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A standard uncertainty expresses a component of measurement uncertainty as an estimated standard deviation. It has the same unit of measurement as the measurand: $u(L)=0.2\mathrm{mm}$ describes a spread in a length, rather than a percentage or a known measurement error. A Type A evaluation of uncertainty uses statistical analysis of observations; a Type B evaluation of uncertainty uses other information, such as a reference certificate or instrument specification. These classify the evaluation method, not whether a physical effect is random or systematic.^[ref]

For $n$ independent repeated readings with common variance, the sample mean has estimated standard uncertainty $s/\sqrt{n}$, where $s$ is their sample standard deviation. This is the standard error of the mean; the scatter $s$ instead describes individual readings. Repetition reduces this contribution, but a shared measurement calibration contribution remains. A quoted tolerance $\pm a$ supplies a different example: assigning a continuous uniform distribution within those bounds gives $u=a/\sqrt{3}$. That assignment is a model of the available information, not a consequence of repeating measurements.^[ref]

A systematic error is a component of measurement error that remains constant or changes predictably when measurements are repeated under specified conditions. A ruler with an incorrect scale, a thermometer with a measurement zero offset, and an unaccounted instrumental drift can all produce such effects. Closely agreeing readings can therefore have poor measurement accuracy: repetition tests their scatter, not the correctness of the shared reference.

An estimated systematic error should be corrected when possible, with the correction's measurement uncertainty included in the measurement uncertainty budget. Suppose a balance reads $m+b$ and a reference gives an estimate $\hat{b}$ of its offset. The corrected result is $m_{\mathrm{read}}-\hat{b}$; uncertainty in $\hat{b}$ remains even if the same unknown offset affected every weighing. Changing the reference, using a blank, or testing systematic-error cancellation by reversal can reveal effects that a long sequence of identical readings misses. The Type A evaluation of uncertainty and Type B evaluation of uncertainty distinction concerns how uncertainty is evaluated, so neither label is synonymous with systematic error.^[ref]

A Type A evaluation of uncertainty obtains an uncertainty component through statistical analysis of observations. For independent repeated readings with sample standard deviation $s$, the estimated standard uncertainty of their mean is $s/\sqrt{n}$.

Independence and stability matter: serially correlated readings do not generally provide $n$ independent pieces of information. Type A and Type B evaluation of uncertainty classify how components are assessed, rather than separating random measurement errors from systematic error.^[ref]

A Type B evaluation of uncertainty uses information other than a statistical analysis of repeated observations of the current quantity. Examples include calibration certificates, manufacturer specifications and knowledge of resolution. It describes the evaluation method, not whether an effect is systematic or random.

If a rounding error is reasonably modeled as uniform on $[-a,a]$, its standard uncertainty is $a/\sqrt{3}$. The distribution assumption is part of the evaluation and should be justified by the available information.^[ref]