Axotek's Normalized Error (En) calculator allows you to verify in seconds whether a measurement result is statistically compatible with a reference value, taking both uncertainties into account. It applies the criterion |En| ≤ 1 defined in ISO 13528, ISO/IEC 17043, and ILAC P10, and is ideal for interlaboratory comparisons, proficiency testing, instrument verification, and calibration result validation.
What is Normalized Error (EN)?
The Normalized Error , also known by its symbol En , is a statistical criterion used in metrology to determine whether a measurement result is compatible with a reference value, taking into account the uncertainty of both. Unlike a simple subtraction of values, the Normalized Error answers a more precise question: is the observed difference reasonable considering how much each measurement could vary, or is there evidence of a real problem?
It is one of the most widely used criteria in proficiency testing , interlaboratory comparisons and verification of measuring instruments , and is formally defined in standards such as ISO 13528 , ISO/IEC 17043 and ILAC P10 .
Normalized Error Formula
The Normalized Error is calculated using the following expression:
En = (X_med − X_ref) / √(U_med² + U_ref²)Where:
X_med — Value obtained in the measurement being evaluated.
X_ref — Reference, pattern or comparison value.
U_med — Expanded uncertainty of the measured value.
U_ref — Expanded uncertainty of the reference value.
√(U_med² + U_ref²) — Combined uncertainty of the difference between both values.
In other words: the difference between the two values is divided by the combined uncertainty of that difference. The result indicates how many times the combined uncertainty fits within the observed difference.
How to interpret the result
The standard acceptance criterion is:
Result | Interpretation |
|En| ≤ 1 | Satisfactory — the difference is explainable by the stated uncertainties. |
|In| > 1 | Not satisfactory — the difference exceeds what was expected; the cause should be investigated. |
An En value close to 0 indicates excellent agreement between the measured and reference values. A value greater than 1 does not necessarily mean the measurement is "wrong": it can also indicate that the uncertainty was underestimated, that there is a systematic bias, or that the instrument requires adjustment or recalibration.
Frequently Asked Questions (FAQ)
What does it mean when the Normalized Error is greater than 1? It indicates that the difference between the measured value and the reference value cannot be explained solely by the stated uncertainties, so the result is considered unsatisfactory and the cause should be investigated.
What is the difference between expanded uncertainty (U) and standard uncertainty (u)? Expanded uncertainty U is obtained by multiplying standard uncertainty u by a coverage factor k (typically k=2, ~95% confidence): U = k·u. The calculator allows you to enter either value.
Is it suitable for calibration certificates with multiple points? Yes. Pro mode is designed precisely for that: it allows you to add as many measurement points as needed and evaluate them all simultaneously using the same criteria.