Relative Uncertainty Near Zero: Keep the Absolute Quantity Visible

Identify the denominator

Relative standard uncertainty divides standard uncertainty by the absolute measured value. Its interpretation requires the value and uncertainty to refer to the same result and compatible units. At zero the ratio is undefined; close to zero it can become very large without a corresponding change in absolute uncertainty.

An invented comparison

Consider standard uncertainty 0.02 g for two illustrative results: 10.00 g and 0.10 g. Their relative values are 0.2% and 20% respectively. The absolute uncertainty is unchanged, but the denominator differs by a factor of one hundred.

For a difference result crossing zero, a relative percentage is a poor standalone display. Retain the signed result and absolute uncertainty, then choose a summary appropriate to the review question. These examples do not set an acceptance requirement for any filling system.

Keep the result understandable

Label whether the uncertainty is standard or expanded, and identify the reference used for any percentage. Do not silently substitute a nominal target when the requested metric uses the measured value. If a target-based percentage is useful, name it as a different metric and retain the absolute statement.

Primary references: JCGM international vocabulary.

Measurement review worksheet

This blank worksheet is for your own project. It contains no H M machine trial result.

Customer Questions

Primary References

These references support the technical principles discussed in this guide. The worked examples and review questions are educational.

• JCGM international vocabulary