Resolution as an uncertainty component
A digital display of resolution d contributes a rectangular component of half-width d/2, giving u = d/(2√3) ≈ 0.29 d. For a 0.1 °C logger that is 0.029 °C — often the largest term in its calibration.
A display showing 5.3 °C tells you the true indication lies somewhere in 5.25–5.35 °C with, absent better information, equal probability. That is a rectangular distribution of half-width 0.05 °C, whose standard uncertainty is 0.05/√3 ≈ 0.029 °C.
Consequences
- A 0.1 °C-resolution logger cannot be calibrated to better than about ±0.06 °C at k = 2 regardless of the reference.
- A 0.01 °C display contributes only 0.003 °C, so other terms dominate.
- If the instrument truncates rather than rounds, the distribution is offset; a correction of d/2 with the same uncertainty is appropriate.
For loggers with a resolution coarser than their sensor's noise, the resolution term is the practical floor and the reason a tighter reference brings no benefit.
Frequently asked questions
- If I take the mean of ten readings that all show 5.3, does resolution uncertainty shrink?
- No. Ten identical readings carry the same information as one; the rectangular resolution component applies to the mean unchanged.
References
- [1]JCGM 100:2008 — Guide to the expression of uncertainty in measurement (GUM)
- [2]EURAMET cg-11: Guidelines on the Calibration of Temperature Indicators and Simulators by Electrical Simulation
General technical guidance written against the cited sources. It is not regulatory or legal advice and does not replace the applicable standard, guideline or a qualified reviewer's judgement.
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