# Measurement Uncertainty Type B Divisor Table > Source: https://netray.co/tools/measurement-uncertainty-type-b-divisor-reference > Publisher: Netray (netray.co), AI and integration engineering for ERP and manufacturing systems. > Section: Free Tools ## Short answer Which divisor to use when converting a stated limit, resolution or certificate value into a standard uncertainty. ## Category quality ## Industry Metrology ## Audience - Calibration technician - Metrologist - Quality engineer ## Tool **Kind:** worksheet **Mode:** reference **Columns:** #### Distribution **Key:** distribution **Type:** text #### Divisor **Key:** divisor **Type:** text #### Numeric value **Key:** numeric **Type:** number **Format:** decimal #### When it applies **Key:** when **Type:** text #### Typical source **Key:** example **Type:** text **Rows:** **Distribution:** Rectangular (uniform) **Divisor:** sqrt(3) **Numeric:** 1.732 **When:** Limits known, no information about where in the interval the value lies **Example:** Manufacturer accuracy specification, drift limits, temperature limits **Distribution:** Rectangular (resolution) **Divisor:** sqrt(3) on half the resolution **Numeric:** 1.732 **When:** Digital display resolution, take half of the least significant digit as the limit **Example:** Resolution of the unit under test or the standard **Distribution:** Triangular **Divisor:** sqrt(6) **Numeric:** 2.449 **When:** Values near the center are more likely than values at the limits **Example:** Interpolation between calibration points, some environmental effects **Distribution:** U-shaped (arcsine) **Divisor:** sqrt(2) **Numeric:** 1.414 **When:** Values are most likely near the limits **Example:** Sinusoidal temperature cycling, mismatch error in RF work **Distribution:** Normal, k = 1 **Divisor:** 1 **Numeric:** 1 **When:** Value is already a standard uncertainty (one standard deviation) **Example:** Standard deviation from repeated readings, certificate quoting 1 sigma **Distribution:** Normal, k = 2 **Divisor:** 2 **Numeric:** 2 **When:** Value is an expanded uncertainty at about 95 percent coverage **Example:** Calibration certificate stating U with k = 2 **Distribution:** Normal, k = 2.58 **Divisor:** 2.58 **Numeric:** 2.58 **When:** Value is stated at 99 percent coverage **Example:** Certificate stating U at 99 percent **Distribution:** Normal, k = 3 **Divisor:** 3 **Numeric:** 3 **When:** Value is stated at about 99.7 percent coverage **Example:** Certificate stating U with k = 3 **Distribution:** Normal, 95 percent (k = 1.96) **Divisor:** 1.96 **Numeric:** 1.96 **When:** Certificate states 95 percent confidence without naming k, large degrees of freedom **Example:** Older certificates, supplier data sheets **Distribution:** Type A, repeated readings **Divisor:** sqrt(n) applied to standard deviation **Numeric:** 1 **When:** Standard deviation of the mean of n readings, no distribution divisor **Example:** Repeatability of n readings of the unit under test **Notes:** 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. ## Content **Intro:** 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. **Sections:** #### How to use the table **Body:** 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 **Body:** 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 **Body:** 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 **Body:** 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. **Cta:** 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. **Faq:** #### Why divide by square root of 3? **Answer:** 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? **Answer:** 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? **Answer:** 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? **Answer:** 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. ## Search terms type b uncertainty divisor, rectangular distribution divisor root 3, triangular distribution divisor root 6, uncertainty budget divisors, resolution uncertainty divisor, u shaped distribution divisor, gum type b evaluation, iso 17025 uncertainty budget --- Talk to an engineer: https://netray.co/contact?intent=erp_ai | Machine catalog: https://netray.co/agent/catalog.json