Efficiency Formula

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.

What This Formula Means

The ratio of useful output energy to total input energy, expressed as a percentage showing how little is wasted.

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

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?

Solution

  1. 1
    Use the efficiency formula: \eta = \frac{\text{useful output}}{\text{total input}} \times 100\%.
  2. 2
    Substitute the given values: \eta = \frac{350}{500} \times 100\%.
  3. 3
    \eta = 70\%

Answer

\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.

Why This Formula Matters

Key to understanding energy use and why we need better technology.

Frequently Asked Questions

What is the Efficiency formula?

The ratio of useful output energy to total input energy, expressed as a percentage showing how little is wasted.

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.

Why is the Efficiency formula important in Physics?

Key to understanding energy use and why we need better technology.

What do students get wrong about Efficiency?

High efficiency doesn't mean low power useβ€”it means less waste.

What should I learn before the Efficiency formula?

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