Applied Math I
Overview
● In this lesson you will learn about:
● The different kinds of calipers.
● The components of a typical caliper.
● Caliper usage.
● Reading English and metric
Introduction
● Calipers are tools used in home, small
shop, and industrial settings.
● They are used to make precise length
Introduction
● Some reasons for their popularity
include:
● Wide measuring range (usually 0 - 6”).
● English and metric scales are usually
found on the same instrument.
● Many different kinds of measurements
Introduction
● While both micrometers and calipers
can make outside length
Introduction
● Calipers can also make inside
Introduction
Introduction
● There are three types of calipers.
Introduction
Introduction
Introduction
● In this lesson, we will concentrate on
Introduction
● These are the main features of a typical
vernier caliper:
Jaws (for outside measurements)
Small jaws (for inside measurements)
Metric vernier scaleMetric fixed scale
English vernier scaleEnglish fixed scale Beam
Reading a Caliper: English
● To determine the length of an object in
inches, you must be able to read the English scale on the caliper.
Reading a Caliper: English
● Most of the measurement information is
Reading a Caliper: English
● Where do you start?
Reading a Caliper: English
● The zero line acts as a pointer, and tells
Reading a Caliper: English
● Reading a caliper is a process of
collecting measurements from the fixed scale and the vernier scale.
● To stay organized, write down each
Reading a Caliper: English
● The largest fixed scale divisions are the
one-inch intervals, so start there first.
Since the zero line is between 1” and 2”, we know the object being measured is at least 1” long.
Measurements
Reading a Caliper: English
● The one-inch intervals are broken down
into ten smaller ones. Each of these is worth a tenth of an inch (0.1”).
0.1” Measurements
1 0.2”0.3”0.4”0.5”
Because the zero line did not go beyond any of the one-tenth lines, you won’t add any of these to the measurement total.
0.0
Reading a Caliper: English
● Notice that between any one-tenth
interval, there are four spaces. Each of
these is 0.025” (0.1” ÷ 4 = 0.025” )
0.025” Measurements
1
0.050”0.075”
0.0
The zero line has gone past two
of 0.025 lines but it hasn’t quite
gone beyond the third one.
Two 0.025” lines equals 0.050”. Add that to your measurement total.
Reading a Caliper: English
● The last step is to get a reading from
the vernier scale.
0.001” Measurements 1 0.002” 0.003” 0.0
Each line on the vernier scale is worth 0.001”
0.050
Reading a Caliper: English
● What you are looking for is a place
where one of the lines on the vernier “lines up” with a line on the fixed scale.
Measurements
1 0.0 0.050
It might be difficult to see on the computer screen, but
Reading a Caliper: English
● Add the vernier scale number to your
Reading a Caliper: English
Reading a Caliper: English
Reading a Caliper: English
● Determine the number of whole
inches...
Reading a Caliper: English
● ...the number of tenths (0.1”)...
1 0.0
The zero line did not go
Reading a Caliper: English
● ...the number of 0.025” lines...
1 0.0
The zero line is beyond the second 0.025” line but not the third.
Reading a Caliper: English
● …and finally the vernier reading.
1 0.0
The 0.020” line seems to line up best with a
division on the fixed scale. 0.050
Reading a Caliper: English
● The sum of all these measurements is
1.070”.
● Let’s obtain a reading from this caliper:
Reading a Caliper: English
Reading a Caliper: English
● Determine the number of whole
inches...
0
Reading a Caliper: English
● …the number of tenths (0.1”)...
0
The zero line on the vernier scale has gone beyond the 0.5” line.
Reading a Caliper: English
● …the number of 0.025” lines...
0
The zero line on the vernier scale has gone beyond the first 0.025” line but not the second.
Reading a Caliper: English
● …and finally the vernier reading.
0 0.5
0.025 The 0.019” line
Reading a Caliper: English
● The sum of all these measurements is
● Let’s obtain a reading from this caliper:
Reading a Caliper: English
Reading a Caliper: English
● Determine the number of whole
inches...
1
The zero line has gone
Reading a Caliper: English
● …the number of tenths (0.1”)...
1 The zero line on the vernier scale has gone beyond the 0.6” line but not quite to the 0.7” line
Reading a Caliper: English
● …the number of 0.025” lines...
1 The zero line on the vernier scale has gone beyond three
of the 0.025” lines. This is equal to 0.075”.
Reading a Caliper: English
● …and finally the vernier reading.
1 0.6 0.075
The 0.014” line
Reading a Caliper: English
● The sum of all these measurements is
● Do this problem on your own. Click to
see the answer.
Reading a Caliper: English
● Determine the number of whole
inches...
4
The zero line has gone
Reading a Caliper: English
● …the number of tenths (0.1”)...
4 The zero line on the vernier
scale has gone beyond the 0.5” line but not the 0.6” line
Reading a Caliper: English
● …the number of 0.025” lines...
4 The zero line on the vernier scale has gone beyond two
of the 0.025” lines. This is equal to 0.050”.
Reading a Caliper: English
● …and finally the vernier reading.
4 0.5 0.050
The 0.013” line
Reading a Caliper: English
● The sum of all these measurements is
Introduction and
Reading a Caliper: metric
● As you are about to see, working with
the metric portion of a vernier caliper is a bit easier to deal with.
● You only need to make two readings:
Reading a caliper: metric
● Start by obtaining a measurement from
the fixed scale...
Reading a caliper: metric
● Use the zero line on the vernier to
Reading a caliper: metric
Each number printed on the
metric scale represents centimeters.
6 cm
However, since your final reading is supposed to be in millimeters, you need view these amounts as millimeters.
Reading a caliper: metric
One “trick” is to mentally add a 0 (zero) behind each centimeter number.
0
60 mm
0 0 0 0
Reading a caliper: metric
Since there are ten spaces between each
numbered interval, these smallest spaces must be 1 mm each.
For example, note the ten spaces in this interval. The smallest interval on this
scale is 1mm. For example, this
Reading a caliper: metric
As you can see in this problem, we have a fixed scale measurement of 63 mm.
Reading a caliper: metric
To finish we must obtain a reading from the metric vernier scale.
On this scale, each line represents 0.05 mm.
Reading a caliper: metric
Just as we did on the English vernier scale, we need to look for a place where a line from the fixed scale “lines up” with a line on the vernier.It appears that these two
Reading a caliper: metric
So based upon the two readings (one from the fixed scale, and one from the ruler) the length must be 63 mm + .50 mm = 63.50 mm
63 mm
.50 mm +
Reading a caliper: metric
Reading a caliper: metric
● First take a reading from the fixed scale.
Use the zero line from the vernier to help.
Remember that we need to read the fixed scale in terms of millimeters. The zero line is close, but not quite up to the 20 mm line. It has gone beyond the 19 mm line however.
19 mm
19 mm
Reading a caliper: metric
● To finish, read the vernier scale.
It appears that these two lines, “line up” the best.
This is read as .35 mm
19 mm
Reading a caliper: metric
● The final reading then is 19.35 mm.
.35 mm +
Reading a caliper: metric
Reading a caliper: metric
● Use the zero line from the vernier scale
to help get a reading on the fixed scale.Remember that we need to read the
fixed scale in terms of millimeters. The zero line is directly above the
8 mm line.
Reading a caliper: metric
● That’s it! Since the zero line on the
vernier matched up with a line on the fixed scale, you quit right there.
Reading a caliper: metric
● Do this one on your own. Click to see
● Start with the fixed scale reading.
Remember that we need to read the fixed scale in terms of millimeters. The zero line is close, but not quite to the 97 mm line. It has gone
beyond the 96 mm line however.
96 mm
0 0 0
96 mm
Reading a caliper: metric
● To finish, read the vernier scale.It appears that these two lines, “line up” the best.
This is read as .60 mm
96 mm
Reading a caliper: metric
● The final reading then is 96.60 mm.
.60 mm +