Digital and vernier calipers
Key idea: A vernier reading is the main-scale reading plus the vernier division that lines up exactly with a main-scale line, which gives a finer reading than the main scale alone.
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Guided steps
- Choose the jaws or depth rod for each measurement and align the caliper with the length.
- Read the complete digital method, including zero, gentle contact and display resolution.
- Remove the signed closed reading once; resetting zero changes which correction is needed.
- Choose the measuring part and correct the signed offset.
- Choose the measuring part and average the new readings.
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A caliper measures lengths from a fraction of a millimetre up to about 15 cm: the outside diameter of a rod, the inside diameter of a tube or the depth of a hole. A rule cannot reach inside a tube or resolve a tenth of a millimetre; a caliper can. In practical work you use a digital caliper. The instrument considered here displays the reading directly in steps of 0.01 mm; that is its display resolution, not a guarantee that every reading is accurate to that amount.
Choose the part that touches the object
A caliper has three measuring parts. Each one puts its two contact faces at the two ends of a different kind of length.
| Length to measure | Part to use | Example |
|---|---|---|
| external diameter or thickness | outside jaws (the large pair) | diameter of a rod, thickness of a coin |
| internal diameter | inside jaws (the small pair) | inside diameter of a pipe or beaker |
| depth | depth rod at the end of the beam | depth of a hole or a step |
Align the measuring direction with the length you want. For a diameter, the contacts must span the centre rather than a shorter chord; avoid tilting across the object. For depth, rest the beam’s end flat on the top surface with the rod perpendicular to it.
Zero, measure and record
- Wipe the jaws, close them gently and look at the display. It should read 0.00 mm.
- If it does not, press ZERO with the jaws closed. A reading left on the display when the jaws are closed is a zero error: it adds the same amount to every measurement.
- Open the jaws, place the object and close them until both faces just touch. Do not squeeze. A soft object compresses, and the reading comes out too small.
- Record the whole display with its unit, for example 12.30 mm. The display resolves 0.01 mm, and the final zero shows it.
- For a wire or rod that may not be uniform, measure at several positions and orientations and take the mean.
If a question tells you the caliper was not zeroed, correct the reading with corrected reading = observed reading - zero error, keeping the sign of the zero error.
Worked example 1
A caliper that was not zeroed
Problem
A digital caliper reads + 0.02 mm with its jaws closed. Without resetting zero, it reads 12.34 mm around an object. Find the corrected length.
Show full solution
Remove the over-reading
Method
Subtract the signed closed-jaw reading from the object reading.Reason
The caliper already shows + 0.02 mm when there is nothing between the jaws, so every reading is 0.02 mm too large.Working
Answer
corrected length = 12.34 mm-(+0.02 mm)Report the corrected length
Working
Answer
corrected length = 12.32 mm
Quick check
Check your understanding 1 Choose the part and correct the reading
A digital caliper reads −0.03 mm with its jaws closed and 18.42 mm when measuring a hole’s depth. It was not zeroed. Choose the measuring part, then find the corrected depth in mm (two decimal places) and cm (three decimal places).
Show the steps Optional working
Show answer
- The depth rod. It extends from the end of the beam to the bottom of the hole while the end of the beam rests on the top surface. The outside jaws close around an object, so they measure an outside width.
- The caliper under-reads by 0.03 mm, so the corrected depth is larger:
Changing the unit moves the decimal point. It does not change the precision, so keep all four digits.
Check your understanding 2 A reset caliper and a tube
A caliper reads +0.04 mm with its jaws closed. It is reset to ZERO, then reads 11.80, 11.82 and 11.81 mm inside a tube. Choose the measuring part and correct calculation. Give the mean diameter to two decimal places.
Show the steps Optional working
Show answer
Use the inside jaws against opposite inner surfaces, with the measuring direction aligned across the diameter rather than along a shorter off-centre chord. Bring the jaws into gentle contact without deforming the tube. Repeat at different positions or orientations if the tube may not be uniform.
The first error is subtracting an offset that was already removed by resetting ZERO before these readings. Their mean is (11.80 + 11.82 + 11.81)/3 = 11.81 mm, not 11.77 mm. Check the closed-jaw zero again if you suspect it has changed; do not apply the old offset twice.
A small spread means the readings repeat closely. For an accurate diameter, align the inside jaws across the centre and avoid tilting or deforming the tube. Check against a known reference if calibration is in doubt.
Reading an analogue vernier caliper
A vernier caliper has the same jaws and depth rod as a digital caliper, but you read it from two scales: a main scale on the beam, marked in millimetres, and a short vernier scale on the sliding jaw.
Scroll across the figure to read all labels.
Why the vernier scale gives an extra digit
Ten vernier divisions span 9 mm, so each vernier division is 0.9 mm, which is 0.1 mm shorter than a main-scale division.
Suppose the vernier zero sits 0.3 mm past a main-scale mark. Vernier line 1 is then 0.2 mm short of the next main mark, line 2 is 0.1 mm short, and line 3 lines up exactly. The number of the line that lines up counts tenths of a millimetre. So the smallest step the caliper can read, its least count, is 0.1 mm = 0.01 cm.
Read the two scales
- Main scale: read the mark immediately to the left of the vernier zero. The jaws have opened past this mark but not past the next one.
- Vernier scale: find the one vernier line that lines up exactly with a main-scale mark. Multiply its number by 0.01 cm. If two lines look close, the better-aligned one is the reading.
- Add the two parts to get the observed reading.
Worked example 2
Read the main scale and the vernier scale
Show full solution
Read the main scale
Method
Take the main-scale mark immediately left of the vernier zero.
Reason
The vernier zero has passed the 10.0 cm mark but not the 10.1 cm mark.
Working
Answer
Main scale reading = 10.0 cmRead the vernier scale
Method
Find the vernier line that lines up exactly and multiply its number by the least count.
Reason
Line 2 lines up, so the vernier zero is two tenths of a millimetre past the main-scale mark.
Working
Answer
Vernier reading = 2 × 0.01 cm = 0.02 cm
Add the two parts
Working
Answer
10.0 cm + 0.02 cm = 10.02 cm
Quick check
Check your understanding 3 Read an aligned vernier line
The vernier zero lies just past the 2.1 cm mark on the main scale, and vernier line 3 lines up with a main-scale mark. Find the reading. Then predict how a trainer reading with the jaws still open beside an object compares with its true width.
Show answer
The open jaws show their separation, which is larger than the object’s width until both jaws touch it. Moving the jaws changes their separation; it does not change the object.
The main scale gives 2.1 cm; the aligned line adds the part beyond it. It does not replace the main-scale reading.
Scroll across the figure to read all labels.
In the trainer, choose an Object, then drag the Sliding jaw until it just touches the object. Read the scales, enter Your reading in cm and inspect Check. You can turn on Highlight the aligned vernier line after making your own estimate.
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.
Check your understanding 4 Compare the trainer reading
Choose Object 1. Close the sliding jaw onto it, read the main scale and aligned vernier line, then enter Your reading. What does Check say? Compare the reading with the open-jaw separation and your prediction. Explain whether the object’s width changed.
Show answer
At the starting settings, the open jaws are 11.00 cm apart. On Object 1, the main-scale reading is 4.9 cm and line 2 aligns, giving 4.92 cm. Entering 4.92 with the jaws touching gives correct feedback. The smaller reading measures the object’s width; the earlier reading measured the wider gap. The object’s width stays unchanged. Compare the main-scale mark, aligned line and contact with your prediction.
Find and correct a zero error
Close the jaws and read the scales before measuring. If the vernier zero does not line up with the main-scale zero, the caliper has a zero error, and you must correct every reading:
Read the zero error from the closed jaws:
- Vernier zero to the right of the main zero: the zero error is positive. The jaws read more than zero when closed. If line n lines up, the zero error is + n × 0.01 cm.
- Vernier zero to the left of the main zero: the zero error is negative. Count back from the vernier’s 10 mark instead. If line n lines up, the zero error is -(10-n) × 0.01 cm.
Why count from 10 in the negative case? The vernier’s 10 mark is 9 mm along the vernier scale. With the vernier zero to the left of the main zero, that 10 mark falls short of the main 9 mm mark by the size of the zero error. Each line back towards the vernier zero closes 0.1 mm of that gap, so the gap is (10-n) × 0.1 mm when line n lines up.
Guided practice 1
Read a negative zero error, then correct
Problem
With the jaws closed, the vernier zero is to the left of the main-scale zero and vernier line 6 lines up with a main-scale mark. Around an object, the caliper reads 3.34 cm. Find the zero error and corrected reading, both to two decimal places.
Read the zero error, then apply the correction
Show the steps Optional working
Hints
Hint 1
find the sign
Which side of the main zero contains the vernier zero?
Hint 2
substitute with brackets
Write corrected reading = 3.34-(zero error) and keep the sign inside the brackets.
Show solution step by step
Read the zero error
Method
Count back from the vernier’s 10 mark and give the result a negative sign.Reason
The vernier zero is left of the main zero, so the caliper reads less than zero when closed.
Working
Answer
zero error = -(10-6) × 0.01 cm = -0.04 cmCorrect the reading
Method
Subtract the signed zero error.Reason
The caliper under-reads by 0.04 cm, so the corrected reading must be larger than 3.34 cm.
Working
Answer
corrected reading = 3.34 cm-(-0.04 cm) = 3.38 cm
Spot the mistake 1
Correct a positive zero error
Learner response
Observed reading = 7.65 cm and zero error = +0.01 cm. A learner adds the zero error and reports 7.66 cm. Find the first error and correct the result to two decimal places.
Correct the sign before viewing the solution
Show solution step by step
Interpret the positive zero error
Method
The caliper reads + 0.01 cm when fully closed.Reason
The same offset is in every reading, so the observed reading is 0.01 cm too large.Working
Answer
Use corrected = observed-zero error.Correct the reading
Method
Subtract the positive zero error.Reason
Removing the over-reading gives the object’s length.Working
Answer
7.65 cm-(+0.01 cm) = 7.64 cm
Common mistake
Avoid reading errors
- Put your eye directly above the line you are reading. Viewed from an angle, the vernier line seems to line up with the wrong main-scale mark (parallax error).
- Close the jaws gently and squarely, and tighten the lock screw before you lift the caliper away to read it.
For more diagrams, work through reading a vernier caliper, finding the zero error and correcting readings for zero error.
Common mistakes
- Using the outside jaws for an inside diameter, or the jaws for a depth. Choose the part that touches the surfaces you are measuring.
- Forgetting to check the zero reading with the jaws closed.
- Adding a zero error instead of subtracting it. Corrected reading = observed reading − zero error, keeping the sign.
- Pressing the jaws so hard that the object is squeezed or the jaws tilt.
Spotted an error? Report a correction
Syllabus and review details
- SEC G3 Physics 2027 · 2027
Content Structure, PDF page 9; Subject Content, PDF pages 10–28