Calculate the relative error, absolute error, and percentage error between a measured value and the true value. Essential for assessing measurement accuracy and precision.
Last updated: March 2026
Relative error is a measure of the accuracy of a measurement compared to the true or accepted value. It expresses the difference between the measured value and the actual value as a proportion of the actual value. Unlike absolute error (which is simply the difference), relative error provides context—showing how significant the error is relative to the magnitude of what's being measured.
For example, an error of 1 unit means something very different when measuring 10 units versus 1000 units. Relative error accounts for this by dividing the absolute error by the magnitude of the true value, making it a normalized measure of accuracy. It's particularly useful in science, engineering, and quality control where assessing measurement precision is critical.
Relative error can be expressed as a decimal or as a percentage. A relative error of 0.04 is equivalent to 4%, indicating that the measured value differs from the true value by 4% of the true value's magnitude.
Follow these steps to calculate relative error:
A scale measures an object's weight as 52.3 kg, but the true weight is 50 kg. Calculate the relative error.
Absolute error is the raw difference between measured and actual values: |Measured - Actual|. Relative error normalizes this by dividing by the actual value, providing context about the significance of the error relative to the measurement scale.
No. Relative error is always expressed as a positive value because we use absolute value in the calculation. However, you might separately track whether the measurement was over or under the true value.
A 0% relative error means the measured value equals the actual value perfectly—your measurement is completely accurate. In practice, getting exactly 0% is rare in real-world measurements due to instrument limitations.
Acceptable thresholds depend on the context. In precision manufacturing, 0.1% might be required. In general science, 1-5% might be acceptable. In survey work, 10% might be tolerable. It depends on the application's requirements.
Relative error allows fair comparison across different scales. An error of 1 kg is huge when weighing 10 kg (10% error) but negligible when weighing 1000 kg (0.1% error). Relative error captures this proportional context.
It's used in quality control (checking if products meet tolerances), experimental validation (comparing calculated vs measured results), instrument calibration (assessing accuracy), and data analysis (quantifying measurement precision).
Use the absolute value of the actual value in the denominator. For example, if actual = -50 and measured = -52.3, relative error = |-52.3 - (-50)| / |-50| = 2.3 / 50 = 4.6%.
Yes. If the measured value is very far from the actual value, relative error can be arbitrarily large. For example, measuring 150 when actual is 50 gives a relative error of 200%.