Calipers
The default modern hand tool, structurally Abbe-violating, and the one whose display most oversells its specification.
Read the caliper reference →Documentation / Instruments
I — The reference
Four mechanisms, wearing different clothes
Abbe error appears in a caliper and again in the structural loop of a coordinate measuring machine. Cosine error appears in a lever indicator and again in laser interferometry. Measuring force appears in a micrometer and again in stylus profilometry. Learn the four once and every instrument page gets shorter.
Reference · No product claim on these pages
II — Abbe’s principle
Abbe’s principle, from 1890: the line of measurement must be collinear with the axis of the reference scale. Where the scale sits offset from the measurement line by a distance h, and the moving carriage tilts through an angle θ, the indicated length is wrong by
εAbbe ≈ h · tan θ ≈ h · θ (θ in radians)
This is a first-order error. It does not cancel, it does not
average out, and it grows linearly with the offset. That single fact explains
why one instrument beats another of similar cost by an order of magnitude.
A micrometer is nominally Abbe-compliant for a simple external measurement: screw axis, spindle axis and measurement line are one line. A caliper is structurally Abbe-violating: the scale lies in the beam, the measurement happens out at the jaw tips. That is the largest single reason a 0–25 mm micrometer sits in a ±2 µm class while a 0–150 mm caliper sits in a ±20 µm one.
Everywhere else it is the same sum with different names. A height gage’s offset is the horizontal reach from the column scale to the scriber, so long overhangs and heavy probe extensions are Abbe amplifiers. A depth micrometer is compliant along its rod axis but sensitive to base rock. For bore gages, snap gages and indicator stands it is the distance from the transducer axis to the contact line.
III — Cosine error
If the measuring axis is misaligned from the true feature axis by an angle α, a displacement along the true axis registers short:
indicated = true × cos α → true = indicated / cos α
Cosine error is second order, and that is the useful part.
Small misalignments are nearly free; larger ones get expensive fast. It is the
opposite temperament to Abbe error, which grows linearly from the first
micron of offset, so the two want different habits from the operator.
IV — Temperature and force
| Mechanism | Where it bites |
|---|---|
| Thermal | The reference temperature is 20 °C. Everything from gage block wringing to CT drift is governed by it, and the error is not the room’s temperature but the difference between part and instrument — which is why a part handled straight from a machine reads differently from the same part half an hour later. |
| Measuring force | Contact deforms both the part and the instrument. A micrometer ratchet exists to make the force repeatable rather than correct. A caliper has no constant-force device at all, so consistency is the only control available. |
| Hysteresis and wear | Approach direction matters, and worn faces bias every subsequent reading rather than scattering them. |
| Operator technique | Not a footnote. On hand gaging it is frequently the largest single term in a Gage R&R, and it is the one an instrument specification says nothing about. |
V — Resolution is not accuracy
The most consequential fact in this whole reference. A digital
caliper displaying 0.01 mm is specified around ±0.02 mm at 150 mm: the
display is finer than the specification by a factor of twenty. Every instrument
page here states resolution and maximum permissible error separately, because
reading the first as if it were the second is the commonest way a measurement
system gets trusted further than it has earned.
VI — The library
Each page covers the same six things: what the instrument is and how it reads, the variants worth knowing, resolution against maximum permissible error, its Abbe posture, the technique that actually moves the numbers, and (the section no reference library on the web carries) how to get data out of it.
Micrometers
Abbe-compliant by construction, force-controlled by design, and 25 mm at a time: the three reasons it beats a caliper.
Read the micrometer reference →Indicators and comparators
Comparative by nature: every reading is relative to whatever it was mastered against.
In preparationBore and internal gaging
Where the measurement is a chord unless the operator finds the true diameter.
In preparation