# Vernier Caliper: Calculation of Least Count in Metric & Imperial Scales

What is a least count? A scale is the defining feature of any measuring instrument. Usually measurements are taken by placing an object on top of a scale and noting the distance between the edges. In this case a larger number of divisions on the scale leads to a more accurate measurement and vice versa. The technical term used to describe this parameter is known as least count, which is the smallest measurement which can be measured by a scale. Its value can be obtained by the division of one unit on the scale by the number of divisions that lie in between.

The correct determination of the least count of a vernier caliper is important for the measurement to be accurate. This is a common difficulty faced by people, even engineers and leads to incorrect readings while measuring heights, diameter, lengths etc. Sometimes both metric and imperial units together on the scale may also cause confusion.

This article will tell you the procedure for calculating the least count of a vernier caliper. The smallest measurement which can be recorded by the Vernier caliper is defined as the least count. For that first we need to determine the least count of the main scale which can be done as described previously.  Then we need to count the number of divisions on the vernier scale and divide the least count of the main scale by it. This will give us the least count of the vernier caliper. The formula for this can be expressed as:

Least Count of Vernier Caliper = Main Scale least count/ number of Vernier scale divisions

## Calculation of Least Count of Vernier Calipers in Metric Scale

In metric scales, the units used for calibration are millimetres i.e one division equals 1 cm and is divided into further divisions in millimetres. The least count can be calculated by dividing 1 cm by the number of divisions that lie between a unit. This way a main scale which contains 10 divisions in a centimeter will have a least count of 1/10 = 0.1cm or 1 mm.

Similarly the vernier scale is also normally divided into ten equal parts. Count the divisions on the vernier scale just to make sure. The least count of the vernier caliper can now be found by dividing the least count of the main scale by the number of divisions on the vernier scale. Usually the least count of the main scale is 0.1 m and the vernier scale has 10 divisions so the least count would be 0.1/10 = 0.01cm.

The least count is related to accuracy in such a way that if a vernier caliper has a least count of 0.01cm then it is said to also have an accuracy of 0.01 cm.

Also if you want to calculate the least count in mm, here is the formula below:

Vernier caliper least count in mm = Vernier caliper least count in cm x 10

So in this case it would be; 0.001 x 10 = 0.01 mm, therefore 0.01 mm is the least count in millimeters for this Vernier caliper. ## Calculation of Least Count of Vernier Calipers in Imperial Scale

There are two types of imperial Vernier calipers discussed in the examples:

Type 1 Imperial Vernier Calipers: In a Vernier Caliper with imperial scale, the main scale has a minimum division of 0.1 inches. There are 40 divisions on the Vernier scale normally in imperial Vernier Calipers. Therefore 0.1 inch of the main scale is divided into 40 divisions of the Vernier scale

So 0.1 divided by 40 = 0.0025 inch

We can say that 0.0025 inch is the accuracy and least count for this type 1 of imperial Vernier Caliper.

Type 2 Imperial Vernier Calipers: If there are 25 divisions on the Vernier Scale

If the vernier scale is divided into 25 parts then the smallest measurement possible from the main scale would be 0.025 inches.

Therefore least count of the Vernier Caliper is calculated by the same formula i.e. dividing 0.025 by 25 = 0.001 inch

We can say that 0.001 inch is the accuracy and least count for type 2 of imperial Vernier Caliper.

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• how to calculation for vernier scale?

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