PRACTICAL GUIDES · Math and geometry
Absolute vs relative error: calculating percent error
Choose a reference and keep measurement units consistent. Distinguish a percentage deviation from measurement uncertainty.
By Puffinmint · Updated
Choose a reference and consistent units
Identify the reference value before calculating an error and convert both measurements to the same unit. A signed difference tells you which side of the reference the measurement falls on; absolute error describes only the distance.
Calculate signed, absolute and relative error
Calculate the distance from the reference, then divide by the reference’s absolute value. Multiply by one hundred only for a percentage. Do not silently switch to the measured value as the denominator: that answers a different question.
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Input
98; 100
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Calculation steps
Choose and apply the method
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Result
2%
TRY THIS STEP
Percent error calculator
Work inside this guide: load an example, run the tool and edit the inputs to compare results. The second experiment tests a different case.
A reproducible example
With a measurement of 98 and a reference of 100, the signed difference is −2 and absolute error is 2. The ratio is 0.02, giving 2% error. Absolute reference magnitude keeps the denominator positive even for negative references.
Repeat with two negative values
With measured −98 and reference −100, signed error becomes +2 but percent error stays 2%. Then try a zero reference: the tool must show an error, not a percentage.
Result
Enter your values to see the result.
Measured 98 against reference 100
With a measurement of 98 and a reference of 100, the signed difference is −2 and absolute error is 2. The ratio is 0.02, giving 2% error. Absolute reference magnitude keeps the denominator positive even for negative references.
Usage scenario
- Input
- 98; 100
- Result
Calculation steps
Calculate the absolute distance
Divide by the absolute reference value
Convert the ratio to a percentage
Zero references and measurement uncertainty
A zero reference makes relative error undefined; it does not mean zero error. A deviation from a reference is not by itself an estimate of uncertainty or repeatability. Measurement method, instrument resolution and, where appropriate, repeated measurements are also needed.
These are example inputs, rather than measurements of a real case. Results use the full tool’s calculation engine. Compare them with the worked steps in this guide, then tick the checks after reviewing.
| Parameter | Value |
|---|---|
| What are the limits of this tool? | Values from −1 trillion to 1 trillion; reference must be nonzero. Use the same unit. |
| Processing and privacy | Inputs and results are processed in your browser and are not sent to the server. Aggregate statistics, when enabled, record only the tool and outcome, without the content. |