---
title: "Vernier caliper and micrometer readings"
subject: "Workshop Technology"
chapter: 4
key: "semester_2/workshop_technology:vernier-micrometer-reading"
source: https://www.bctengineer.com/q/semester_2/workshop_technology/vernier-micrometer-reading
site: BCT Engineering
---

# Vernier caliper and micrometer readings

Workshop Technology · Chapter 4: Measuring and Gauging

- Asked in: year not given, 4+4 marks
- Video: [How to Read a Metric Vernier Caliper](https://www.youtube.com/watch?v=vkPlzmalvN4) — WeldNotes
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_2/workshop_technology/vernier-micrometer-reading
- Whole chapter: https://www.bctengineer.com/md/semester_2/workshop_technology/chapter-4

## Question

(a) A vernier caliper has 50 divisions on the vernier scale equal to 49 mm on the main scale (1 mm divisions). Find its least count. The main scale reads 34 mm to the left of the vernier zero, the 27th vernier line coincides with a main-scale line, and the instrument has a zero error of +0.06 mm. Find the correct reading.
(b) An outside micrometer has a screw pitch of 0.5 mm and 50 divisions on the thimble. The sleeve shows 7.5 mm and the thimble reading line is the 32nd division. The zero error is -0.02 mm. Find the correct reading.

## Short answer

Vernier least count = 1 – 49/50 = 0.02 mm; correct reading = 34 + 27×0.02 − 0.06 = 34.48 mm. Micrometer least count = 0.5/50 = 0.01 mm; correct reading = 7.5 + 32×0.01 + 0.02 = 7.84 mm.

## Answer

#### (a) Vernier caliper
Least count (LC) = 1 main-scale division - 1 vernier division.

$$
\begin{aligned} 1\ \text{VSD} &= \frac{49}{50} = 0.98\ \text{mm} \\ \text{LC} &= 1 - 0.98 = 0.02\ \text{mm} \end{aligned}
$$

Reading = main scale reading + (coinciding division x LC)

$$
\begin{aligned} \text{Observed} &= 34 + 27 \times 0.02 = 34.54\ \text{mm} \\ \text{Correct} &= \text{Observed} - \text{zero error} = 34.54 - 0.06 = 34.48\ \text{mm} \end{aligned}
$$

A positive zero error means the instrument reads +0.06 mm when closed, so it is subtracted.

**Answer (a): LC = 0.02 mm; correct reading = 34.48 mm.**

#### (b) Micrometer
$$
\text{LC} = \frac{\text{pitch}}{\text{thimble divisions}} = \frac{0.5}{50} = 0.01\ \text{mm}
$$

$$
\begin{aligned} \text{Observed} &= 7.5 + 32 \times 0.01 = 7.82\ \text{mm} \\ \text{Correct} &= 7.82 - (-0.02) = 7.84\ \text{mm} \end{aligned}
$$

A negative zero error means the closed micrometer reads -0.02 mm, so the correction is added.

| Item | Value |
|---|---|
| Sleeve reading | 7.50 mm |
| Thimble reading | 0.32 mm |
| Observed | 7.82 mm |
| Zero error | -0.02 mm |
| Correct | 7.84 mm |

**Answer (b): LC = 0.01 mm; correct reading = 7.84 mm.**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. For 50 vernier divisions equal to 49 mm on the main scale, the least count is
   A. 0.01 mm
   B. 0.02 mm
   C. 0.05 mm
   D. 0.98 mm
   Answer: B. LC = 1 - 49/50 = 0.02 mm. (Key point: Vernier least count)

2. With a main scale reading of 34 mm and the 27th line coinciding, the observed reading is
   A. 34.27 mm
   B. 34.54 mm
   C. 34.48 mm
   D. 35.54 mm
   Answer: B. Observed = 34 + 27 x 0.02 = 34.54 mm. (Key point: Vernier observed reading)

3. A zero error of +0.06 mm is dealt with by
   A. Adding 0.06 mm
   B. Subtracting 0.06 mm, giving 34.48 mm
   C. Ignoring it
   D. Doubling it
   Answer: B. A positive zero error means the closed instrument reads +0.06, so it is subtracted from the observed reading. (Key point: Zero error correction)

4. A micrometer shows sleeve 7.5 mm, thimble 32 divisions (LC 0.01 mm) with a zero error of -0.02 mm. The correct reading is
   A. 7.80 mm
   B. 7.82 mm
   C. 7.84 mm
   D. 7.52 mm
   Answer: C. Observed = 7.5 + 0.32 = 7.82 mm; the negative error is subtracted, i.e. 0.02 is added, giving 7.84 mm. (Key point: Micrometer reading with negative zero error)

## Related in Workshop Technology

- [Gear manufacturing and simple indexing](https://www.bctengineer.com/question.md?key=semester_2%2Fworkshop_technology%3Agear-milling-indexing-numerical) — Workshop Technology, chapter 11
- [Slip gauges: wringing and building a size](https://www.bctengineer.com/question.md?key=semester_2%2Fworkshop_technology%3Aslip-gauge-wringing-build-up) — Workshop Technology, chapter 4
- [Drilling time and metal removal rate](https://www.bctengineer.com/question.md?key=semester_2%2Fworkshop_technology%3Adrilling-time-numerical) — Workshop Technology, chapter 5
- [Turning time and metal removal rate](https://www.bctengineer.com/question.md?key=semester_2%2Fworkshop_technology%3Alathe-turning-time-mrr-numerical) — Workshop Technology, chapter 6
- [Blanking force and press capacity for washer](https://www.bctengineer.com/question.md?key=semester_2%2Fworkshop_technology%3Ablanking-force-press-capacity) — Workshop Technology, chapter 8
- [Upsetting diameter and force calculation](https://www.bctengineer.com/question.md?key=semester_2%2Fworkshop_technology%3Aupsetting-diameter-force-numerical) — Workshop Technology, chapter 9

## Related in other subjects

- [Vernier caliper and micrometer readings](https://www.bctengineer.com/question.md?key=semester_3%2Fmetrology%3Avernier-and-micrometer-readings) — Metrology, chapter 4