# Least Count of a Vernier Calliper

I was reading some text about the vernier calliper and it was written that it's least count is equal to 1 Main Scale Division unit - 1 Vernier Scale Division Unit = Vernier Constant. Can someone explain how is the least count, that is the least distance that can be measured on the calliper, equal to 1 MSD - 1 VSD?????

Interesting. I've used a vernier caliper but have never put in the effort to see how it works.

The main scale is marked off in hash marks every 0.025".
The slide has hash marks from 0 to 25. These marks span from 0" to 1.125" on the main scale when the caliper is closed.
So for 25 divisions on the slid, there are 49 divisions on the main scale
Surely, what gets the thing to work is that 25 and 49 are mutually prime.

The resolution is 0.001".

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I would conclude that this definition of Vernier Constant you've given is not general enough to include my own calipers which would have a Vernier Constant of -0.024" (0.025"-0.049") whereas it's actual resolution is 0.001" (2*0.025 - 0.049").

Ranger Mike
Gold Member
Don't forget there is a big difference between accuracy and precision

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uart
I was reading some text about the vernier calliper and it was written that it's least count is equal to 1 Main Scale Division unit - 1 Vernier Scale Division Unit = Vernier Constant. Can someone explain how is the least count, that is the least distance that can be measured on the calliper, equal to 1 MSD - 1 VSD?????

Mathematically the Vernier scale works as follows.

A vernier scale containing "n" divisions fits exactly into the length of n-1 divisions of the main scale. Thus if we call the main scale divisions 1 unit then the vernier scale divisions are (n-1)/n units.

Now if we open the verniers by an amount "x" and observe that the k-th vernier division aligns with some main scale division then it follows that x + k(n-1)/n = whole number.

Expanding gives x + kn -k/n = whole number, from which it follows that the fractional part of "x" is equal to k/n of one main division unit.

uart. Can you come up with an equation for my Mitutoyo Calibers which has 49 divisions on the main scale of 0.025" spacing, matching 25 divisions on the Vernier scale?

Ranger Mike
Gold Member
I caution all that it is very easy to confuse accuracy with precision. A vernier caliper has graduations to .001" but this is not to say the caliper is capable of measuring dimensions throughout its measurement range to this accuracy.

In fact the vernier principle ( invented by Pierre Vernier in 1631) and slide caliper design is credited to Joseph R. Brown in 1851 ( (brown & Sharpe MFG. CO).

Older " open setup " measuring systems, including the above, used the Gage Makers Rule of Ten in an attempt to eliminate the human error of measurement. This pre WW2 rule of thumb is:
Rule: The instrument must be capable of dividing the tolerance into ten parts.

The Purpose: To eliminate 99% of the instrumentation error of previous steps in measurement.

When Applied: To every step in the measurement sequence until the limit of the available instrument is reached.

The results: Fewer bad parts accepted and good parts rejected.

If the main scale is graduated in 10 divisions the slider of the vernier is equal in length to 9 division of the main scale but is also divided into 10 equal divisions.
Whichever division on the vernier lines up with a scale division on the main scale gives the next significant figure to the main scale reading corresponding to the zero on the vernier.
ie if the zero on the vernier is between 6 and 7 on the main scale and division 8 on the vernier coincides with a main scale division then the distance is 6.8

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