Example 2

medium

An electric motor with

85\%

efficiency lifts a

200 \text{ kg}

load by

10 \text{ m}

. How much electrical energy is consumed? Use

g = 10 \text{ m/s}^2

Example 3

medium

An electric motor is

70\%

efficient. It must do

1400

J of useful work. How much input energy is required?

Common Mistakes

Getting an efficiency above 100% — this means you mixed up input and output or made a calculation error; efficiency cannot exceed 100% by conservation of energy. - Fix this by naming the system, checking "Can I define the system and track energy before and after the interaction or process?", and attaching units or direction to the final statement.
Confusing efficiency with power — a low-power device can be highly efficient, and a high-power device can be very inefficient. - Fix this by naming the system, checking "Can I define the system and track energy before and after the interaction or process?", and attaching units or direction to the final statement.
Forgetting to express efficiency as a percentage — dividing output by input gives a decimal (e.g., 0.25), which must be multiplied by 100 to get 25%. - Fix this by naming the system, checking "Can I define the system and track energy before and after the interaction or process?", and attaching units or direction to the final statement.
Using efficiency from a keyword alone - Signal words like energy, work, power only point to a possible model; the system must match too.

Why This Formula Matters

Efficiency lets students solve problems where the detailed path is less important than the change from one state to another. It also connects mechanics, heat, electricity, waves, and modern physics through one conservation habit.

Frequently Asked Questions

What is the Efficiency formula?

The ratio of useful output energy (or power) to total input energy, expressed as a percentage — always less than 100% due to energy losses.

How do you use the Efficiency formula?

What fraction of the energy you put in actually goes where you want it to go, rather than being wasted as heat.

What do the symbols mean in the Efficiency formula?

$\eta$ (eta) is the efficiency as a fraction or percentage, $E_{\text{useful}}$ is useful output energy in joules, $E_{\text{total}}$ is total input energy, $T_H$ and $T_C$ are the hot and cold reservoir temperatures in kelvin.

Why is the Efficiency formula important in Physics?

What do students get wrong about Efficiency?

Students often know a formula related to efficiency but skip the recognition step: Can I define the system and track energy before and after the interaction or process? That leads to a correct-looking substitution attached to the wrong physical model.

What should I learn before the Efficiency formula?

Before studying the Efficiency formula, you should understand: energy, work.

← Back to Efficiency See All Examples Practice Problems

Related Concepts

Energy Work Power

Related Formulas

Work Formula Power Formula