When you buy a measuring instrument, the least count is the key factor that you usually look into an instrument.
The least count decides how precisely you can measure a dimension with that instrument. Let’s talk more about the least count and how to calculate the least count of the vernier caliper and micrometer.
What is the least count?
The least count of an instrument is the smallest measurement that can be measured using that instrument. The lower the count, the smaller and more precise the dimension that you can measure.
Let’s take the example of a ruler. It has 10 marks in between 1 centimeter. So the least count for a ruler is 1/10= .1 cm or 1 mm. So with a ruler, the smallest dimension that you can measure is .1 cm or 1 mm.
General Least Count Formula
Here is how you can calculate the least count of an instrument having a single scale
Formula: 1
Least Count = Value of 1 main scale division / Total main scale divisions.
The least count formula for an instrument.
Here is the least-count formula for an instrument having a secondary scale along with the main scale. This rule also can be termed as the formula of least count of vernier caliper
Formula: 2
Least Count of main scale = Value of 1 main scale division / Total main scale divisions
Least Count Of Secondary Scale = Value of 1 secondary scale division / Total secondary scale divisions
Least Count of an instrument = Least count of primary scale / Total secondary scale divisions
Least count of a ruler
We can calculate the least count of rulers using Formula 1 mentioned before.
Least count of a ruler = 1/10 CM= .1 CM =1 MM
Least count of micrometers
The least count of the vernier caliper can be calculated using formula 2
Least count of main scale= .5/10 CM= .05 CM= .5 mm
Total secondary scale divisions= 50
Least count of vernier scale= .05/50 CM=.001 CM=.01 MM
Least count of vernier caliper= .05/50 CM=.001 CM=.01 MM
Least count of vernier caliper
Least count of micrometer can be calculated using formula 2
Least count of main scale= 1/10 CM=.1 CM=1 MM
Total secondary scale divisions= 50
Least count of vernier scale= .1/50 CM=.002 CM=.02 MM
Least count of vernier caliper= .1/50=.002 CM=.02 MM
Least count and precision
The least count is directly linked with precision. The smaller the least count number, the more precise the instrument is. For example, the mechanical vernier has the lowest count of .02, but for the electronic vernier, the lowest count is .01. So the electronic vernier is more precise as it can measure dimensions unto .01 mm.
What is vernier caliper zero error?
When the jaws of the vernier caliper come into contact, the zero of the main scale should coincide with the zero of the secondary scale. If both do not coincide then it is called zero error. There are two types of zero error.
- Positive zero error
- Negative zero error
Positive zero error
If the zero of the vernier scale is on the right side of the zero of the main scale then it’s a positive zero error. So, in this case, the zero correction value will be negative
Negative zero error
If the zero of the vernier scale is on the left side of the zero of the main scale then it’s a negative zero error. So, in this case, the zero correction value will be positive
How to use a vernier caliper to measure a dimension?
You can use the formula mentioned below to calculate the value of the measurement
A=B+Zc
Where A= Length to be measured (CM)
B ( Variable)= M+X (CM)
X (Variable)= n * LC (CM)
LC= Least count = .02 (CM)
Zc=Zero Correction= .07(-)—Lets Assume negative correction (CM)
M= Main scale reading (CM)
n= Number of vernier divisions coinciding with the main scale division
Let’s take an example of a cylinder that was measured using a vernier caliper.
| Sample Sl# | Main Scale Reading( M) | # Of Vernier scale division(n) | Variable X=n*LC.02 | Variable B=M+X | Dimension A=B+Zc |
|---|---|---|---|---|---|
| 1 | 10 | 5 | 5*.02=.10 | 10+.10=10.10 | 10.10+(-.07)=10.03 |
| 2 | 15 | 6 | 6*.02=.12 | 15+.12=15.12 | 15.12+(-.07)= 15.05 |
| 3 | 20 | 7 | 7*.02=.14 | 20+.14=20.14 | 20.14+(-.07)= 20.07 |
Conclusion
I hope you got a fair idea about the least count and how to calculate the least count for the Vernier caliper and micrometer. Though the logic is straightforward, please write in the comment section if you still have questions, and I will be happy to assist you.
Also, if you have any examples that you want to discuss here, you are always open to putting them up in the comment section.
Frequently asked questions ( FAQ)
What is the least count?
The least count is the smallest measurement that an instrument can measure.
What is the relation between least count and precision
The smaller the value of the least count, the more precision the instrument has.
How to calculate the least count of vernier caliper
The least count of vernier caliper can be calculated as follows
Least count of vernier caliper= Least count of main scale/ Number of scale divisions in the vernier scale
