Enter your measured (experimental) value and true (theoretical) value to calculate the relative error and absolute error. The Relative Error Calculator shows you how far off your measurement is as both a raw difference and a percentage of the true value — useful for lab work, engineering checks, or everyday estimates.
Relative Error
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Absolute Error
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Measured Value
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True Value
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Absolute error is the absolute value of the difference between your measured value and the true value: |measured − true|. It tells you the size of the discrepancy in the same units as your measurement, without regard to direction.
Relative error expresses the absolute error as a fraction of the true value: |measured − true| / |true|. It is dimensionless and is often multiplied by 100 to give a percentage, making it easy to compare errors across different scales of measurement.
They describe the same thing, just expressed differently. Relative error is the ratio (e.g. 0.00578), while percent error multiplies that ratio by 100 to give a percentage (e.g. 0.578%). This calculator shows both forms.
Yes — relative error is also commonly called percent error, percentage error, or approximation error. In science and engineering contexts the terms are used interchangeably, though 'relative error' strictly refers to the decimal ratio before multiplying by 100.
First, find the absolute error: subtract the measured value from the true value and take the absolute value. Then divide that result by the absolute value of the true value. Multiply by 100 if you want the percentage. For example, if true = 121.2 and measured = 120.5, absolute error = 0.7, relative error = 0.7 / 121.2 ≈ 0.578%.
The absolute error is |42 − 40| = 2. The relative error is 2 / 40 = 0.05, or 5%. This means your measurement is 5% away from the accepted true value.
Whether an absolute error is acceptable depends entirely on context. A 1 cm error is negligible when measuring a room but enormous when machining a microchip. That's why relative error is more useful — it normalises the error against the size of the true value, letting you judge accuracy consistently across different scenarios.
Relative error accounts for the scale of the measurement. An absolute error of 1 kg means something very different when weighing a 2 kg parcel versus a 2000 kg vehicle. By expressing the error as a proportion of the true value, relative error gives a fairer picture of measurement accuracy regardless of the units or magnitudes involved.