Around 6th century BC, the oldest caliper was found within a ship called the “Greek Giglio Wreck” near the Italian island Giglio, back then the caliper was made of wood.5 During the Han Dynasty (202 BC – 220 AD), the earliest calipers without a vernier scale originated in Ancient China and they were made out of bronze.4 It was not until a French Scientist named Pierre Vernier developed a secondary scale that provided an extra precision on the measurement scale. He is credited with the invention of the Vernier Caliper which was named after him.6 In 1631, Pierre Vernier published his journal entitled as “La construction, visage, et les proprietes fue quadrant nouvea de mathmatiques”, which paved the way for the introduction of the Vernier scale and through this scale, it enabled users to acquire precise measurements of objects at a greater level of accuracy.4
In addition to this, it was Jerome Lalande who popularized the name “Vernier” through his book “Traité d’astronomie”.4 In the present day, a vernier caliper is an instrument designed to gauge the dimensions and depth of the different objects, this tool is known to measure to a precision of one hundredth of a millimeter and one thousandth of an inch and it is also useful especially when it comes to measuring the diameter of circular objects such as cylinders because its jaws can be secured on both sides of the circumference.8
On the other hand, William Gascoigne invented the first micrometer caliper, also a measuring device, in the 17th century.1 In 1848, French inventor Jean Laurent Palmer was the one who first documented the development of handheld micrometer calipers because of him it was often called palmer screw.7 The micrometer caliper model that was developed by Palmer was then the foundation on which all the modern micrometer calipers were built. The micrometer caliper is also known as the micrometer screw gauge, it is an instrument which can measure the depth, thickness, and length of an object that fits between its spindle and anvil and is used for the precise measurement of small distances.3 The mechanism behind the modern micrometer caliper is based on the rotation of the screw that helps in achieving accuracy, its calibrated screw is used for precise measurements wherein it has a very high accuracy of 0.01 compared to the vernier caliper accuracy of 0.02.2
This paper aims to use the Vernier Caliper and Micrometer Caliper in the measurement of lengths; to accurately measure the dimensions of geometric objects by means of the Vernier and micrometer calipers; to determine the density of some solids by direct measurement of mass and volume and to compare the measured densities of some solids with listed standard densities from references.

Vernier caliper
A caliper is the equipment used in measuring distances of two opposite sides of an object. A Vernier Caliper, invented by Joseph R. Brown in 1851, is extremely precise measuring equipment that was used as the first concrete tool for exact measurements. It consists of main scale, vernier scale, inner measuring jaws/internal jaws, outer measuring jaws/external jaws, retainer, tail-depth probe, and retainer.
The Main Scale, located on the upper portion of the equipment, holds the inner and outer jaw of the tool. It is used to determine the main reading of the dimension using units of centimeters or inches.
The Vernier Scale, also called as sliding scale, found on the lower portion of the equipment, is fixed by the retainer in any position and used in determining the first and second decimal readings of the measurement.
The Inner Measuring Jaws/Internal Jaws are used in determining the inner dimensions of an object.
The Outer Measuring Jaws/External Jaws are used in determining the outer dimensions of an object.
The Retainer is used in retaining or blocking the movable part of the equipment within the jaws of the caliper to convey the measurement easily.
The Tail-depth Probe is used in determining the depth of objects or liquids.
In using the vernier caliper, one must first identify the main scale and vernier scale properly. The main scale contributes the main reading that has one decimal place while the vernier scale provides the second decimal place to the reading.
When obtaining the measurement of the main scale, the person performing the experiment must look at the value to the immediate left of the zero on the vernier scale. The vernier scale measurement, on the other hand, can be determined by looking at the value that coincides on the main scale. In reading the final measurement, the values obtained from the measurements of the main scale and the vernier scale will be added.
Least count is computed to identify the highest degree of accuracy of measurement that can be achieved. It can be obtained by acquiring first the least count of the main and vernier scales. Count the number of divisions on the main scale in one cm of it and then divide 1 cm to the total number of divisions counted. If 10 divisions in one cm can be seen from the main scale = 1/10 = 0.1cm. Therefore, in one cm with ten divisions on the main scale, 0.1cm is the least count.
To get the least count of the vernier scale, divide the least count of the vernier caliper on the main scale by the number of divisions on vernier scale. Most Vernier calipers have the least count of 0.01 cm of main scale and 10 divisions on vernier scale. If 0.01 cm will be divided by 10 divisions of the vernier scale, 0.001 cm will be attained. Thus, 0.001 cm is the least count of vernier caliper which measures the accuracy you can obtain using a Vernier Caliper.
Micrometer caliper
The micrometer caliper, also referred as micrometer screw gauge, is also a tool in measuring like vernier caliper. However, this equipment is made especially for measuring the thickness or the diameter of smaller dimensions. It has two scales namely, the main and secondary scales, which produce more enhanced results than the vernier caliper. It has been extensively used in the field of engineering to obtain precise measurements. This equipment comprises the anvil, spindle, sleeve (with main scale), frame, lock, thimble (with rotating vernier scale), and ratchet knob.
The anvil is the cylindrical part of the equipment which is connected to the frame of the micrometer used in supporting the objects needed to be measured.
The spindle is the cylindrical end of the screw that the thimble causes to move toward the anvil.
The object to be measured is placed between the anvil and the spindle.
The sleeve attaches the frame to the cylindrical tube and carries the screw, the most important part of the equipment. This part is fixed and has a scale inscribed over it that is identified as the main scale.
The frame is a C-shaped body holding the anvil and barrel in constant relation to each other from which the measurement is read.
The lock is a ring-shaped part used to keep the measurement obtained by holding the screw in its final position.
The thimble, also called as head, is defined as the end of the cylindrical tube carrying the vernier or secondary scale. This part is circled to adjust the spindle.
The ratchet knob obstructs the screw when the pressure on the object being measured is sufficient.
In measuring an object using a micrometer caliper, the object must first be placed between the anvil and the spindle. The readings obtained from the two scales, main and secondary, of the instrument are used to get the final measurement of the object.
The measurement of the micrometer caliper acquired on the thimble is called pitch and indicates the secondary scale which determines the distance moved by the thimble per rotation.
The main scale measurement can be acquired by recording the value where the spindle stopped after the ratchet knob put sufficient pressure on the object being measured. It consists of 25 short vertical lines above and below a long horizontal line. The vertical lines above the horizontal line correspond to a millimeter reading. Meanwhile, the vertical lines below correspond to a millimeter reading with values of 0.5 mm.
These calipers differ on their physical features. Vernier caliper has two sliding scales with different spacing between markings on each scale while a micrometer has a screw to decode small distances moved by its jaws to larger distances along the marked scale. Regardless of their difference, both of them are used to obtain precise measurement.

The experiment aims to measure the dimensions and calculate the density to identify the percentage error of the following materials: Metallic cube, metallic washer, and glass sphere.

Both vernier caliper and micrometer caliper are utilized for measuring the dimensions for the metallic cube, and a balance to measure their mass. There were ten trials conducted for measuring the dimensions of the metallic cube, where the average of the trials was taken to compute for the volume of the material using the formula V=S3. The density is calculated by using the formula ?=m/v. To identify the percentage error of the density, the difference of the standard density and the experimental density is divided by the standard density multiplied by one hundred.

In measuring the mass and dimensions (Inner diameter, outer diameter, and height) of the metallic washer, a balance and a vernier caliper is used, the average of ten trials in measuring was taken. The radius is then identified and used in the formula V=?h(r02-ri2) to acquire the volume. Using the formula ?=m/v, the density of the metallic washer is calculated. The percentage error of the density is computed by dividing the difference of standard density and experimental density to the standard density multiplied by one hundred.

The final object that is measured is the glass sphere where the micrometer caliper is utilized in measuring the dimensions and balance for its mass. Ten trials were taken in measuring the diameter, and the average of the trials is used for its measurement. The volume of the glass sphere is computed by using the formula V= (4/3)?r3. Its density is calculated by following the formula ?=m/v. The percentage error density is identified by getting the difference of the standard and the experimental density divided by the standard density.


Material Mass Length Volume Density (g/cm3)
Aluminum g mm cm cm3 Experimental Standard Percentage Error (%)
44.90 26.435 2.644 18.47 2.431 2.7 9.963
Table 1.1 Metallic Cube (Vernier Caliper)
Table 1.1 shows the data collected from measuring a given material and in this case an aluminum cube. A Vernier caliper was used as the measuring device in this experiment. The researchers first get the mass of the metallic cube which is 44.90 grams, then using the Vernier caliper they measured one side of the cube since every side of the cube is equal. The measurement is obtained through looking at the main scale of the Vernier caliper and the Vernier scale. The measurements retrieved was converted into centimeters since the unit used in the Vernier caliper is in millimeters; then they get the volume of the cube to get the density of the material, they multiplied the measured length into itself by three times since it is the formula to the volume of a cube. The density is obtained by dividing the mass by its volume (g/cm3); and lastly the percentage error is achieved through subtracting the standard value from the experimental value, next take the absolute value of the difference, then divide it by the accepted value, and lastly multiply it to 100% to get the percentage error.

Material Mass Height Diameter Radius Volume Density (g/cm3) Percentage Error
Steel g cm Outer Inner Outer Inner cm3 Experimental Standard
56.05 0.33 cm cm cm cm 8.160 6.869 7.8 11.94
6.24 2.730 3.12 1.365
Table 1.2 Metallic Washer (Vernier Caliper)

Table 1.2 shows the data for the obtained measurements from a metallic washer using a Vernier Caliper. The performers of the experiment first get the mass of the metallic washer which will be used for the derivation of the density of the metallic washer; they now proceed to the length measurements, using a Vernier caliper they get the following: inner and outer diameters, and inner and outer radii. The performers of the experiment first get the inner and outer diameters of the metallic which happens to be the longest cord of any circle that runs from one edge of the circle passing through the center then ends in the opposite edge of the circle; then they get the radii of the metallic washer which happens to be the half of a diameter, so they simply divide the obtained diameter (in centimeters) by 2 to get the radius. The units present in the main scale of the caliper was in millimeters (mm) but the needed unit for the volume needs to be in centimeters (cm), so they divide their obtained data in millimeters (mm) by 100 to convert it to centimeters (cm). The volume of the metallic washer was obtained through the formula: V= ?h(r02 – r12), which pi is a constant, height (h), outer (r02) and inner (r12) radii is measured, getting the volume 8.160 cm3. The density is derived from dividing the mass by volume or d= m/V, which they get 6.869 g/cm3. To get the accuracy of the experiment, the percentage error must be computed, the formula for getting the percentage error is the absolute value of the difference of the standard value and experimental value, divided by the standard value then multiply to 100 percent. The percentage error was 12%.

Material Mass Length Volume Density (g/cm3)
Aluminum g mm cm cm3 Experimental Standard Percentage Error (%)
44.90 25.34 2.534 16.73 2.68 2.7 0.7407
Table 2.1 Metallic Cube (Micrometer Caliper)

Table 2.1 shows the data collected from using the micrometer caliper on a metallic cube. Using the micrometer caliper, they first measure a side of the metallic cube to derive the volume of the cube. To get the volume of the cube, they used the formula, obtaining 16.73 cm3. To get the density of the material the mass of the cube is divided by its volume , hence getting 2.68. The percentage error is derived by getting the absolute value of the difference of the standard value and experimental value, then divide it by the standard value multiply by 100%, and they got 0.74 %.

Material Mass Diameter Radius Volume Density (g/cm3) Percentage Error
Glass g mm cm cm cm3 Experimental Standard %
5.69 16.39 1.639 0.8195 2.305 2.469 2.6 5.038
Table 2.2 Glass Sphere (Micrometer Caliper)

Table 2.2 shows the data obtained by using a micrometer caliper on a glass sphere. The micrometer caliper was used to get the dimensions of the sphere to get its volume and apparently its density. The radius was obtained by dividing the diameter (in cm) by 2.
The volume was derived by using the formula: V=4/3?r2, hence getting 2.305 cm3. The density is achieved by dividing the mass over volume. d=m/v getting an experimental density of 2.469 g/cm3. The percentage error is derived by getting the absolute value of the difference of the standard value and experimental value, then divide it by the standard value multiply by 100 %, and they got 5.038 %.

Both the Vernier Caliper and Micrometer Caliper was used in order to attain the results in finding the dimensions of the three objects which are the metallic washer, aluminum cube and the glass sphere. To be precise, the Vernier Caliper was used to measure the diameter of the inner and outer edge of the metallic washer due to its size which was perfect while both the glass sphere and aluminum cube’s dimension was measured by using the Micrometer Caliper. By using the given formulas for each object, we computed the volume of each of it and there was also a given standard density of the given materials as guide to see how precise our computations are.
Three of the objects were measured in 10 trials since ten is the required amount of trials and in each trial, it showed different measurements which means that our objects were faulty, and we have a random error. In measuring the metallic washer using the Vernier Caliper, both the inner and outer edge of it was unequal due to the buildup of rust around it. Some part of the aluminum cube’s edges was chipped off that may be caused by other factors such as age, how often it was used and etc. In finding the dimensions of the glass sphere, it also showed different measurements on each trial but the object was like still in pristine condition but, yet random errors still occur. The mass of the objects was not that accurate as well since the weighing scale was also faulty and not in balance. As observed throughout the experiment, it showed us that random error will always be there but can be minimized by doing more trials and by doing so, averaging it.
3. Three out of four percentage errors attained in this experiment were ?10%, but it is also evident that an error is still present.
Based on the observations during the experiment, the percentage error of >10% was obtained in measuring the metallic washer using vernier caliper. The main source of error, as the group conclude, came from the material itself. The metallic washer used was not anymore in quality condition; rust condition. Its circumference was also evident to not be in equal measure. The inner radius of the material was deformed already which could have been the cause why the measurements in the vernier caliper resulted to be inaccurate.

4. Percentage error
% error = x100

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