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1.3.5Development of Practical Skills in Physics

Calipers, Micrometers and Vernier Scales

5 min read 8 parts Lesson 22 of 29 1 quiz

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Lesson summary

1.3.5 Calipers, Micrometers and Vernier Scales — OCR A Level Physics A notes: Read vernier calipers and micrometer screw gauges accurately, correct for zero error and quote the resulting uncertainty.A ruler is too coarse for small objects.

  • Worked example 1
  • Worked example 2
  • Worked example 3
  • Note the main scale reading immediately to the left of the vernier zero. This gives the whole millimetres
  • Find which vernier line coincides best with any main scale line. If it is the 4th line then add 4 × 0.1 = 0.4 mm
  • Add the two: main reading + vernier reading

Section 1 of 8Why special instruments are needed

A ruler is too coarse for small objects. The diameter of a wire, the thickness of a coin or the width of a slot may be only a millimetre or less, and a ruler marked in millimetres gives a percentage uncertainty far above 10%. Vernier calipers and the micrometer screw gauge have a much smaller resolution, typically 0.1 mm or 0.05 mm for calipers and 0.01 mm for the micrometer.

Section 2 of 8The vernier scale

A vernier caliper has a fixed main scale in millimetres and a sliding vernier scale.

The vernier scale
The vernier scale has divisions that are slightly shorter than the main scale divisions.
On a common type, 10 vernier divisions span 9 mm on the main scale,
  • so each vernier division is 0.9 mm and the difference between a main and a vernier division is 0.1 mm.
This difference is the resolution.

To read it:

The vernier scale
Note the main scale reading immediately to the left of the vernier zero. This gives the whole millimetres.
Find which vernier line coincides best with any main scale line. If it is the 4th line then add 4 × 0.1 = 0.4 mm.
Add the two: main reading + vernier reading.

For example, if the zero lies just past 23 mm and the 6th vernier line coincides, the reading is 23.6 mm. The uncertainty is normally ± 0.1 mm (the resolution), or ± 0.05 mm for a 20-division vernier. Calipers have jaws for external diameters, smaller jaws for internal diameters and a rod for depth.

Section 3 of 8The micrometer screw gauge

A micrometer has a screw of pitch 0.5 mm. One full turn of the thimble advances the spindle 0.5 mm, and the thimble has 50 divisions, so one thimble division is 0.5 / 50 = 0.01 mm. This is its resolution.

The reading is the sleeve (main) scale reading plus the thimble reading. The sleeve shows millimetres on one side of the datum line and half-millimetres on the other. Suppose the sleeve shows 6.5 mm exposed and the thimble line 28 is aligned with the datum line: the reading is 6.5 + 0.28 = 6.78 mm.

Always use the ratchet (friction clutch) to close the jaws on the object. It slips at a fixed torque, so the object is gripped with the same, light force each time. Overtightening damages soft samples such as wire and gives a reading that is too small.

Section 4 of 8Zero error

Both instruments can have a zero error.

1
Close the jaws and read the scale.
2
If the reading is not zero, this offset is a systematic error that must be removed.
3
A positive zero error (reading above zero) is subtracted from all measurements; a negative zero error is added.
4
On a micrometer with a thimble line one division below the datum line, the zero error is −0.01 mm and it is added.
5
Always record the zero reading before starting the experiment.

To reduce random error and the effect of non-uniform objects, measure at several places along a wire, and rotate by 90° at each place because wires may not be perfectly circular. Take the mean of the readings, subtracting the zero error from the mean.

Section 5 of 8Applications and uncertainty

The cross-sectional area of a wire is found from A = πd2 / 4. Since the diameter is squared, the percentage uncertainty in A is twice the percentage uncertainty in d.

A wire of diameter 0.50 mm measured with a micrometer (± 0.01 mm) has a diameter uncertainty of 2%, so A has 4%.
Measuring with calipers (± 0.1 mm) would give a 20% uncertainty in d and 40% in A, showing why the micrometer must be chosen for thin wires.
What the symbols mean:
These measurements feed into resistivity experiments (ρ = RA / L) and Young modulus experiments met later in the course.
What the symbols mean: R = resistance (Ω) · ρ = resistivity (Ω m) · L = length (m) · A = cross-sectional area (m2)
See 1.3.1 for the general method for percentage uncertainty.

Section 6 of 8Worked examples

  1. The vernier zero of a caliper lies between 31 mm and 32 mm. The 7th vernier line coincides with a main scale line. The resolution is 0.1 mm and the zero error is +0.2 mm. Find the corrected length.

  2. A micrometer shows 4.5 mm on the sleeve and thimble division 37 at the datum. It has zero error −0.02 mm. Find the diameter and the area of the wire.

  3. A wire's diameter is measured at 5 positions: 0.51, 0.49, 0.52, 0.50 and 0.50 mm. The micrometer zero error is +0.01 mm. Find the mean diameter.

Section 7 of 8Key terms

TermMeaning
Vernier scaleSliding scale that allows fractions of a main-scale division to be read.
Micrometer screw gaugeInstrument using a precision screw to measure small lengths to 0.01 mm.
PitchDistance advanced by a screw in one full turn.
RatchetFriction clutch that limits the force on the object in a micrometer.
Zero errorNon-zero reading when the jaws are closed.
ThimbleRotating part of the micrometer carrying the divisions.

Section 8 of 8Exam technique

1
Reading the vernier line next to the zero instead of the one that coincides with a main scale line.
2
Forgetting to read the half-millimetre mark on the micrometer sleeve, giving an answer 0.5 mm too small.
3
Subtracting a negative zero error instead of adding it.
4
Squeezing the micrometer directly rather than using the ratchet.
5
Measuring a wire only once, rather than at several positions and orientations.
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