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The vernier calliper and the screw gauge are the first instruments most students use in a physics lab, and the questions about them are worth easy marks in both practicals and entrance tests. The marks are lost in three places: least count, the sign of zero error, and the final subtraction. This post works through each instrument with numbers.
Where are these instruments tested?
The JEE (Main) 2026 syllabus lists, under experimental skills, "Vernier calipers - its use to measure the internal and external diameter and depth of a vessel" and "Screw gauge - its use to determine the thickness/diameter of thin sheet/wire". The NEET (UG) 2026 syllabus has the same two experiments. The CBSE 2025-26 curriculum puts both among the Class 11 practicals, and JEE Advanced 2026 asks for error analysis in experiments using them. Check the current year's list before your practical.
How do you find a vernier calliper's least count?
A vernier has a main scale and a sliding vernier scale. Usually 10 vernier divisions span 9 main scale divisions of 1 mm each.
1 vernier division = 9/10 mm = 0.9 mm.
Least count = 1 MSD − 1 VSD = 1 − 0.9 = 0.1 mm = 0.01 cm.
Equivalently, least count = (value of 1 MSD)/(number of vernier divisions). If 20 vernier divisions span 19 mm, the least count is 1/20 = 0.05 mm. The NCERT Class 11 exercises ask you to compare a 20-division vernier with a screw gauge for exactly this reason.
How do you take a vernier reading?
Main scale reading (MSR): the main scale mark just to the left of the vernier zero. Say 2.3 cm.
Vernier coincidence (VC): the vernier division that lines up exactly with any main scale mark. Say the 7th.
Observed reading = MSR + VC × LC = 2.3 + 7 × 0.01 = 2.37 cm.
What is zero error, and which way do you correct it?
Close the jaws fully. If the vernier zero does not line up with the main scale zero, there is a zero error.
Positive zero error: the vernier zero lies to the right of the main zero. If the 4th vernier division coincides, zero error = +4 × 0.01 = +0.04 cm.
Negative zero error: the vernier zero lies to the left. If the 6th vernier division coincides, zero error = −(10 − 6) × 0.01 = −0.04 cm.
Corrected reading = observed reading − zero error.
With +0.04 cm: 2.37 − 0.04 = 2.33 cm.
With −0.04 cm: 2.37 − (−0.04) = 2.41 cm.
How does a screw gauge work?
A screw gauge turns rotation into a small linear movement. The pitch is the distance the spindle moves in one full turn of the thimble.
Least count = pitch / number of circular scale divisions.
With pitch 0.5 mm and 50 divisions: 0.5/50 = 0.01 mm.
With pitch 1 mm and 100 divisions (the NCERT exercise case): also 0.01 mm.
Worked reading. A wire is held between the faces. The linear (sleeve) scale shows 3.5 mm, and the 27th circular division lines up with the reference line.
Observed reading = 3.5 + 27 × 0.01 = 3.77 mm.
Zero error. Bring the faces together using the ratchet.
If the circular zero is below the reference line and the 3rd division is on the line, zero error = +3 × 0.01 = +0.03 mm. Corrected: 3.77 − 0.03 = 3.74 mm.
If the circular zero is above the line and the 47th division is on it, zero error = −(50 − 47) × 0.01 = −0.03 mm. Corrected: 3.77 + 0.03 = 3.80 mm.
Backlash error comes from slack in the screw threads. Turn the thimble in one direction only while taking a reading, and use the ratchet so the faces are not over-tightened.
An NCERT exercise asks whether you can make a screw gauge more accurate just by adding more circular divisions. Think about it before your viva: a finer scale cannot beat the quality of the screw thread, wear and your ability to judge which line coincides.
Why take several readings?
Measure a wire's diameter at several places and in two perpendicular directions, then average. Research shows students do not always see the point: Allie and colleagues (1998) found that first-year science students' reasoning about repeating measurements and the spread of data depended on context. Repeated readings reveal a wire that is not perfectly round and reduce random error.
Common mistakes and how to avoid them
Reading the main scale to the right of the vernier zero. Always take the mark just before it.
Getting the least count wrong by using 1 VSD instead of 1 MSD − 1 VSD.
Adding the zero error. The rule is to subtract it, with its sign.
Writing the negative zero error as −(VC × LC). It is −(N − VC) × LC for a scale of N divisions.
Forgetting the half-millimetre marks on a 0.5 mm pitch gauge's sleeve.
Mixing units. Keep cm or mm throughout.
Errors in these readings then feed into calculated results. Our guide to error propagation in measurement shows how, and the board practical and viva guide covers how to present the observation table.
If you want to see why a vernier coincidence works rather than just apply it, the Fermi Concept Library covers every concept in physics, each with its own lesson.
A practice routine for this topic
Day 1: find the least count for five made-up vernier and screw gauge designs.
Day 2: ten vernier readings from diagrams, half with zero error.
Day 3: ten screw gauge readings from diagrams, half with zero error.
Day 4: in the lab, measure one wire at five places with a screw gauge and report mean ± mean absolute error.
Day 5: write out the viva answers on least count, zero error and backlash in three lines each.
Next time you are in the lab, check the zero error of your instrument before your first reading and write it at the top of the observation table.
