MEASUREMENT UNCERTAINTY
Absolute and relative uncertainty across the range
Changing the units of expression does not justify extrapolating a performance claim.
Revised 30 September 2026. The original publication date and address are retained.
Two expressions of the same estimate
For a non-zero result x, relative standard uncertainty is u(x)/|x|. Multiply by 100 to express it as a percentage. If expanded uncertainty U is used instead, label the quantity consistently and state its coverage basis. A percentage is not inherently more comprehensive or more valid than an uncertainty expressed in the result’s units.
At a single result
At x = 100 units, a standard uncertainty of 4 units is a relative standard uncertainty of 4%. These express the same information. If k = 2 is justified, expanded uncertainty is 8 units or 8%; changing from u to U is a different operation from changing units to percent.
Across the measuring interval
A constant SD model predicts that relative uncertainty becomes larger as the result approaches zero. A constant CV model predicts that absolute uncertainty increases in proportion to the result. Real procedures may need a combination or a piecewise description. Select the model from suitable evidence, not from which expression looks tidier.
The synthetic curve uses u(x) = √[1² + (0.04x)²], with independent contributions in compatible units. At 10 units, u is about 1.08 units (10.8%); at 100 units, about 4.12 units (4.1%). These are illustrative numbers, not performance specifications for an assay.
At the low end
Relative uncertainty becomes unstable or undefined near zero. An absolute uncertainty or suitable coverage interval may communicate the estimate better. Detection capability and quantification claims need their own evidence; MU alone does not establish a limit of detection or quantification.
A useful reporting habit
- Name the result, procedure and concentration range.
- Label standard or expanded uncertainty explicitly.
- State the model and its supported range.
- Do not extrapolate a QC percentage to an unstudied decision level without justification.
Sources & further reading
- JCGM 200 — standard and relative standard uncertainty
- Eurachem 2026 — overview of uncertainty as a function of concentration
Educational material. Examples are synthetic. Consult applicable full guidance and your locally approved procedure for operational decisions.