# Vernier Caliper Working Principle

The human ability to quantify things has a prominent role in our evolutionary process. In other words, the ability to map our observations and experiences into quantities is one of the most fundamental frameworks that describe the dynamics of the modern world. Historical data dating back to the agricultural revolution suggests that length is likely to be one of the earliest measurements that humans may have attempted. Humans have made several changes in length quantification with their transition from nomadic groupings to a well-civilized society. Today, several length measuring equipments such as meter scale, measuring tape, meter rod, etc. can be used conveniently to measure the length correctly up to a millimeter. To measure a length correctly up to a fraction of a millimeter, the division must be further subdivided, which is not easily practicable beyond a certain limit as it is difficult to clearly see the smaller divisions. This is where a vernier caliper becomes applicable. It is an amazing measurement tool that can measure length accurately up to 1/10th or 1/100th of a millimeter. For instance, if someone needs to measure the diameter of a wire or inside and outside dimensions of a hollow tube, it can easily be done with a vernier caliper rather than a ruler. Vernier caliper was invented by a French mathematician, Piere Vernier, in 1631. Although vernier calipers are mostly used to measure small dimensions, they were originally developed for angle-measuring instruments such as astronomical quadrants. Let’s try to understand how a vernier caliper works.

## Components of a Vernier Caliper

• Main Scale: The main scale consists of a steel metallic strip that runs along the body of the vernier caliper. It is measured either in centimeters and millimeters or inches, depending on the type of units it is built for. In SI units, the lowest measurement of the main scale is normally 1mm. When the two jaws are in contact with each other, the zero of the main scale and the zero of the Vernier scale should coincide. If both the zeros do not coincide, there will be a positive or negative zero error.
• Vernier Scale: A vernier scale slides on the strip. It can be fixed in any position by the retainer. On the Vernier scale, 0.9 cm is divided into ten equal parts. The Vernier scale is the defining component of the caliper, and this is what it is named after. The vernier caliper is a smaller scale attached to the main scale and can move along the main scale as the jaws are opened or closed. The vernier scale provides accuracy to the measurement of the main scale by further dividing the lowest reading of the main scale into increments. In a metric caliper, the vernier scale is divided into 50 increments each representing 0.02 mm.
• Outer Measuring Jaws: The outer jaws help measure the outer dimension of an object. They are present at the lower side of the vernier caliper, and therefore, these are also called lower jaws. One tooth of the jaw is firmly attached to the main scale and does not move, while the other one is attached to the movable vernier scale. They are designed to hold the object tightly, whose outer dimensions, e.g., length, diameter, or width, are to be measured.
• Inner Measuring Jaws: The inner jaws are used to measure the inner dimensions of an object. They are present at the upper side of the vernier caliper and are smaller in size than outer measuring jaws. Similar to the lower, or outer measuring jaws, they also have one immovable tooth attached to the main scale, while the movable one is attached to the vernier scale. The jaws are placed inside the space to be measured, and then these are opened till they touch the edges to take a reading.
• Retainer or Locking Screw: The lock screw is used to fix the position of the jaws once the object is positioned properly so that readings can be taken without spoiling the position.
• Thumb Screw: The thumbscrew is located at the bottom of the vernier scale. Its purpose is to provide a grip for the user to slide the jaws easily and adjust the position of the jaws and depth rod while maintaining a firm grip on the object.
• Depth Rod: The depth rod is another useful feature of the vernier caliper that can be used to measure the depth of certain vessels. It is a thin rod located at the end of the main scale. To measure with the depth rod, the edge of the main scale is placed on the top surface of the vessel (opening), and then the jaws are opened till the rod touches the bottom surface of the vessel, and the reading is taken as usual.

## Working Principle of Vernier Caliper

The vernier calipers work on the basic principle of alignment of measurement markings on the vernier scale and main scale. When a certain marking on the vernier scale aligns exactly to the marking on the main scale for a particular object whose dimensions are being measured, the value of the vernier scale reading is added to the main scale reading to obtain the decimal value of the reading in millimeters. Before we understand how this works out in practice, let’s understand the meaning of a few terms that are necessary magnitudes in vernier caliper measurement.

• Main Scale Divisions: The main scale divisions (MSD) refer to the divisions present between two successive marks on the main scale of a vernier caliper. Suppose that there are 10 divisions in between the 0 and 1 cm marking of the vernier scale, then the least measurement that we can take with just the main scale is 1 mm (1/10 cm).
• Vernier Scale Divisions: The vernier scale divisions (VSD) refer to the divisions present between two successive marks on the vernier scale. The vernier scale is constructed such that its divisions are spaced at a constant fraction of the fixed main scale. In other words, the 10 divisions present on the vernier scale do not exactly coincide with all the 10  main scale divisions.
• Least Count: In simple terms, the least count (LC) is the smallest value that can be measured by a given scale. For instance, the main scale mentioned above can provide the least measurement only up to 1 mm on its own. It is important to note that the vernier scale cannot give any measurement on its own as it is an auxiliary scale that provides precision to otherwise visually estimated measurement between two divisions of the main scale.
• Zero Error Count: Zero Error Count is defined as the condition where a measuring instrument registers a reading when there should not be any reading. In the case of the vernier caliper, the zero error occurs when the zero value on the main scale does not coincide with the zero value on the vernier scale. When the zero value of the vernier scale is slightly toward the number greater than zero on the main scale, it is known as positive zero error; otherwise, it’s a negative zero error. For example, if the zero on the sliding scale lines up with 1 mm on the fixed scale then the vernier caliper has a positive zero error of +1 mm.

## How to Take Measurement on a Vernier Caliper

For simplicity, let us consider that the vernier caliper does not have any zero error, i.e., the zero of the main scale coincides exactly with the zero of the vernier scale when nothing is placed between the outer measuring jaws. Let us suppose, the 10 divisions on the vernier scale correspond to only 9 divisions on the main scale (Figure A). Also, the least count of the main scale is 1 mm. To calculate the least count of the vernier scale, i.e., how much one division on the vernier scale values for, proceed as follow:

Figure A

10 VSD = 9 MSD or 9 mm

1 VSD = 0.9 mm

So, the least measurement one can take with the combination of these two scales is the difference between them.

Therefore, Least Count (LC) = 1 MSD – 1 VSD

= (1 – 0.9) mm = 0.1 mm

Next, place the object, whose length is to be determined, between the jaws of the caliper, and look for the best coinciding markings on both scales. Multiply the number indicated on the best coinciding line of the vernier scale (VSR) to the least count and add this value to the main scale reading (MSR). This will give the observed measurement.

Observed Measurement = MSR + LC × VSR

If there is a positive zero error in the vernier caliper, subtract it from the observed measurement to get the true measurement. On the contrary, if the zero error is negative, add it to the observed measurement.

True Measurement = MSR + LC × VSR ± Zero Error

## Precautions while Taking Measurements on a Vernier Caliper

• Parallax Error: The parallax error is one of the most common types of errors associated with analog measuring instruments. The expression “parallax” comes from the Greek word “parallaxis,” which means “alteration.” When an object is viewed from an angle, it causes a parallax error. This causes the item to appear to be in a slightly different location than it really is, which may cause us to misread a measuring scale. The observer should position his vision directly above the scale when taking the Main Scale reading and the Vernier Coincidence to eliminate this error.
• It’s important to make sure that all of the readings one takes during the measurement are all in the same unit system. For example, in the MKS system, length, weight, and time are measured using the units meter, kilogram, and second, respectively, whereas the CGS system uses the centimeter, gram, and second for the same. If any measurements are taken in another system, they should be converted to the appropriate units before using in any calculations.
• It is important to look for zero error before making any observations. This can be done by bringing the two jaws together and making sure that the zero reading on both scales coincides. If not, then the required correction should be incorporated in the calculations.
• To ensure the firm grip of jaws on the object, the locking screw should be used.