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Measurement Uncertainty Type B Divisor Table

In a measurement uncertainty budget, every contribution must be converted to a standard uncertainty before they are combined. This table lists the divisor for each common distribution, what it applies to and where such values typically come from in a calibration lab.

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Distribution	Divisor	Numeric value	When it applies	Typical source
Rectangular (uniform)	sqrt(3)	1.732	Limits known, no information about where in the interval the value lies	Manufacturer accuracy specification, drift limits, temperature limits
Rectangular (resolution)	sqrt(3) on half the resolution	1.732	Digital display resolution, take half of the least significant digit as the limit	Resolution of the unit under test or the standard
Triangular	sqrt(6)	2.449	Values near the center are more likely than values at the limits	Interpolation between calibration points, some environmental effects
U-shaped (arcsine)	sqrt(2)	1.414	Values are most likely near the limits	Sinusoidal temperature cycling, mismatch error in RF work
Normal, k = 1	1	1	Value is already a standard uncertainty (one standard deviation)	Standard deviation from repeated readings, certificate quoting 1 sigma
Normal, k = 2	2	2	Value is an expanded uncertainty at about 95 percent coverage	Calibration certificate stating U with k = 2
Normal, k = 2.58	2.58	2.58	Value is stated at 99 percent coverage	Certificate stating U at 99 percent
Normal, k = 3	3	3	Value is stated at about 99.7 percent coverage	Certificate stating U with k = 3
Normal, 95 percent (k = 1.96)	1.96	1.96	Certificate states 95 percent confidence without naming k, large degrees of freedom	Older certificates, supplier data sheets
Type A, repeated readings	sqrt(n) applied to standard deviation	1	Standard deviation of the mean of n readings, no distribution divisor	Repeatability of n readings of the unit under test

Divisors follow the GUM (JCGM 100) treatment of Type B evaluation. Assume a rectangular distribution when you have no better information, as it is the most conservative common choice. Always record the basis for the distribution you chose.

Connect uncertainty budgets to equipment records

Optional: discuss linking uncertainty data to gage and equipment masters in your ERP.

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How to use the table

For each input in your budget, decide what kind of information you have. A plus or minus limit from a data sheet usually means rectangular, so divide the half-width by 1.732. A certificate quoting an expanded uncertainty with k = 2 is divided by 2. A standard deviation from repeated readings needs no divisor, though the standard deviation of the mean is divided by the square root of the number of readings. Search for your situation and copy the divisor.

Worked example

A reference thermometer has a stated accuracy of plus or minus 0.10 C. Treated as rectangular, the standard uncertainty is 0.10 / 1.732 = 0.058 C. Its calibration certificate says U = 0.04 C, k = 2, so the standard uncertainty is 0.02 C. A 0.01 C display resolution gives a half-width of 0.005 C, divided by 1.732 gives 0.0029 C. Combine these by root sum of squares, then multiply by the coverage factor.

Choosing the distribution honestly

Rectangular is the default when you only know limits. Triangular needs a reason, for instance knowing the central value is more probable. Using a larger divisor than the evidence supports shrinks your uncertainty and can make your capability claim look better than it is. Auditors under ISO/IEC 17025 will ask for your basis, so write it in the budget next to the divisor.

Common mistakes

Applying a divisor to a value that is already a standard uncertainty, forgetting that the certificate value is an expanded uncertainty, and using the full resolution rather than half of it are the three most common slips. Another is dividing a sensitivity coefficient by the divisor; the coefficient multiplies after the divisor.

Frequently Asked Questions

Why divide by square root of 3?

For a rectangular distribution with half-width a, the standard deviation is a divided by the square root of 3. That is about 0.577 times the half-width. It converts a limit into a one-standard-deviation value you can combine.

What divisor do I use for resolution?

Take half of the least significant digit as the half-width, then divide by the square root of 3. A display that reads to 0.01 gives 0.005 / 1.732 = 0.0029.

Is U with k = 2 always 95 percent?

It is approximately 95 percent when the underlying distribution is normal and the effective degrees of freedom are large. For few degrees of freedom the coverage is lower unless a larger k from the t-distribution is used.

Should I use a triangular distribution to reduce uncertainty?

Only if you have evidence that central values are more likely. Choosing it just to lower the total is not defensible. When in doubt, use rectangular and document the reasoning.

If your lab or calibration group keeps uncertainty budgets in spreadsheets, we can help connect the budgets to the equipment record in your ERP or QMS.

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