= Primary measurement standard
A <primary measurement standard> is a <measurement standard> established by a <primary reference measurement procedure>, or an artifact selected by convention. A <primary reference measurement procedure> obtains its result without calibration against a standard of the same kind of quantity; it may still require measurements of other kinds of quantity.<International vocabulary of metrology by JCGM>[VIM3 entries 5.4 and 2.8; entry 5.4 example 2, pressure from force and area]{ref}
For an original ideal <pressure> realization, independently established <force> $F=10.000\,\mathrm{N}$ acts on an effective piston area $A=1.0000\times10^{-4}\,\mathrm{m^2}$. The <measurement model> gives
$$
p=\frac FA=100000\,\mathrm{Pa}.
$$
If the inputs have independent <standard uncertainties> $u(F)=0.010\,\mathrm{N}$ and $u(A)=2.0\times10^{-7}\,\mathrm{m^2}$, first-order <propagation of uncertainty> gives
$$
\frac{u(p)}p\simeq\sqrt{\left(\frac{u(F)}F\right)^2+\left(\frac{u(A)}A\right)^2}=0.002236,
$$
so $u(p)\simeq224\,\mathrm{Pa}$. This is an illustrative model, not a complete piston-gauge uncertainty budget: a physical realization must also account for effects such as piston deformation and friction.<Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results by Barry N. Taylor and Chris E. Kuyatt>[Appendix A, equation A-3, first-order propagation law]{ref}
The essential distinction is how the <pressure> value is established. Merely comparing a gauge with another pressure gauge does not make it a <primary measurement standard>. Primary status also does not mean zero <measurement uncertainty>.
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