Measurement Uncertainty Calculator

Work out measurement uncertainty instantly with clear inputs, formula shown and shareable results.

About Measurement Uncertainty Calculator

Uncertainty components are combined in quadrature as standard uncertainties. A resolution of d contributes a rectangular distribution of half-width d/2, so its standard uncertainty is d/(2 x sqrt 3). Multiplying the combined standard uncertainty by a coverage factor of 2 gives roughly 95% confidence.

Formulas

Combined uncertainty

uc = sqrt(u1^2 + u2^2 + u3^2)

Expanded uncertainty

U = k x uc, with k = 2 for approximately 95% coverage

Worked example

With the default values below, Measurement Uncertainty Calculator returns Expanded Uncertainty of 0.019732. Change any input above and every figure here is recalculated in your browser.

Inputs used

Repeatability Standard Uncertaintyminimum 0 mm: 0.008 mm
Calibration Uncertaintyminimum 0 mm: 0.005 mm
Instrument Resolutionminimum 0 mm: 0.01 mm
Coverage Factoraccepts 1–4: 2

Results

Expanded Uncertainty: 0.019732
Combined Standard Uncertainty: 0.009866
Resolution Contribution: 0.002887
Dominant Uncertainty Source: Repeatability

Step by step

1Values used
2Combined uncertainty
3Expanded uncertainty
4Expanded Uncertainty= 0.019732
5Combined Standard Uncertainty= 0.009866
6Resolution Contribution= 0.002887
7Dominant Uncertainty Source= Repeatability

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why divide resolution by 2 x sqrt 3?

A reading quantised to steps of d could be anywhere within d/2 of the true value, uniformly distributed. The standard deviation of a rectangular distribution of half-width a is a/sqrt 3.

Should uncertainty be added to the tolerance decision?

Yes for conformity assessment. A guard band equal to the expanded uncertainty is applied inside the specification limits so that accepted parts are conforming with the stated confidence.