Vernier zero correction ($L=r-z$)

A Vernier zero correction removes an indicated offset observed at a known zero setting of a Vernier scale. If the raw indication is $r$ and the indication at true zero is $z$, the additive model givesThe zero error is $z$; the correction applied to a later reading is its negative. This model addresses an offset, not every possible scale or contact error.

For an original signed example, a raw reading $r=12.35\mathrm{mm}$ with closed-jaw indication $z=+0.10\mathrm{mm}$ gives $L=12.25\mathrm{mm}$. If the zero indication is instead $-0.10\mathrm{mm}$, the corrected reading is $12.45\mathrm{mm}$. A negative zero indication therefore requires adding its magnitude. It does not imply a negative object length.

The reference setting must represent the intended zero: clean, properly contacting outside faces on a caliper are one example. Record the actual signed indication and the scale convention, rather than relying on a memorized rule about which engraved zero lies to the left. The manufacturer guide explains the coincidence reading and identifies jaw tilt, force and viewing geometry as separate error sources.^[ref]

For standard uncertainties, the additive model givesWith stipulated independent $u(r)=0.03\mathrm{mm}$ and $u(z)=0.02\mathrm{mm}$, the combined value is approximately $0.0361\mathrm{mm}$. Subtracting a measured offset does not make that offset known exactly. Correlation can matter when both observations share an uncertain reference or drift contribution.^[ref]

A second reference checks the limitation. Suppose true zero reads $0.10\mathrm{mm}$ but a known $50.00\mathrm{mm}$ separation reads $50.60\mathrm{mm}$. Removing the zero offset leaves $50.50\mathrm{mm}$, still $0.50\mathrm{mm}$ high. A model $r=aL+z$ would have $a=1.01$ here. Measurement calibration across the working interval is needed to distinguish scale error from a zero correction, with the relevant measurement uncertainty retained.