Distinguish exact model values, rounded approximations and estimates from measurements. Declare the rounding rule, preserve information through calculations and unit changes, and interpret resolution, precision, accuracy and the stated uncertainty type without turning a report’s digits into guaranteed bounds.
Key knowledge
Measurement uncertainty describes the spread of values assignable to a specified measurand using the available information. A standard uncertainty expresses this spread as a standard deviation.
Conditions and scope
Uncertainty is non-negative and is distinct from the unknown measurement error.
An interval requires a stated coverage interpretation; one standard uncertainty is not a guaranteed bound.
Sources · 13
References
Sources retain their recorded scope. A source link alone does not establish verification of every statement.
Joint Committee for Guides in Metrology (JCGM)3 sources
2026-10-10 · Uncertainty/standard-uncertainty terminology only; no uncertainty budget or numerical coverage probability has been established for a particular measurement.
Foundational review
2026-10-10 · Fresh primary-source inspection of the complete compact record, including every statement, equation, quantity and material condition, followed by independent AI editorial review. This check does not certify all linked lessons or every passage of every cited publication.
Sources from other places
Scope or convention differs
Standard uncertainty expressed through a standard deviation, distinct from measurement error.
The older guide focuses on an average and coverage factors; the repository measurand definition is broader.
Type A evaluates an uncertainty component by statistical analysis of measured values under defined conditions. Type B uses other available information. Both contribute to an uncertainty evaluation; they are not synonyms for random and systematic effects.
Different evaluation methods supply components of a measurement uncertainty assessment.
Expanded uncertainty is U = k u_c. Reporting y ± U requires the factor k, intended coverage and how that coverage was obtained; k = 2 does not universally guarantee 95% coverage.
Expanded uncertainty scales a combined standard uncertainty under an explicit coverage model.
A maximum permissible measurement error is an extreme error value permitted by specifications or regulations for a measurement, instrument or system. An accuracy class groups instruments or systems meeting stated metrological requirements intended to keep errors or instrumental uncertainties within specified limits under stated conditions. Neither label automatically supplies the standard uncertainty of a particular measurement result.
This relation concerns the stated maximum permissible error and accuracy class claim and its conditions; it does not assert an unqualified prerequisite or an additional theorem.
Definitional uncertainty results from the finite detail in a measurand definition. It is a component of measurement uncertainty and gives a minimum uncertainty achievable under that definition. A length measurand without adequately specified endpoints or relevant thermal state can retain ambiguity even if indication noise is reduced by repetition. Refining the definition can change that component and may change the quantity being measured.
This relation concerns the stated definitional uncertainty claim and its conditions; it does not assert an unqualified prerequisite or an additional theorem.
Relative standard uncertainty is standard uncertainty divided by the absolute measured quantity value. For y≠0, u_r=u(y)/|y|; its percentage form is100u_r%. Near zero, relative uncertainty can become arbitrarily large while absolute uncertainty remains finite. The scale’s zero must have the intended meaning: an offset temperature conversion changes relative ratios even when the same temperature is represented.
This relation concerns the stated relative standard uncertainty claim and its conditions; it does not assert an unqualified prerequisite or an additional theorem.
A blank indication is obtained for a phenomenon, body or substance similar to the investigated one but with the quantity of interest assumed absent or not contributing. Null measurement uncertainty is associated with a null or near-zero measured quantity value. Neither a blank nor a null indication guarantees zero uncertainty; subtracting a blank requires the measurement model and the uncertainties and any covariance of the sample and blank results.
This relation concerns the stated blank indications and null measurement uncertainty claim and its conditions; it does not assert an unqualified prerequisite or an additional theorem.
Decimal places count positions after the decimal separator. Significant digits in a nonzero reported decimal start at the first nonzero digit and end at the last explicitly retained digit. Leading zeros locate the decimal point; trailing zeros can communicate retained precision. Nearest rounding must declare its halfway rule.
Retained digit precision alone does not determine uncertainty.
For a pure compound of fixed composition, convert each constituent element's measured mass to amount using its appropriate molar mass. Divide those amounts by a common reference amount and identify a smallest whole-number atom ratio consistent with the measurements. This gives an empirical formula, not atom connectivity. For a molecular compound with independently known molar mass, the ratio to the empirical formula-unit molar mass gives the positive integer multiplier for molecular subscripts, within measurement uncertainty.
Measured composition and molar mass must support the proposed integer ratio within uncertainty.
Learning guidance · 3 / 3
Preserved learning suggestions. They are not proof, empirical evidence or mandatory prerequisites.