How Do You Calculate the Efficiency of a Machine or Energy Transfer?

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How the Calculation Works

Efficiency measures the proportion of input energy transferred into the desired form. Because energy is conserved, the remaining energy is transferred to less useful forms, often as thermal energy or sound.

Use this method:

1. Identify the total input energy or input power supplied to the device.
2. Identify the useful output named in the question, such as gravitational potential energy gained or mechanical power delivered.
3. Divide the useful output by the total input, then convert to a percentage if requested.
4. Check that the answer lies between 0 and 1, or between 0% and 100%.

For a machine lifting a mass, the useful output may need to be calculated first from $\Delta E_p = mg\Delta h$. If a $20\ \text{kg}$ load rises $3.0\ \text{m}$ while the machine receives $1000\ \text{J}$, then useful energy is $20 \times 9.8 \times 3.0 = 588\ \text{J}$ and efficiency is $588/1000 = 0.588$, or $58.8\%$. This combines energy transfer with the efficiency relationship.

For example, a machine receives $500\ \text{J}$ of energy and performs $350\ \text{J}$ of useful work:

Therefore, $150\ \text{J}$ is transferred into less useful forms because $500-350=150\ \text{J}$.

The same ratio applies to power. If a motor takes in $800\ \text{W}$ and produces $600\ \text{W}$ of useful mechanical power,

A common misconception is that efficiency equals useful output divided by wasted energy. This is incorrect: the denominator must always be the total input. Efficiency has no unit and cannot exceed $1$, or $100\%$, for an ordinary machine.

IB Exam Technique

For a Calculate question in topic A.3, show the equation, substitution, and final value. Check that the numerator and denominator use matching quantities and units: compare energy with energy or power with power, not energy with power.