Practice: reading a vernier caliper
Read nine vernier caliper diagrams with no zero error, with a checked answer and a worked solution for each. Analogue verniers are beyond the G3 Physics syllabus.
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Each caliper below has no zero error. Give each reading in centimetres to 0.01 cm, in three lines:
- Main scale: the mark immediately to the left of the vernier zero, to 0.1 cm.
- Vernier scale: the number of the vernier line that lines up exactly, multiplied by 0.01 cm.
- Reading: the sum of the two.
The digital and vernier calipers lesson explains why the method works.
Warm up with the trainer
Measure a few objects with the trainer, then work through the diagrams below.
A vernier caliper open beside a metal block. Drag the sliding jaw to close it on the object.
- Check
- Close the jaws onto the object first.
Try this
0 of 3 doneDrag the sliding jaw until it just touches the object. (not done yet)
The jaws should touch the object without squeezing it; the caliper then shows the object's width.
Read the caliper and enter the width to 0.01 cm. (not done yet)
Reading = main scale reading just before the vernier zero + (aligned vernier line × 0.01 cm).
Read three different objects. (not done yet)
With practice you can read a vernier in seconds: main scale first, then the one line that aligns.
You’ve tried every task.
Read the scales
Worked example 1
Read both scales
Problem
Read the vernier caliper in centimetres.
Show full solution
Read the main scale
Method
The main-scale reading immediately left of vernier zero is 8.6 cm.
Reason
The value to the right has not yet been passed.Working
Answer
x main = 8.6 cm
Read the vernier
Method
Division 2 aligns, giving 0.02 cm.Reason
Each vernier division represents 0.01 cm.
Working
Answer
x vernier = 2(0.01) = 0.02 cm
Add the readings
Method
The observed reading is 8.62 cm.Reason
The vernier part refines the main-scale reading.Working
Answer
x = 8.6 + 0.02 = 8.62 cm
Quick check
Keep the final answer to 0.01 cm, matching the instrument resolution.
Guided practice 1
A main-scale reading of zero
Problem
Read the vernier caliper in centimetres.
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Hints
Hint 1
separate the two scale parts
Write 0.0 cm + 6(0.01 cm).
Show solution step by step
Read both parts
Method
The main scale is 0.0 cm and division 6 contributes 0.06 cm.
Reason
Aligned vernier division n contributes n × 0.01 cm.
Working
Answer
0.0 + 6(0.01)State the reading
Method
The reading is 0.06 cm.Reason
The zero main-scale contribution does not remove the vernier contribution.
Working
Answer
x = 0.0 + 0.06 = 0.06 cm
Quick check
Do not drop the leading zero in a decimal measurement.
Guided practice 2
Combine both scales
Problem
Read the vernier caliper in centimetres.
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Hints
Hint 1
convert division 3
The vernier contribution is 3(0.01 cm).
Show solution step by step
Read both parts
Method
The main scale is 6.4 cm and the vernier contributes 0.03 cm.
Reason
Division 3 is the aligned vernier mark.Working
Answer
x vernier = 3(0.01) = 0.03 cm
Add
Method
The reading is 6.43 cm.Reason
Observed reading equals main plus vernier.Working
Answer
x = 6.4 + 0.03 = 6.43 cm
Quick check
Write 6.43 cm, not 6.4 cm, so the recorded precision matches the vernier.
Spot the mistake 1
Hundredths, not tenths
Learner claim
A learner reads the scale as 1.60 cm because division 6 aligns. Diagnose the reading.
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Show solution step by step
Diagnose the place value
Method
Division 6 means 0.06 cm, not 0.60 cm.
Reason
The least count is 0.01 cm per vernier division.
Working
Answer
6(0.01) = 0.06 cmCorrect the reading
Method
The observed reading is 1.06 cm.Reason
Add the vernier contribution to the 1.0 cm main scale.
Working
Answer
x = 1.0 + 0.06 = 1.06 cm
Common mistake
The aligned division is a count; multiply it by the stated least count before adding.
Spot the mistake 2
Take the main-scale mark on the left
Learner claim
A learner uses 5.4 cm as the main-scale value and reports 5.41 cm. Diagnose the method.
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Show solution step by step
Correct the main scale
Method
The main-scale reading is 5.3 cm.Reason
The vernier zero has passed 5.3 cm but not 5.4 cm.
Working
Answer
x main = 5.3 cm
Add the vernier
Method
The reading is 5.31 cm.Reason
Aligned division 1 adds 0.01 cm.Working
Answer
x = 5.3 + 1(0.01) = 5.31 cm
Common mistake
Always read the main-scale value immediately left of vernier zero, never the next mark to its right.
Exam-style question 1
Show both scale readings
Examination question
Read the vernier caliper in centimetres and show the main-scale and vernier contributions. [3 marks]
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Show solution step by step
Main scale
1 markMethod
3.8 cm.Reason
This is immediately left of vernier zero.Working
Answer
x main = 3.8 cm
Vernier
1 markMethod
0.03 cm.Reason
Division 3 aligns.Working
Answer
3(0.01) = 0.03 cmTotal
1 markMethod
3.83 cm.Reason
Add the two scale contributions.Working
Answer
3.8 + 0.03 = 3.83 cm
Self-mark with the mark scheme
Tick each mark point that your answer includes.
Self-mark the main scale, vernier contribution and final reading.
Common mistake
Reading the main scale at the mark after the vernier zero, 3.9 cm, gives 3.93 cm and loses two marks.
Exam-style question 2
A high vernier line
Examination question
Read the vernier caliper in centimetres and show both scale contributions. [3 marks]
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Show solution step by step
Resolve the scales
2 marksMethod
The parts are 4.2 cm and 0.07 cm.
Reason
Division 7 aligns and each division is 0.01 cm.
Working
Answer
x vernier = 7(0.01) = 0.07 cm
Add
1 markMethod
The reading is 4.27 cm.Reason
Observed reading is main plus vernier.Working
Answer
x = 4.2 + 0.07 = 4.27 cm
Self-mark with the mark scheme
Tick each mark point that your answer includes.
Self-mark both scale parts and their sum.
Common mistake
Converting division 7 to 0.7 cm instead of 0.07 cm gives 4.9 cm and loses the last two marks.
Exam-style question 3
A whole number of centimetres
Examination question
Read the vernier caliper in centimetres and show both scale contributions. [3 marks]
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Show solution step by step
Resolve the scales
2 marksMethod
The parts are 7.0 cm and 0.05 cm.
Reason
Division 5 aligns.Working
Answer
x vernier = 5(0.01) = 0.05 cm
Add
1 markMethod
The reading is 7.05 cm.Reason
The two contributions have different decimal places.
Working
Answer
x = 7.0 + 0.05 = 7.05 cm
Self-mark with the mark scheme
Tick each mark point that your answer includes.
Self-mark both scale parts and the final precision.
Common mistake
Reading division 5 as 0.5 cm gives 7.5 cm and loses the last two marks: each vernier division is 0.01 cm.
Try it yourself 1
A small reading, then millimetres
Problem
Read the vernier caliper in centimetres, then express the same length in millimetres.
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Show the steps Optional working
Hints
Hint 1
finish the instrument reading first
Calculate 0.2 + 4(0.01) in centimetres before converting units.
Show solution step by step
Read the scale
Method
The observed reading is 0.24 cm.Reason
The main scale is 0.2 cm and division 4 adds 0.04 cm.
Working
Answer
x = 0.2 + 4(0.01) = 0.24 cmConvert the representation
Method
The same length is 2.4 mm.Reason
1 cm = 10 mm.
Working
Answer
0.24 × 10 = 2.4 mm
Quick check
The physical length is unchanged; only the numerical value and unit representation change.
Check your understanding 1 Why read at eye level?
Why must you look straight down at the vernier scale when you read it?
Show answer
From an angle, the vernier lines appear shifted against the main-scale marks, so a different line seems to line up (parallax error). Looking straight down shows which line really lines up.
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