I'm calculating the combined measurement uncertainty u(c) of a measurement for a length displacement sensor. Amongst other factors, one individual uncertainty affecting the error of measurement is the uncertainty of the gage block I'm using. In the calibration certificate of the gage block the uncertainty of measurement is expressed as:

$U(E)=0.08\ \mathrm{µm}+1.2\ \mathrm{L}$

With the coverage factor $k=2$.

The nominal thickness of the gage block is 10 mm and usually uncertainty is expressed as just ±0.08 µm. In this case, what does $L$ stand for?

  • 1
    $\begingroup$ Can you add references to the above equation? $\endgroup$ Feb 21, 2016 at 2:02

1 Answer 1


Found it at NIST:

There are four defined tolerance grades in ISO 3650; 00, 0, 1 and 2. The algorithm for the length tolerances are shown in table 2.3, and there are rules for rounding stated to derive the tables included in the standard.

$$\text{Table 2.3} \\ \begin{array}{cc} \text{Grade} & \text{Deviation from Nominal} \unicode{0x000A} \text{Length (µm)} \\ 00 & (0.05 + 0.0001L) \\ 0 & (0.10 + 0.0002L) \\ 1 & (0.20 + 0.0004L) \\ 2 & (0.40 + 0.0008L) \\ \end{array}$$

Where L is the block nominal length in millimeters.

The ISO standard does not have an added tolerance for measurement uncertainty; however, the ISO tolerances are comparable to those of the ANSI specification when the additional ANSI tolerance for measurement uncertainty is added to the tolerances of Table 2.1.

  • $\begingroup$ So do I just substitute L with 10mm in the formula U(E)=0.08um+1.2L? $\endgroup$
    – spe4ker
    Feb 19, 2016 at 21:19

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