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Measurement Uncertainty Budget Worksheet

An uncertainty budget is the table that shows where your measurement doubt comes from and how big each piece is. This worksheet follows the GUM approach: list sources, convert each to a standard uncertainty, combine in quadrature and expand.

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Uncertainty source	Type	Distribution	Value (half-width or std dev) (um)	Divisor	Sensitivity coefficient	Standard uncertainty u(i)	u(i) squared
						0.6	0.36
						0.5	0.25
						0.2887	0.0833
						0.2309	0.0533
						0.1732	0.03

Sum of squares

0.7767

Combined standard uncertainty uc

0.8813

Expanded uncertainty U (k=2, about 95%)

1.7626

Keep one unit across all rows. Use a divisor of 1 for a standard deviation, 2 for a certificate value quoted at k=2, 1.732 (root 3) for rectangular limits, 2.449 (root 6) for triangular and 1.414 (root 2) for U-shaped. The 95% coverage claim assumes a large effective degrees of freedom. Check this before quoting k=2.

Standardize uncertainty budgets across your lab

We can help turn recurring budgets into reusable templates linked to your instrument records.

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How to use it

Add one row per source of uncertainty: repeatability, reference standard, resolution, temperature, drift, alignment, operator effect and so on. Enter the value in a single unit, pick the distribution and enter its divisor, then add a sensitivity coefficient (1 when the source adds one for one to the result). The worksheet computes each standard uncertainty and its square, sums the squares and gives combined and expanded uncertainty. Export to Excel to attach to a calibration procedure or a lab record.

The method

JCGM 100 (the GUM) splits sources into Type A, evaluated statistically from repeated readings, and Type B, evaluated from certificates, specifications or judgment. Each is reduced to a standard uncertainty. They combine as the root of the sum of squares, weighted by sensitivity coefficients. Expanded uncertainty multiplies the combined value by a coverage factor, k=2 for roughly 95% coverage under a normal distribution. ISO/IEC 17025 requires accredited labs to evaluate uncertainty, and customers use it to judge conformance decisions.

Type A: from repeated measurements
Type B: from certificates, specs, experience
Combine in quadrature
Expand with k, usually 2

Common mistakes

The classic error is dividing by the wrong number: a certificate U quoted at k=2 needs a divisor of 2, not 1.732. Another is double counting, for example including both the standard's resolution and the same effect in its certificate. Do not add uncertainties linearly, and do not forget the unit under test's own resolution and repeatability. Finally, state the coverage factor and the confidence level next to the result, since a bare plus-or-minus number is ambiguous.

Frequently Asked Questions

What is the difference between type A and type B?

Type A uncertainty comes from statistical analysis of repeated readings, such as the standard deviation of the mean. Type B comes from everything else: calibration certificates, manufacturer specifications, handbooks and engineering judgment.

Why divide by 1.732 for rectangular limits?

If a quantity could lie anywhere within plus or minus a with equal probability, its standard deviation is a divided by the square root of 3, about 1.732. Use it for resolution, specification limits and similar bounds with no further information.

Is k=2 always 95%?

Only when the combined distribution is close to normal and the effective degrees of freedom are large. With few repeat readings the coverage factor should come from the Student t distribution, giving k above 2 for 95%.

Do I need an uncertainty budget for shop gages?

Usually not for routine shop gaging, but you do for calibration work, accredited labs and any measurement where a pass or fail decision sits close to the limit. A budget is also the basis for the test uncertainty ratio.

If you want uncertainty budgets tied to calibration records in your ERP or QMS, Netray can help design that link.

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