= Gauge block
A \b[gauge block] is a physical <length standard> with carefully finished, approximately flat and parallel opposing measuring faces. Its calibrated length transfers a reference dimension to a comparator, a <caliper> or another measuring system. The nominal inscription identifies its intended size; the certificate supplies the measured departure and <measurement uncertainty>.<The Gauge Block Handbook by Ted Doiron and John S. Beers>[§2.2.2, Nomenclature and Definitions; §5.3, comparative measurements]{ref}
The reference definition uses a block face wrung to an auxiliary plane and a specified point on the opposite face. <Gauge block wringing> also permits blocks to form a stack; the defined length convention includes a wringing layer. Clean contacts, the calibrated departures and the thermal conditions matter.<The Gauge Block Handbook by Ted Doiron and John S. Beers>[§2.2.2 and §6.1, definition and wringing-layer convention]{ref}
An original stack uses nominal lengths $10\,\mathrm{mm}$, $2\,\mathrm{mm}$ and $1.5\,\mathrm{mm}$, giving nominal total $13.5\,\mathrm{mm}$. If their certified departures under compatible reference conditions are $+0.10$, $-0.04$ and $+0.02\,\mathrm{\mu m}$, the sum is $13.50008\,\mathrm{mm}$. The nominal sizes alone would omit the $0.08\,\mathrm{\mu m}$ correction. Combining uncertainties also requires their <covariance>, not just adding the certificate values.
For a separate illustrative <thermal expansion> calculation, a $100\,\mathrm{mm}$ block with stipulated linear expansion coefficient $11.5\times10^{-6}\,\mathrm{K^{-1}}$ lengthens by $2.3\,\mathrm{\mu m}$ when heated by $2\,\mathrm K$. These are chosen model parameters, not a certificate for a particular block. NIST's handbook treats correction to the reference temperature $20\,{}^{\circ}\mathrm C$ and temperature differences in comparisons.<The Gauge Block Handbook by Ted Doiron and John S. Beers>[§5.4.3.1, Temperature Effects, Eq. 5.8]{ref}
NIST describes two complementary routes: optical <interferometry> establishes block lengths, while a <differential length comparator> transfers calibrated differences. The apparatus and thermal control determine which uncertainty contributions matter. Handling a block warms it; waiting for thermal equilibration is part of the measurement rather than idle time.<The Gauge Block Handbook by Ted Doiron and John S. Beers>[§§5.4.3–5.5 and 6.2, environmental control, handling and interferometers]{ref}
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