Vernier Caliper, Micrometer and Sine Bar Calculator

Work out a vernier or micrometer reading from its scale marks, or the gauge-block stack for a sine bar angle.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

For a vernier caliper, enter the main scale reading just before the vernier zero, the size of one main scale division, the number of vernier divisions and the vernier line that lines up. The reading is the main scale plus the line times the least count (the division size over the number of vernier divisions).

For a micrometer enter the sleeve reading in whole and half millimetres and the thimble division. Enter any zero error and it is taken off the reading.

For a sine bar enter the roller distance and the angle to set. The stack height is the length times the sine of the angle. Or enter a stack height to find the angle it gives.

Formulas used

  • LC = \frac{\text{main division}}{\text{vernier divisions}}
  • \text{reading} = \text{main} + n\,LC
  • h = L\sin\theta

Worked example

With the default numbers in the calculator above:

  1. Least count of the vernier: 0.0500 mm
  2. Reading: 12.35 mm
  3. Corrected reading (zero error removed): 12.35 mm

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: What do you want? Micrometer reading.

  1. Reading: 7.78 mm
  2. Corrected reading (zero error removed): 7.78 mm

Common questions

What is the least count?

The smallest reading the instrument can make: 0.05 mm for a vernier with 20 divisions, 0.02 mm with 50, and 0.01 mm for a micrometer.

What is zero error?

What the instrument reads when it is closed. Subtract it from the reading.

Why is a sine bar limited to 45 degrees?

Above that, a small error in the stack height makes a large error in the angle.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: AS 2103 (vernier and dial calipers); AS 2193 (calibration of measuring instruments); machinists handbook (sine bars).

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