# Vernier Calipers

Aim: To determine i) The volume of the given cylinder by measuring its length and diameter

ii ) The volume of the given sphere by measuring its diameter.

Apparatus : Vernier Calipers,Cylinder and sphere.

Description of Vernier Calipers: A Vernier calipers consists of mainly two parts i) A 2cm wide 15cm long rectangular metal strip .The left end bottom side of this strip consists of a fixed jaw 1 (A) and at the same end jaw 2(C) at the top of this strip. On the strip a scale (5)is graduated in Inches along the upper edge and another scale(4) is graduated in Centimeters along the lower edge. This is called Main Scale ‘S’ .

ii) A metal frame V called vernier slides over the Main Scale ‘S’ . At the bottom of this frame V a button 8(P) is attached,which helps to fix this vernier at any desired place on the main scale.This verier frame consists of jaw1 (B) at the bottom and a jaw 2(D) at the top .Two scales are graduated on this frame corresponding to two scales on the Main Scale ‘S’. The two scales 6 and 7 on the vernier are called Vernier scale.Vernier scale consists of equal number of divisions. When we move vernier frame over the main scale, a thin strip (3) will be projected out.The projection will be exactly equal to the distance between Jaws 1(AB) i.e the thickness of the object between jaws.

The lower jaws 1,1(AB) are used to measure the thickness or external diameter of the tubes,cylinders or spheres.

The upper jaws 2,2 (CD) are used to measure the inner diameters of hallow bodies like tubes or holes.

The thin strip ( 3) is used to measure the depth of the objects like test tubes.

Theory :  Principle of vernier calipers – N divisions on the vernier scale is equal to (N-1) divisions on the main scale.

N V.S.D = (N-1) M.S.D

1 V.S.D = $\frac{(N-1)}{N}$ M.S.D

Least count (L.C) of vernier calipers : Minimum length or thickness measurable with the vernier calipers is called its least count.

Least count (L.C) = 1 M.S.D – 1 V.S.D

L.C = 1 M.S.D – $\frac{(N-1)}{N}$ M.S.D

L.C = 1 M.S.D [ 1-$\frac{(N-1)}{N}$]

L.C = $\frac{1 M.S.D}{N}$  = $\frac{S}{N}$

Where S is the value of  one Main scale division and N is the number of equal divisions on the vernier scale.

Procedure : First we have to determine the least count count of the given vernier calipers.

To determine the volume of the  cylinder we have to determine a)the length of the cylinder and b) radius of the cylinder and substituting these values in the equation for the volume of the cylinder we can calculate it.

a) To determine the length of the cylinder : Given cylinder is held gently between jaws 1,1 of the vernier calipers.The reading on the main scale just before the zero of the vernier is noted.This is called Main scale reading (M.S.R).The number of division (n) on the vernier which coincides perfectly with any one of the main scale divisions is noted.This is called vernier coincidence (V.C).The vernier coincidence (V.C=n) is multiplied by least count to get the fraction of a main scale division.This is added to the main scale reading (M.S.R) to total reading or total length of the cylinder.

Total reading = M.S.R + ($V.C\times L.C$)

Take the readings,keeping the cylinders between jaws 1,1 at different positions.Post the values of M.S.R and vernier coincidence (n) in the table.Take at least 5 readings, get the average of these 5 readings which is mean length(l )of the cylinder.

b)To determine the diameter of the cylinder : Place the cylinder diametrically between the jaws 1,1 of the vernier calipers, as in the above case post the values of M.S.R and vernier coincidence (n) in the table. Take at least 5 readings, calculate the average of these readings which gives the mean diameter ( d=2r ) of the cylinder.

c) To determine the volume of the cylinder :Substituting the values of mean length (l ) of the cylinder and mean diameter ( r) of the cylinder which is already determined, in the formula V = $\pi r^2 l cm^3$.

d)To determine the diameter of the sphere : The given sphere is held firmly between jaws of the vernier calipers, in such a way the points where the jaws are in contact with sphere should be the two extremes of the chord of the cylinder.Post the values of the M.S.R and vernier coincidence (n) in the table . Take at least 5 readings, calculate the average of these readings which gives the mean diameter (d=2 r ) of the sphere.

e)To determine the volume of the sphere :Calculate the radius of the sphere  r = d/2 .Substitute the value of  mean radius (r)  in the formula of the volume of the sphere V = $\frac{4}{3} \pi r^3 cm^3$ .

Precautions to be taken while doing the experiment : 1) Take the M.S.R  and vernier coincide every time without parallax error. 2)Record all the reading in same system preferably in C.G.S system. 3) Do not apply excess pressure on the body held between the jaws. 4) Check for the ZERO error.When the two jaws of the vernier are in contact,if the zero division of the main scale coincides with the zero of the vernier scale no ZERO error will be there.If not ZERO error will be there, apply correction.

Observations:

I) Least count of Vernier calipers :

a) Value of 1 Main scale division  = 1 M.S.D = S = ……..  cm,

b) Number of divisions on the vernier scale   N= ……… cm,

Least count              L.C = $\frac{S}{N}$   = ………. cm.

c) Zero error =x ( positive error)

II) Volume of the Cylinder :

a)Length of the cylinder :

 S.No M.S.R                acm Vernier Coincidence   (n) Fraction   b=(n-x)*L.C Total Reading (a+b) cm 1. 2. 3. 4. 5.

Average length of the cylinder l = ……… cm.

b) Diameter of the cylinder :

 S.No M.S.R                acm Vernier Coincidence   (n) Fraction   b=(n-x)*L.C Total Reading (a+b) cm 1. 2. 3. 4. 5.

Average diameter of the cylinder  d = 2r = …………. cm,

Mean radius of the cylinder           r = d/2 = ………….. cm,

Volume of the cylinder                   V = $\pi r^2 l cm^3$.

III ) Volume of the sphere :

a) Diameter of the sphere :

 S.No M.S.R                acm Vernier Coincidence   (n) Fraction   b=(n-x)*L.C Total Reading (a+b) cm 1. 2. 3. 4. 5.

Average diameter of the sphere  d = 2r = …………. cm,

Mean radius of the sphere           r = d/2 = ………….. cm,

Volume of the sphere                   V = $\frac{4}{3} \pi r^3 cm^3$.

Result : 1. Volume of the given cylinder  V= ……….. $cm^3$

2.Volume of the given sphere      V= ……….. $cm^3$.

Watch this vedio :

Review Questions – Vernier calipers.

During practical examinations  the examiner can shoot any question related to the experiment you are doing.Here I will try to answer few Frequently asked questions by   examiner.

1Q: What is the advantage of vernier calipers over a regular  scale graduated in millimeters?

Ans: We can measure up to a millimeter with regular scale which is graduated in millimeters, Where as  with a vernier calipers with 10 equal divisions on the vernier scale we can measure up to 1/10 (0.1) mm accurately.

2Q:What is the principle of vernier ?

Ans: (N-1) main scale divisions  = N divisions on vernier scale,

(N-1) M.S.D = N V.S.D   is the principle of vernier.

3Q:What do you mean by least count of vernier calipers?

Ans: The difference  of 1 M.S.D  and 1 V.S.D is called least count of a vernier calipers. (or) The minimum

length which can be measured by a vernier calipers is called its least count.

4Q:What is the use of lower jaws of a vernier calipers?

Ans: The lower jaws or used to measure the  thickness of object,outer diameters of tubes,spheres   and  cylinders.

5Q:What is the use of upper jaws?

Ans: The upper jaws of the vernier calipers are used to measure the inner diameters of rings,tubes and inner diameters of hallow cyliders , hallow spheres.

6Q:What is the use of the thin strip moving behind the main scale?

Ans: The strip is used to measure  the depths of the tubes and level of the liquid inside tubes or jars.

7Q:Two different vernier calipers  have different number of equal divisions on their vernier scales i) 10 equal divisions ii) 50 equal divisions . Which can measure more accurately.

Ans: The least count of the I vernier calipers  = S/N = $\frac{1mm}{10}$ =0.1mm

The least count of the II vernier calipers  = S/N = $\frac{1mm}{50}$ =0.02mm.

That is the II vernier calipers with 0.02mm of L.C can measure up to 0.02mm accurately.Hence the accuracy of II vernier calipers in more than I vernier calipers.

8Q:What is the ZERO error of a vernier calipers?

Ans:When two lower jaws of the vernier calipers are in contact, if the zero division of main scale does not coincide with the zeroth division of vernier scale, such vernier calipers will have zero error.

9Q: What is the formula of least count?

Ans: Least count L.C = $\frac{S}{N}$.

10Q:What is the formula to calculate the volume of the cylinder?

Ans: Volume of the cylinder V = $\pi r^2 l$. , where r = radius of the cylinder and l = length  of the cylinder.

11Q:What is the formula to calculate the volume of a Sphere?

Ans: Volume of the Sphere V = $\frac{4}{3} \pi r^3$, where r = radius of  the sphere.

12Q:What is the formula to calculate total reading with a vernier calipers?

Ans: Total reading = M.S.R + $n\times L.C$.

13.How many types of Zero errors will be possible in vernier calipers?

Ans: Two types of Zero errors are possible in vernier calipers they are i) Negative Zero error ii) Positive Zero error

14. What is Positive zero error,how do we correct such an error in a vernier calipers?

Ans:When two lower jaws of the vernier calipers are in contact, if the zero division of main scale does not coincide with the zeroth division of vernier scale and the zero of the vernier is to the right of zero of main scale such an error is called Positive Zero error.So,the zero correction should be subtracted from the reading which is measured.

Ex:When two lower jaws of the vernier calipers are in contact, if the zero division of the vernier is to the right of  zeroth division of main scale and if the vernier coincidence is 1.Then the correction is subtraction i.e Total Reading – $1 \times L.C$

15.What is Negative zero error,how do we correct such an error in a vernier calipers?

Ans:When two lower jaws of the vernier calipers are in contact, if the zero division of main scale does not coincide with the zeroth division of vernier scale and the zero of the vernier is to the left of zero of main scale such an error is called negative Zero error.So,the zero correction should be added to the reading which is measured.

Ex:When two lower jaws of the vernier calipers are in contact, if the zero division of the vernier is to the left of  zeroth division of main scale and if the vernier coincidence is 8.Then the correction is addition i.e Total Reading + $8 \times L.C$

## 134 thoughts on “Vernier Calipers”

1. Param

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2. gyaunnrraje

Hi,
Mr.Paramdesai I am pleased to see your comment.I request you to comment on my blog and help me to improve its quality.

3. trisha

hi….

its really the excellent way for clearing the confusion toward least count of any instrument y the example of vernier calipers.

thanks a lot….

4. gyaunnrraje

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5. Nick

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6. gyaunnrraje

Nick,
Let me know in which standard you are studying.What way my blog helped in completing your home work faster than usual.

7. piyanka

What happens if instead if N-1 divisions, the N divisions of my vernier calipers divides N-2 or N-3 divisions on the main scale? Is it possible? what changes should we make to find the least count? which caliper would be more accurate?

8. gyaunnrraje

Hi,
PIYANKA,
As you said if (n-2) M.S.D = n V.S.D
Then I V.S.D = {(n-2)/n} M.S.D
L.C = 1 M.S.D – 1 V.S.D = 1mm – {(n-2)/n} mm = 2/n if n =10
L.C = 2/10 = 0.2 mm
i.e when (n-1) divisions are changed to (n-2)divisions least count is increased from 0.1mm to 0.2mm
i.e the accuracy of the vernier calipers is decreased.
so, if (n-3) M.S.D s are divided in to n equal divisions on vernier scale the L.C further increases and the accuracy further decreases.
Hope this explanation will clarify your doubt.

9. vani

thank you so much for this detailed information

10. nilay

such a good information about vernier caliper….thanks

11. nitin

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12. noor

hii,me noor
“THANX” for this information,

13. rajesh

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i want to thx a lot to Mr. Noor

14. A R

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15. abdul mateen

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16. Ganesan

Thanks for ur explanation. Thank u…

17. rupa

if n divisions on MS are divided into N-1 divisions on VS, what happens to LC?
Why only 49 MSD are made into 50, why not 39 into 40 or 79 into 80?

18. gyaunnrraje

If (n-1) divisions of MS are divided in to n divisions on VS then the least count will be positive L.C = 1 M.S.D – 1 V.S.D, where as if n divisions of MS are divided in to (n-1) divisions on VS then the LC of the Vernier Calipers will be negative(such device doesn’t exists)
you can manufacture vernier calipers by dividing 49 MSD are made into 50 VSD or 39 MSD in to 40VSD ………………. with different Least Counts.

19. Pingback: Contents 1 « A to Z of Physics

20. manu

thanx for the information its very simple nd easy to enter in to our minds. it would be much better if u put information regarding positive and negative errors… thax alot

21. jay

thanks

22. Vikrant Singh Rajput

Sir,
I want to measurement of vernier caliper
pls issue me soonly.

23. read about vernier calipers the first time and got everything right into my head,,,,,,
REALLY HELPFUL…..thanks a lot

24. purav

awesome work done….thans alot

25. raja

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26. raju

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27. Mohd. Aslam Shaikh

This website is really good for learning. Do u have this type of learning for chemistry also?

28. Mohd. Aslam Shaikh

29. ravindra sharma

what is the defination of vernier principle

30. It really helped me a lot. Thank u sooooooooooo much and I kindly request from u to insert more prctical questions with answers.

31. sanoop

how to change least count of a vernier caliper?

32. gyaunnrraje

L.C = S/N
S= 1 M.S.D ; N= No of equal divisions on vernier scale.
Now for example N=10 then the L.C = 1/10 =0.1 M.S.D or 0.1mm (if M.S.D = 1mm)
If N=9 then the L.C=1/9 M.S.D or 1/9 mm (if M.S.D = 1mm)
like that you can change the least count of vernier calipers by changing the no. of equal divisions on vernier scale.
you can manufacture vernier calipers by dividing 49 MSD are divided into 50 VSD or 39 MSD in to 40VSD ………………. with different Least Counts.
Hope my explanation clarifies your doubt.

33. Knowntonone

Why is it called Vernier calippers?

34. Manish

Respected gyaunnrraje, How to measure inches dimension on vernier caliper?

35. Manish

Respected gyaunnrraje, what are the smaller units of inches?

36. Aman Sethi

thank you so somuch clearly explained . :)

37. MAHESH

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I SEE YOUR WORDPRESS THIS IS VERY EXCELLENT.
I FEEL DIFFICULT ABOUT CALIPERSE IN MY PRACTICALS.AFTER SEEING YOUR SITE I FEEL VERY HAPPY.THANKS

38. ashit

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39. sandhya

thank you so much for this detailed information

i want to know about the 3/4 point contact vernier callipers and the advantages/scope of use .

41. thanx body!!!!!!!!!!!!!!!!!!!!11

42. it was vry vry helpful for me thank u so much :-)

43. ata plz read this

44. very nice collection.thnx

45. chitti

46. imran

what do you mean by 1 M.S.D .if i have a vernier caliper.having M.S in cm.then 1M.S.D will b 1cm or 0.1cm?????????

47. sravs

thank you.it is very useful to me.

48. yamini

thank you for the info,it is very helpful thank you sooo…….much

49. Ani

Why is it called a vernier caliper?

50. gyaunnrraje

If you have a vernier calipers in cms each division will be 1mm or 0.1cm .Hence 1M.S.D(1MainScaleDivision ) will be equal to 1mm

51. gyaunnrraje

3Point Vernier calipers is used to measure the diameters of round objects or milling tools.

52. thanks ur infermetion

Dear Sir, i have a confusion about vernier calliper. why we multiply least count with the division of vernier scale coincides with main scale, in order to add it with the main scale reading? plz help me out.

54. gyaunnrraje

Hi, Aftab, The product of vernier coincidende and least count gives the fraction.When we add this fraction value to Main scale reading we get total length of the object

up to 0.1mm accuracy.Hope this explanation will convince you.

55. archana

its really excellent

56. prajeesh fv

so nice & excellent

57. bhagya sri

can you tell how to apply correction factor

58. Hey..Just got a doubt about vernier calliper..
What does it mean by Zero error and Zero corrections..??

59. gyaunnrraje

For answer to your question,please go through through the review question no’s 8,14&15 in Vernier calipers

60. bhagya sri

thank you very much gyaunnrraje. it was helpful.

61. ritz

gr8.. w0rk buDdy..!! such a gud explanati0n of DiZ t0pic..!! :P

62. RAMANA

THANKS 2 VERNIER&SCREW GAUGE.ITS VERY USEFUL 2 US

63. thanks 2 vernier&screw gauge.its very useful 2 us

64. it is very useful website for us
it is very useful for learning

give experiments with different type of callipers

66. BiAncA...

hi……
thnx a lot for the information..this thn hlpd me a lot…
i was pretty messud up with the zero errorss…
THANKS once again =)=)

67. That’s very benefical for me..

68. IT’S very benefical for me..

69. gr8 work!!….. such a good exp.of DiZ. topics..!!:P

70. AMARDEEP GAUTAM

i want all the theory and numerical for iit-jee based on verniar caliper

71. yasir khan

thanxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

72. aashu

it ix good for learning physics practical of vernier caliper

73. nisha n

hi
Very well compiled information about the vernier calipers.But, in Q 15 about the negative Zero Error ….

Ex:When two lower jaws of the vernier calipers are in contact, if the zero division of the vernier is to the left of zeroth division of main scale and if the vernier coincidence is 8.Then the correction is addition i.e Total Reading + 8

I think the correction should be Total Reading + (10-8) …if the Vernier coincidence is 8
i.e. the correction is Total Reading + 2

Thanks for the information.
It is very useful for the improvement of science.
Great idea!

75. Hi, Thanks a lot for this amazing article! I must bookmark Vernier Calipers A to Z of Physics. Thanks.

76. sonia

thnx 4 de deatiled xplanation.its really helpful.

77. Sravan

Its really gud for the students which u given….thanks alot for this…and but its better to mention some examples here…for the better clarification…thanku…

78. ram

79. Hi,
I really like this side and i learn many things from this side.

80. chathu

normally a vernier caliper has a minimum scale of 0.1mm. but i have heard there some caliper which have another minimum scales which is below or above to the above value. so i want to how we could calculate such scales. for an example main scale going with the inches and vernier scale also going with inches and devided in to some parts. so how could we calculate the measure .?????????

81. Nazraar

Good Explanation.

82. prudhvi

it helped me a lot
thanx

83. smathur

Hi. Can you accurately measure the thickness of a fine wire using a vernier calliper?

84. Jackshana Maria

thanx!!!!helped me a lot for my practicals

85. Prasant

hi, thanx a lot..i am preparing for AIEEE and this really helped coz they dont explain vernier callipers in our textbook :)

86. Pooja

Hello, very well explained theory.EXCELLENT!!

87. natasha

hi natasha here thanx Gyaunnrraje 4 this website .I was preparing for my weekly exam on vernier callipers and this informative page has helped me a lot. Thanks once again.

88. vinod

hi Vinod hear Thanks for this all information

89. Ammar

Good videos are shown in this.I thank for this.

90. sachin

at firt

91. wow lc and all

92. nandini

what all can we measure with vernier calipers

93. Avinash

thanks, but don’t given least count of inches series

deep information in simple words.

95. Kalhara

it’s realy simple to understand,,,,,,,,,,,,,
thanks…………

96. kirtan

what is the logic behind:

L.C.=1 M.S.D.-1L.S.D

97. kirtan

sorry it is L.C. = 1msd – 1vsd

98. hassan

wrong ruined my physics

99. Balvinder kumar

very nice..a good and easly understandable english to be used.

100. Gollapudi R K Mohan

Really its very nice.. so useful to understand without confusion

101. itS heLps me bUt i want defects of using V.C..

102. karthik

it was really fantabulous

this is really good to … :)

104. akash

its very helpful for me,thnksss. ..

105. teebrocker

hey can yoy please tell me if the vernier scale reading has has errors or no? please reply fast….i have my assignment due on friday!!!

106. teebrocker

also how do i divide 5.14 cm ± 0.005cm by 2

107. komal

What is the logic behind 1M.S.D-1V.S.D?? Why that?

108. DON ODUOR

am really satisfied with the way this person who wrote about the vernier calipers ….,I’ve understood every single bit of it.

109. RISHMIT

hlo…
i’m Rishmit thanks a lotttttt…:D
tomorrow is my practical test and just because of you now, i have no worry…

110. gyaunnrraje

(5.14+.005)/2=5.145/2=2.5725 or (5.14-.005)/2=5.135/2=2.5675

sinthu

112. Vipin sen

Pleas give me my questins answer (on the which principal vernier caliper worked) perhaps= rac and pinion im correct B-)

113. saurabh

thank u vry much for information…

114. thank uuuuuuuuuuuuuuuu soooooooooo much!!!!!!!!!!!!!!!!!!!!!

115. Wikum

To find the negative zero error should we substract the number of vernier divisions coincided from the no of vernier divisions and then multiply by the least count

116. rishab garg

to find negative eroer we have to adour obesrve reading and negative eror and obeserv reading=msd reading+vsd coincidingmultiply leasst count
and negative eror = least count multiply dividion coincind with msd when both jaws are touch

your site is very helpful to me it is very easy to understand.

118. jyoti

thnks

hi i m zeeshan and the matter is very good i read all matter and i found more knownoledge about these thanks a lot to clear my topic

120. Kuldeep

wow by reading this I knew all useful info. for my experiment exam…..thanks a lot sir

121. could u please write the calculations too?We dont have any apparatus to do…….!

122. IQRA RANA

hmmmmmmm…..nice information about vernier caliper…

123. Wanjitha Gayan Withanage

thanks alot for these informations. :)

124. I want to learn more about physics practical too(: who could help me?

125. Rajasekaran.r

All is whel

126. thaaaaank you very much,

127. Shubham Varshney

I am a student at ALIGARH MUSLIM UNIVERSITY and was looking for some information that could help me with vernier calliper. Thanks man, you made it really easy to use callipers

128. Mbona Bhekimpi

Your point is good but how that LC is derived is the point of my wory.lwill find out the formula l wants had it.

129. rachael mafumo

can u pls send me information about vernier calipers

130. rachael mafumo

can u pls send me information about vernier calipers via email

131. if the diameter observed by vernier calliper is b/w 2.3and2.4.at this stage 8th division coincides with main scale .find correct answer……………………………………………..can u plz give the answer

132. Firdous khan

It is really helped me a lot for sort outing all my doubts about it thanks…….

133. deepshikha

thanks alot for information

134. Prince Sharma

thanks a lot 4 information….