ASSUMPTION UNIVERSITY
Faculty of Engineering
Physics Laboratory
Name:_________________________________________ Code:_________________ Sec:______
1. Experiment
: Vernier calipers
2. Objective
: To determine the dimensions of given small objects by using vernier calipers.
3. Apparatus
: Vernier calipers, rectangular object, cylindrical object and electronic digital scale.
4. Theory
: The Vernier Calipers is a precision instrument that can be used to measure internal
and external dimensions of small objects extremely accurately. The vernier calipers enable us to
obtain an accurate result up to the second decimal place in millimeter. (e.g. 0.05 mm and 0.02 mm)
The main scale divisions are marked on the main bar of the instrument and vernier scale
divisions are marked on the moving part of the instrument. The required dimension of the of the
object is the sum of three measurements, called main scale measurement, vernier scale measurement
and zero error correction (or) zero error reading of the vernier caliper.
To use the vernier scale, Least count (LC) and zero error reading (or) zero error
correction of the vernier caliper must be checked and recorded before measuring the object.
(a) Least Count of vernier calipers
Least Count (LC) for an instrument is the minimum measurement that can be made accurately
by a measuring device. A measuring instrument cannot measure anything whose dimensions are less
than the magnitude of least count. The instrument will have more precise measurement if the
magnitude of least count is smaller value.
Last Count of vernier calipers is the minimum measurement by vernier calipers. The
magnitude of least count of vernier calipers is depending on the nature of the scale (mm, cm, inch, etc.)
and the number of division on vernier scale. The least count of vernier calipers can be calculated
by two methods, they are (1) the difference of one vernier scale division and main scale
division(s), which is nearest to the one vernier division. (2) Taking reciprocal of number of
vernier divisions.
Examples of least count calculation for different vernier scale divisions
Example I
1 main
0
1
0
1
division = 1 mm
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
10
10
Calculation of Method (I)
Least count of vernier calipers can be calculated by the difference of one vernier scale division
and main scale division(s), which is nearest to the one vernier division.
10 vernier division = 9 main division
1 vernier division = 0.9 main division
1 vernier division = 0.9 mm
According to the diagram, 1 main division is close to 1 vernier division.
L.C. = 1 main division – 1 vernier division
= 1 mm – 0.9 m
Least count (LC) = 0.1 mm
Calculation of Method (II)
Least count for that scale can be calculated by reciprocal of number of vernier divisions.
1 main division
number of vernier divisions
1mm
Least count (LC) =
= 0 .1 mm
10
Least count (LC) =
Example II
1 main
20
10
0
0
1
2
3
5
4
division = 1 mm
30
6
7
50
40
8
9
10
Calculation of Method (I)
Least count of vernier calipers can be calculated by the difference of one vernier scale division
and main scale division(s), which is nearest to the one vernier division.
20 vernier division = 39 main division
1 vernier division = 1.95 main division
1 vernier division = 1.95 mm
According to the diagram, 2 main divisions are close to 1 vernier division.
 L.C. = 2 main division – 1 vernier division
= 2 x 1 mm – 1.95 mm
Least count (LC) = 0.05 mm
Calculation of Method (II)
Least count for that scale can be calculated by reciprocal of number of vernier divisions.
Least count (LC) =
1 main division
number of vernier divisions
Least count (LC) =
1mm
= 0.05 mm
20
Example III
1 main
0
20
10
0
1
2
3
4
division = 1 mm
30
5
6
50
40
7
8
9
10
Calculation of Method (I)
Least count of vernier calipers can be calculated by the difference of one vernier scale division
and main scale division(s), which is nearest to the one vernier division.
50 vernier division = 49 main division
1 vernier division = 0.98 main division
1 vernier division = 0.98 mm
According to the diagram, 1 main division is close to 1 vernier division.
L.C. = 1 main division – 1 vernier division
= 1 mm – 0.98 mm
Least count (LC) = 0.02 mm
Calculation of Method (II)
Least count for that scale can be calculated by reciprocal of number of vernier divisions.
Least count (LC) =
=
1 main division
number of vernier divisions
1mm
50
= 0.02 mm
According to the least count calculations of vernier calipers, if there one vernier scale division
makes difference with main scale division(s), then one least count (LC) is taken.
(b) Zero error reading of vernier calipers (zero error correction for the measurement)
When the two jaws of the vernier calipers are in contact, the number of divisions of
vernier scale which are getting difference with respect to the zero mark of main scale is called
“zero error reading”.
1. When the two jaws are in contact, if the zero mark of vernier scale coincides with the zero mark
of main scale, zero error reading of the instrument is zero.
2. When the two jaws of the vernier calipers are in contact and if the zero mark of vernier scale is
leading before zero mark of main scale, the measurement is shortening the length because the
measurement is started from zero mark of vernier scale even though the measurement must be
started from two scales zero marks together. The shortening length is the length of between zero
mark of main scale and zero mark of vernier scale. To get the shorten length the number of
vernier scale divisions must be counted from extreme right-hand side of vernier scale toward the
same positions of two scales divisions. The counted number of vernier divisions x LC is the
positive value of zero error reading (or) measurement for zero error correction.
3. When the two jaws of the vernier calipers are in contact and if the zero mark of vernier scale is
lagging behind zero mark of main scale, the measurement is longer the length because the
measurement is started from zero mark of main scale even though the measurement must be
started from two scale zero marks together. The longer length is the length of between zero mark
of main scale and zero mark of vernier scale. To get the longer length the number of vernier scale
divisions must be counted from extreme left-hand side of vernier scale toward the same positions
of two scales divisions. The counted number of vernier divisions x LC is the negative value
of zero error reading (or) measurement for zero error correction.
Examples of zero error readings for vernier calipers
0
0
0
0
1
2
3
4
5
6
7
8
9
10
Fig. C (1)
When zeros of both scales coincide
No zero error reading
0
1
2
3
4
5
6
7
8
9
10
0
Fig. C (2)
1
2
3
4
5
6
7
8
9
10
Fig. C (3)
When vernier scale starts before When vernier scale starts after
the zero on the main scale,
the zero on the main scale,
three divisions vernier reading
three divisions vernier reading
from the right (+3 x LC)
from the left (-3 x LC)
Fig. C (1) --- No zero error reading (No zero error correction of measurement)
Fig. C (2) --- Total measurements should be increased by (+3 x LC)
(Positive value of zero error correction should be made for total measurement.)
Fig. C (3) --- Total measurements should be decreased by (-3 x LC)
(Negative value of zero error correction should be made for total measurement.)
Measurement of objects by using vernier calipers
To measure the dimension of an object by using vernier calipers, place the object
accordingly by using upper jaws (or) lower jaws (or) depth finder. Then need to take two different
measurement readings by using two scales on the instrument, main scale reading and vernier scale
reading.
The sum of above two measurements and zero error reading (or) zero error correction of the
vernier caliper is the measurement of the required dimension of the object.
The required measurements for the dimension of the object are,
(1) Main scale measurement
[Complete number of main scale divisions between main zero mark and vernier zero
mark with no estimation x LC]
(2) Vernier scale measurement
[Number of vernier divisions between vernier zero mark and another vernier scale
division, which coincides with any main scale division x LC.]
(3) Zero error reading (or) Zero error correction of the measurement
[Zero error reading on vernier scale (number of vernier scale divisions) x Least Count (LC)]
[If you measure the external dimension of an object, the object is placed between the lower jaws. If you
measure the internal dimension of an object, put the upper jaws (or) stem inside the object. Then move
the sliding jaw until the object is secured without over force. Then screw clamp be tightened to ensure
the reading does not change while the main scale reading and vernier scale reading are being made.]
(1) Main scale reading and main scale measurement
Main scale reading must be read maximum complete number of main scale divisions on the
main scale at the left- hand-side of the zero mark of the vernier scale (or) before zero mark of
the vernier scale in mm unit. [There must be no estimate value or no decimal value in mm.]
(2) Vernier scale reading and vernier scale measurement
The vernier scale reading is taken for the needed length of between taken maximum main scale
divisions mark to vernier zero mark.
Vernier scale reading is the number of vernier divisions between vernier zero mark to another
vernier scale division which coincides with any main scale division.
To take the vernier scale reading, check the vernier scale divisions, which one of the vernier
scale division is same position (coincides) with any main scale division. Count the number of vernier
divisions between vernier zero mark to two scales coincide division, that number of vernier divisions is
the vernier scale reading. [Be careful that number of vernier divisions is not the same as numbers
on the vernier scale.]
To get the vernier scale measurement, vernier scale reading must be multiplied by last count
(LC) of vernier calipers (or) vernier scale reading x (LC).
5. Instructions
1. Find and record the least count (LC) of the vernier calipers.
2. Find the Zero error reading when two jaws in contact and record the zero error correction of the
measurement of the vernier calipers.
3. Measure two trials for the external length, width and height of the rectangular object, the object is
placed between the lower jaws, and then move the sliding jaw until secure the object without over
force. Then screw clamp be tightened to ensure that the reading does not change while the main
scale readings and vernier scale readings are being read.
4. Measure two trials for the external length of cylinder object, the object is placed between the lower
jaws, and then move the sliding jaw until secure the object without over force. Then screw clamp
be tightened to ensure that the reading does not change while the main scale readings and vernier
scale readings are being read.
5. Measure two trials for the external diameter of cylinder object, the object is placed between the
lower jaws, and then move the sliding jaw until secure the object without over force. Then screw
clamp be tightened to ensure that the reading does not change while the main scale readings and
vernier scale readings are being read.
6. Measure two trials for the internal diameter of a cylinder object the upper jaws are placed inside the
cylinder and then moved the sliding jaw until secure the object without over force. Then screw
clamp be tightened to ensure that the reading does not change while the main scale reading and
vernier scale reading are being read.
7. Measure two trials for the internal length of a cylinder object the stem (or) depth finder (or) sliding
tail is placed inside the cylinder until the stem (or) depth finder (or) sliding reached the bottom of
the cylinder without over force. Then screw clamp be tightened to ensure that the reading does not
change while the main scale reading and vernier scale reading are being read.
8. Find the sum of (a) main scale measurement, (b) vernier scale measurement and (c)
measurement for zero error reading to get the measurement of the required dimension. Then
convert the total measurement mm to in meter unit with scientific notation.
9. Measure the mass of rectangular object and cylindrical object by using electronic digital scale.
Assignment questions
1. Calculate (a) the volume (b) total surface areas of the rectangular object.
2. Calculate the net material volume of the cylindrical object.
3. Calculate the density of rectangular object and cylindrical object.
4. How can get the main scale reading of an object by using a vernier calipers instrument?
5. When you measure the dimensions of an object by using vernier caliper, which positions of main
scale readings are not correct main scale readings of an object?
6. How can get the vernier scale reading of an object by using a vernier calipers instrument?
7. Explain the relationship between number of divisions and magnitude of least count value for a
given vernier calipers. [Do not show the calculation of least count.]
8. How can you calculate least count of vernier calipers?
9. Explain about the zero error correction of vernier calipers?
10. Find the zero error correction of the measurement of given vernier calipers, if the positions of
the scales are according to the following diagram.
0
10 mm
Main scale
0
0
1
2
3
4
5
6
7
8
9
10
Vernier scale
11. Find the measurement of an object when object is between two lower jaws of given vernier
calipers, if positions of the scales are according to the following diagram.
[Zero error reading of given vernier is zero.]
0
10 mm
Main scale
object
Vernier scale
0
10
Answer should be included according to the following steps.
LC =
Main scale measurement =
Vernier scale measurement =
Zero error correction of measurement =
Measurement of an object =
Name:_________________________________________ Code:_________________ Sec:______
Object: RECTANGULAR BLOCK
Least Count (LC) = ___________________
Measurements
Main scale reading x 1 mm
(Main scale measurement)
Vernier scale reading x LC mm
(Vernier scale measurement)
() Zero error reading x LC mm
( Zero error correction)
Total measurement in mm
Average measurement in mm
Average measurement in m
Mass of the rectangular block =
Length
Width
Height
Name:_________________________________________ Code:_________________ Sec:______
Object CYLINDER
Least Count (LC) = ___________________
Measurements
External Length
Internal Length
External Diameter
Internal Diameter
Main scale reading x 1 mm
(Main scale measurement)
Vernier scale reading x LC mm
(Vernier scale measurement)
() Zero error reading x LC mm
( Zero error correction)
Total measurement in mm
Average measurement in mm
Average measurement in m
Object CYLINDER
Measurements
Main scale reading x 1 mm
(Main scale measurement)
Vernier scale reading x LC mm
(Vernier scale measurement)
() Zero error reading x LC mm
( Zero error correction)
Total measurement in mm
Average measurement in mm
Average measurement in m
Mass of the cylinder =
Some concepts, important points and examples the measurement and
about the Vernier calipers
(Don’t use this part for your report.)
Since the whole structure and application of science depends on measurements, we must
be able to evaluate the uncertainties, report them in a meaningful fashion, and minimize them.
Scientists or engineers have to consider what accuracy they need and how far the measurement can be
accomplished with the instrument use in measuring.
Meter Stick (or) meter ruler
Scale on meter stick are divided the same small lengths as divisions in millimeter. There are
one thousand divisions in millimeter or one hundred divisions in centimeter for one meter length.
The numbers of divisions are counted according to length of the object and then number
of divisions should be multiplied by length of smallest division (1mm) to get the length of the
object. If the end point of ruler cannot be used (or) cannot use zero mark of the scale of ruler,
zero error correction must be counted for.
The meter stick is not for accurate measurement, but it is adequate for ordinary purpose. The
smallest division (or) the smallest measurement that can make by meter stick (or) least count (LC)
of meter stick is 1mm, so the accuracy of the meter stick is to the nearest 0.1cm or 1mm.
To measure the length of an object the meter stick must be placed such that the marking are in
contact with the object measured. To avoid the parallax error, make sure that scale is read from directly
above.
Correct position
Incorrecr position
Incorrect position
0
1
Meter
stick
2
3
4
object
Measurement of an object = 31mm [31 divisions x LC, (LC = 1mm)](for the above diagram)
Accurate measurement of an object = (3.1±0.05) cm = (3.1±0.05) 10-2 m
Note: You can take estimation of 0.5 mm 0r 0.05 cm even though smallest division is 1 mm
(or) 0.1 cm because the smallest measurement (LC) of length by using meter stick
(1mm) is too large for accurate measurement.
Vernier Calipers
The vernier calipers enable us to obtain an accurate result up to the second decimal place
in millimeter. (e.g. 0.05 mm and 0.02 mm)
Figure (B)
The vernier calipers consist of a fixed scale with a fixed jaw attached at one end and a sliding
scale on another jaw. The sliding scale is a short sale, which is called vernier scale, and the fixed scale is
called main scale. The lower jaws are used for external dimensions and the upper jaws are used for
internal dimensions. Depth finder or depth measuring blade (sliding tail or stem to measure the depths)
can be used to measure the depth of the cylinder. [See fig. B]
Example of measurement taken by vernier calipers
Example: Take the measurement of an object according to the following positions of vernier calipers; if
two jaws are in contact, zero mark of vernier scale coincides with zero mark of main scale
of the vernier calipers instrument.
Note: 1. If two jaws are in contact, zero mark of vernier scale coincides with zero mark of
main scale of the vernier calipers instrument the vernier calipers instrument has no
zero error reading,
2. When the objet is placed between two lower jaws to measure the external length of
objet, the length of objet is the distance between zero mark of main scale and
zero mark of vernier scale.
3. Main scale reading can’t take the position of the object or position of the moving
jaw on main scale. Main scale reading can take only the position of zero mark of
vernier scale on the main scale.
4. There are 20 divisions on vernier sale for given instrument, Least count (LC) can be
calculated as follow.
1mm
Least count LC =
= 0.05 mm
20
11th vernier scale division line coincides with one main scale division line
0
10
20
30
50
40
Object
0
1
2
3
4
5
6
7
8
9
10
Main scale reading can take the position of zero mark of vernier scale on the main
scale.
The following readings can be seen on the above diagram.
(a) Maim scale measurement = 24 main scale divisions x 1mm = 24 mm
[The measurement over 24mm can get by vernier scale reading accurately.]
(b) Vrnier scale measurement =11 vernier scale divisions x Least count = 11 x 0.05 mm = 0.55 mm
[The eleventh vernier scale division line coincides with one main scale division line.]
(c) () zero error correction of measurement = zero division x Least count (LC) = 0 x 0.05 = 0.00 mm
[When two jaws are in contact main scale zero mark coincides with vernier scale zero mark.]
Taking data for measurement
(a) Main scale measurement
24 x 1 mm
= 24.00 mm
(b) Vernier scale Measurement (vernier scale reading x LC)
11 x 0.05 mm
= 0.55 mm
(c) Zero error correction of measurement (() zero error reading x LC)  0 x 0.05 mm = 0.00 mm
_______________
Measurement of an object
= 24.55 mm
The measurement value in scientific notation with SI unit is
= 2.455x10–2m.
(We need to state the measurement value in scientific notation with SI unit.)
Example of measurement errors and causes of error
1. Main scale reading error –
– reading the position of object or position of instrument (jaw) position.
– not zero mark of vernier scale position on the main scale.
– main scale reading includes estimated vale..
– using over pressure or less pressure on jaws with object.
– not using the clamp screw and loose tighten or over tighten the clamp screw.
2. Vernier scale reading error –
– reading at the not coincide position of vernier and main scale divisions.
– reading not the complete number of divisions before the coincide position of main
scale and vernier scale division lines.
– reading number on vernier scale and not number of vernier scale divisions.
– using over pressure or less pressure on jaws with object.
– not using the clamp screw and loose tighten or over tighten the clamp screw.
3. Zero reading error –
– taking the scale reading without touching two jaws.
– reading number on vernier scale and not number of vernier scale divisions.
– reading includes estimation and not complete number of divisions.
– wrong position of reading by not thoroughly checking the coincide position of
vernier and main scale.
4. Measurement of the object error –
– main scale measurement error by not taking main scale reading x 1 mm.
– vernier scale measurement error by not taking vernier scale reading x LC.
– zero correction measurement error by not taking zero error reading x LC.
– Total measurement error by not taking the addition of above three measurements.
Take care of using Vernier calipers.
1. Don’t forge not to use the screw clamp over force when you measure the dimensions of an object.
2. If you would like to move out the object, don’t forget the clamp screw is tightened. If you move out
the object with the tightened screw situation the object can be damage.