The Vernier Calipers is an instrument used to measure the length of objects with
a higher precision, mostly up to the extent of 0.01cm.

Parts of Vernier Calipers
1.       Main Scale: It is a simple ruler made of metal.
2.       Inside Jaws: They are used to measure the internal features of an object such as the internal diameter of a hollow cylinder. One of these is fixed while the other is movable.
3.       Outside jaws: They are used for normal measurements of lengths of various objects. One of these is fixed while the other is movable.
4.       Screw: It is used to fix the length between the jaws once the measurement of the object has been taken by the jaws.
5.       Vernier Scale: It is similar to a normal scale but it has divisions which are different from the common 1 mm.
6.       Depth Probe: It is a metal depth that is used for measuring depths, such as the depth of a cylinder.


Least Count of Vernier Calipers

Least Count refers to the smallest distance that can be measured using an instrument. It indicates the degree of precision of an instrument. Most of the vernier Calipers have a least count of 0.1mm. Least count can calculated using the formula.
Least Count = Length of 1 MSD – Length of I VSD
Where MSD and VSD refer to Main Scale Division and Vernier Scale Division respectively
Generally N divisions on main scale coincide with N-1 divisions on vernier scale
1 VSD is equivalent to (N-1)/N main scale divisions
Using the formula for Least Count, we get
LC = 1 MSD – 1VSD
= 1 MSD – (N-1)/N MSD
= 1/N MSD

Example for Calculation of Least Count of Vernier Calipers:
A vernier scale has the length of 9 main scale divisions and is divided in to 10 divisions. Calculate the Least Count of the Vernier Calipers.
Solution:
Since 9 divisions of the vernier scale coincide with 10 divisions of the main scale
VSD = 9 / 10 mm = 0.9 mm
MSD= 1 mm
Least Count= 1 MSD- 1VSD = 1mm - 0.9mm = 0.1mm

Formula for finding length using Vernier Calipers

Length = MSR + (VSR * LC)
Where MSR, VSR and LC refer to Main Scale Reading, Vernier Scale Reading and Least Count respectively.


Zero Error

Zero Errors quite often occur in measuring instruments due to defects in manufacturing.  Vernier Calipers is said to have a Positive Zero Error is the zero of the Vernier Calipers does not coincide with the zero of the main scale when the two jaws are in contact with each other i.e. no object is held between the jaws. Appropriate correction is applied to get the correct length. Zero errors are of two types: Positive zero Error and Negative Zero Error.

Positive Zero Error

The Vernier Calipers is said to have a positive Zero Error when the zero of the vernier scale is to the right of the vernier scale when the two jaws are in contact. This means that the instrument is giving us some positive length when the length being measured is actually zero. Hence, a corresponding length has to be subtracted from the results obtained to get the correct length. The correction applied here is known as negative correction.  In order to correct positive zero error, the length in the absence of any object in the jaws is noted down and the same length is subtracted from the final result after measuring the length of an object.
Suppose the nth division of the vernier scale coincides with the main scale division when no object is held between the jaws, the correct that needs to be applied is - n* LC

Negative Zero Error


The Vernier Calipers is said to have a negative Zero Error when the zero of the vernier scale is to the left of the vernier scale when the two jaws are in contact. This means that the instrument is giving us some negative length when the length being measured is actually zero. Hence, a corresponding length has to be added from the results obtained to get the correct length. The correction applied here is known as positive correction.
Negative zero error correction is done in a similar way as positive zero error, the only difference being that the correction to be applied is positive i.e. + n * LC



Procedure for finding length using Vernier Calipers

  1. The object whose length is to be found is held between the outer jaws and the screw is tightened. In case of measuring internal dimensions, the inner pair of jaws is used and similarly for measuring depth, the depth probe is used)
  2. The reading of the main scale (MSR) which is to the left of the zero of the vernier scale is noted. This reading is the Main Scale Reading. One commonly committed mistake is to take the reading of the main scale which is closest to the zero of the vernier scale. For example: When the zero of the vernier scale is between 3rd and 4th division of the main scale, the MSR is 3 irrespective of how close the zero of the vernier scale is to the 4th division of the main scale.
  3. To take the vernier scale reading (VSR), look up for the division on the vernier scale which exactly coincides with any of the main scale reading. It has to be noted that exactly one division coincides with the main scale divisions under any circumstances.
  4. The length of the object is calculated using the formula: Length = MSR + (VSR * LC)
Care has to be taken to ensure that MSR and LC have the same units. Appropriate correction has to be applied if the vernier scale possesses any zero error.

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