# Vernier Caliper – Working, Calculation Of Least Count & Zero Error

Vernier Caliper: A device which is used to measure small lengths or distance such as diameter of a cylinder or sphere is called Vernier caliper. With the help of Vernier caliper we can calculate correctly up to 1/1000th of centimeter or 0.1mm

Construction: A Vernier caliper consist of a rectangular steel bar whose one side is graduated in centimeters. This scale is also known as “Main Scale (M.S)”. There is also a small scale consisting of ten division which slides over the main scale. This scale is known as Vernier scale (V.S). It has two sets of jaws which enables it to measure the internal  and external diameter of the cylindrical objects.

Working: To measure the length of an abject, it is placed between the two jaws of the Vernier calipers. The distance between the zero of the main scale and the zero of the Vernier scale is equal to length of object. First we find the reading of main scale then find the number of Vernier division which coincide with one of the main scale division. We multiply the vernier divisions by the least count and then ass to main scale reading to get the required length. To get the correct  measurement we adjust for the zero error.

Least Count Or Vernier Constant: The difference between the value of one main scale division and one vernier division is called as “Least count (L.C) or vernier constant (V.C)”

Calculation Of Least Count: Mathematically, the value of least count or vernier constant is calculated as following.
10 vernier division = 9 main scale division =9mm
1 vernier division= 9/10mm
1 vernier division= 0.9mm
1 main scale division= 1mm
Least count= 1-0.9
Least count= 0.1mm
Least Count= 0.01cm
The least count of vernier calipers can also be calculated as following
L.C= Value of smaller division on MS/Total Number of division on VS
L.C= 1/10
L.C= 0.1mm
L.C= 0.01cm

###### Zero Error #####

The error which arises due to the incorrect gradation of the scales of the verneir calipers is called Zero Error.

1. No Zero Error: If the zero of main scale coincide with the zero of the Vernier scale then the instrument has no zero error.
2. Positive Zero Error: If the zero of the venier scale on the right of zero of the main scale then the zero error will be positive, but the zero correction will be negative. To find the positive zero error, look at the Vernier scale and not the number of divisions of the venier scale which coincide with one the main scale divisions and multiply this number by least count.
3. Negative Zero Error: If the zero of the Vernier scale is one the left of the main scale zero, then the zero error will be negative and zero correction will be positive. To find the zero error note the number of Vernier scale division which coincide with one of the main scale and multiply with least count.

• That is good for physics student.

• Nice explanation for L.C. . But what to do with the zero error was not dealt with

• It is so important chapter in physics

• Least count of vernier is 0.02 mm but you explain it as 0.1 mm it is wrong your method for leasg count calculation is wrong

• But that calliper contains only 5 division in vernier scale

• Presentation is in proper sequence. Basics of vernier in simple way. Excellent.

• Question is asked from vernier calliper in jee-main and jee-advanced. In ncert and many physics books this topic has not been explained. Reading about vernier calliper as given above one can solve question in competitive exam. Thanks a lot.

• What is the formula to calculate total reading with a vernier calipers?

• The answer & calculations are correct because least count of vernier calliper depends upon the no. of divisions in MS & VS.

• Thank you so much ! 😃😀

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