- true/reference value
Worked example
Measured value 49, actual value 50. Find the percentage error.
Step by step
- Absolute error = |49 - 50| = 1.
- Divide by actual and multiply by 100%.
Final answer
2%
Smaller is better: A smaller percentage error means the measurement or estimate is closer to the true value relative to the size of the quantity.
| Percentage error | Interpretation |
|---|---|
| 1% | very accurate |
| 5% | moderate error |
| 20% | large error |
Context matters: A 5% error might be acceptable in one context and poor in another. Always link your answer to the situation.
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Worked example
An object is measured as 12 cm, actual length 12.5 cm. Find the percentage error.
Step by step
- Absolute error = 0.5 cm.
- Percentage error = 0.5 / 12.5 × 100%.
Final answer
4%
Use the actual value: Percentage error is based on the true/reference value, not the measured one.
Worked context example
A student estimates a journey as 18 km, but the actual distance is 20 km. Interpret the percentage error.
Step by step
- Absolute error = 2 km.
- Percentage error = 2/20 × 100% = 10%.
- Interpretation: the estimate is 10% away from the actual distance.
Final answer
The estimate has a 10% error, so it is moderately inaccurate.
Interpret, do not just calculate: If the question asks you to comment, say what the percentage means for the quality of the estimate.