How to find Vernier caliper least count formula?

The Vernier caliper least counts formula can be calculated by dividing the smallest readings of the main scale by the total number of divisions of the Vernier scale. The least Count of the Vernier caliper is the difference between the smallest readings of the main scale and the smallest readings of the Vernier scale that is (0.1 mm 0r 0.01 cm).

Vernier caliper is the equipment used to measure the length, radius, diameter, etc. It can measure up to (1/10 of mm or 0.1 mm 0.01 cm) which is called at least count of V.C. It can be used by the lathe mechanic for making metallic cylinders of different sizes.

There are two scales of Vernier Caliper

·         Vernier scale

·         Main scale

The main scale can be developed in centimeters period the Vernier scale slides along the main scale and is developed in divisions less than the millimeters.

Parts and functions of Vernier caliper   

There are two sets of jaws:

Two jaws

1.      Lower Jaws

2.      Upper Jaws

1.    Lower Jaws:

The lower jaws can be used for measurements of length. The thickness or external diameter of any object.

2.    Upper Jaws:

The upper jaws can be used to measure the internal diameter of any object like a hollow cylinder or tube.

The jaw's main scale is fixed and the main scale jaws are movable. These movable jaws are fastened to the Vernier and they slide along the main scale.

Least count  

The smallest reading that can be accurately measured with a Vernier caliper is called its least count (L.C), it is also known as the Vernier constant. It is the difference between one main scale division which is 1 mm and one Vernier division which is (0.9).  

L.C = 1 mm – 0.9 mm =0.1 mm

There is another method to find the least count which is given as:

Least count of Vernier caliper formula

Vernier caliper zero error

When the jaws of Vernier calipers are moved into contact, the zero of the Vernier must coincide with the zero of the main scale. Otherwise, the equipment has an error called zero error. Zero error can be negative or positive.

Negative Zero Error

If the zero of the Vernier scale is to the left of the zero of the main scale then the error is called a negative error. The zero error correction will be positive.

Positive zero error

If the zero of the Vernier scale is to the right of the zero of the main scale then the error is called a positive error. The zero correction will be negative.

How to read a Vernier caliper?

We can learn about the use of V.C. with the help of an example by measuring the area of the cross-section of a solid cylinder by measuring its diameter with a V.C. We will solve this example step by step.

·         Find the least count. Close the jaws to check the Zero error and calculate the zero correction.

·         Hold the cylinder between the two jaws of the Vernier caliper. Tighten the jaws slowly.

·         Note the main scale divisions that are either coinciding or is on the left of the Vernier scale zero.

·         Record this value as the main scale readings (M).

·         Note the Vernier division (n) that completely coincides with any one division of the main scale.

Multiply this “n” with the least count and calculate the value of fraction (x) which is to be added to the main scale reading.

X = (n × LC)

·         Add the values ‘M ‘and ‘X ‘to the observed value (Y) of diameter.

Y = (M + X)

·         Apply zero correction to obtain the correct diameter. (D)

D = (Y ± Z C)

·         Take at least two readings to insert the cylinder cross-section-wise between the jaws and get the average diameter.

·         Calculate the radius of the cylinder

Observations and Data   

Cautions about the use of V caliper

·         Jaws of V C should be closed slowly

·         Zero error correction should be applied

·         Both jaws should touch the cylinder

Uses of Vernier caliper

·         It can be used to find diameter internally and also externally.

·         Lathe Mechanics, Plumbers, and aluminum and steel window makers also used it.