Caliper

A caliper measures a dimension by relating the separation of contacting measuring faces to a scale or readout. A sliding-jaw caliper has a fixed jaw and a movable jaw; appropriate faces can measure outside dimensions, inside dimensions or steps, while a depth bar can supply a separate depth measurement. These modes use different contact geometries even when they share one slider.^[ref]

A Vernier scale, dial or electronic readout converts slider position into a measurement indication. It does not remove the need to align the contacts with the desired length. For an outside measurement, the opposed faces must meet the intended surfaces without dirt, excessive force or tilt. An inside measurement uses its designated faces and can require geometry-specific corrections; it is not merely the outside-jaw reading with a different label.

An original small-angle calculation shows why jaw geometry matters. Suppose the displacement reference and contact point are separated by $h=40\mathrm{mm}$, and a moving-jaw tilt produces angle $\theta =0.002\mathrm{rad}$. The resulting offset contribution has magnitude approximatelyIt exceeds a $0.05\mathrm{mm}$ reading increment. These are stipulated dimensions and tilt, not a measured error for a particular caliper. The primary guide gives the same lever-arm mechanism for caliper jaw tilt error and identifies contact force, wear and thermal differences as physical error sources.^[ref]

A useful check closes clean outside faces under consistent light force, then compares readings at several separations with suitable calibrated artefacts such as gauge blocks. Repeating the comparison near different contact positions can reveal a geometry-dependent error that a single zero check misses. Apply a Vernier zero correction when using that readout, while retaining uncertainty from the reference, alignment and repeatability.

The measurement result concerns the specified object dimension under stated conditions, not just slider displacement. Thermal expansion of either the object or instrument, deformation under contact force and the selected faces belong in the measurement model. More displayed digits or a finer scale cannot by themselves establish better measurement accuracy.

Caliper jaw tilt error is a change in the indicated dimension caused by rotation of a caliper's moving jaw relative to its reference geometry. If a contact lies distance $h$ from the displacement reference, a small rotation $\theta$ gives a signed offset contributionThe sign depends on the direction of rotation and contact geometry. The approximation requires small $|\theta |$; it describes this angular contribution rather than every possible measurement error.

Mitutoyo gives a concrete geometry: a jaw slope of $0.01\mathrm{mm}$ over $50\mathrm{mm}$ and a contact depth of $40\mathrm{mm}$ produce a tip error of $0.008\mathrm{mm}$. Excessive contact force and wear of the guide can cause the moving-jaw rotation.^[ref]

An original diagnostic repeats a gauge block comparison at contact depths $h_1=10\mathrm{mm}$ and $h_2=40\mathrm{mm}$. With stipulated constant $\theta =2\times 10^{-4}\mathrm{rad}$ and other effects unchanged, the angular contributions are approximately $2\mu \mathrm{m}$ and $8\mu \mathrm{m}$. Their $6\mu \mathrm{m}$ difference isolates a depth-dependent effect that a single closed-jaw zero reading could miss. Real contacts may also change force or deformation, so this comparison does not uniquely identify rotation without controls.

A Vernier zero correction removes an estimated constant offset; it cannot generally remove an error proportional to contact depth or varying force. Use consistent light contact, a clean reference and a stable temperature, and compare several separations and contact positions. A fine Vernier scale improves reading increments without guaranteeing that these mechanical contributions are small.

This lever-arm mechanism is distinct from merely projecting a fixed length onto a tilted measurement axis: the latter involves $\cos \theta$ and has a quadratic small-angle change, whereas the offset term above is linear in $\theta$. Keeping the geometry in the measurement model prevents applying the wrong angular correction.