Measurement Tools

Vernier Caliper, Definition, Least Count Formula, Types, Parts, And Uses

We explain the Vernier caliper least count formula with its definition, parts, types, uses, and measurement errors with the caliper and complete information to better understand for students, teachers, and engineers…Let’s Read Physics. vernier caliper least count formula 

What is a Vernier caliper and what is it for? vernier caliper least count formula 

A vernier caliper also called a caliper is a precision measuring instrument. The vernier caliper includes two sets of calipers that are used to measure exteriors and interiors. In addition, thanks to the depth probe, the vernier caliper can also be used to measure the bottom of a blind hole, grooves, cavities, etc.

Analog caliper with a scale graduated in inches and in millimeters of 0.02 mm appreciation (0.001 inches)

Why is it called a vernier caliper?

Before the invention of the meter as a unit of measurement, feet and spans were used to take measurements. The foot does not measure the same everywhere: an English foot does not measure the same as a Castile’s foot, for example.

And obviously, the feet of all the people who live in a place do not measure the same either. The foot that was used as a reference was the foot of the king of the place, that is, the royal foot.

The vernier caliper used in engineering and architecture to measure lengths measured to 30 cm is called a vernier caliper in reference to this ancient measurement. Other names for this measuring instrument are caliper and slide caliper.

What is a Vernier caliper for?

With this instrument, you can measure elements and mechanical parts or other objects with great precision: much higher than that achieved with a tape measure or ruler.

The appreciation of a caliper, that is, the smallest measure that the instrument is capable of measuring or appreciating, ranges from 0.1 mm to 0.02 mm, approximately.

In comparison, a metal ruler or a tape measure has an appreciation of 1 mm or 0.5 mm. In the latter case, in addition, appreciating the half-millimeters is very complicated, since the graduated scale lines are excessively close together and blend into one another.

What kinds of objects can be measured? Anything that can lodge between its jaws. It is important that the object is rigid and not compressible since the measurement would be altered.

Taking the measurement of the outside diameter of a metric threaded screw is one of the most common uses of the caliper. It is also possible to measure the inside of a threaded nut or cavity, rods and studs, the depth of a cavity, for example, the bottom of a cylinder of an internal combustion engine, etc. vernier caliper least count formula 

In all the examples in the previous paragraph, you can approximate your measurement using the meter or a graduated ruler. However, these measurement instruments lack the appreciation necessary for the measurement to be really useful. For example, when carving a thread or looking for a screw in the hardware store, even an error of 2 or 3 tenths of an mm is not admissible and the appreciation of the meter or the rule is still much lower than this tolerance.

On the other hand, the calibrator is not used to measure those elements that require even greater precision of measurement. That is, the vernier caliper is no longer adequate when its appreciation is not small enough. In this case, the next measuring instrument to consider would be the micrometer, whose appreciation is equal to or greater than 10 microns (1 micron = µ = 1/1000 mm). vernier caliper least count formula 

In summary: the caliper type is used to measure parts more precisely than the meter or the ruler and with less precision than the micrometer. In practice, some of the most common uses of the vernier caliper are to take measurements of hardware items: screws, nails, nuts, wire, rivets, bits, etc. It is also very useful in automotive mechanics, industrial maintenance, plumbing, electricity, and especially in machining: turning, milling, drilling, etc. vernier caliper least count formula 


What is the least count of a Vernier caliper?

The least count that the name suggests is the best measurement you can take with the help of Vernier calipers. It is measured by dividing the smallest count on the major scale by the total number of divisions on the Vernier scale.
The minor count (LC) of the Vernier scale is given as least count = least count of the main scale / Number of divisions on the Vernier scale. Less counting of the main scale: The main scale is calibrated in millimeters.
To get the lowest count on the major scale, count the number of divisions on the major scale in one cm. Divide 1 cm into that many divisions; The value obtained is the lowest count on the main scale in cm.
For example, if there are 10 divisions in a centimeter of the main scale, its smallest count is = 1/10 = 0.1 cm. A number of divisions on the Vernier scale: In most Vernier calipers, the Vernier scale has 10 divisions. Count the number of divisions on the Vernier scale. Use a magnifying glass if necessary.
For most vernier calipers, the major scale least counts = 0.01 cm, and the number of divisions on the Vernier scale = 10 divisions.
So Vernier Least Count Gauges = 0.01 / 10 cm Vernier Count Bottom Calculus = 0.001 cm since the least count of the vernier caliper is 0.001 cm, it can be said that by measuring with the help of this vernier caliper, you can get an accuracy of 0.001 cm.

Vernier Caliper Least Count Formula

  • The smallest reading that can be accurately measured with a vernier is called least count (LC), Least count is also known as the vernier constant. It is the difference between one main scale division which is 1mm and 1 vernier division which is 0.9.

L.C = 1 mm – 0.9 mm = 0.1 mm
There is another way to find the least count which is given as:

Vernier Caliper Least count Formula

How to read a caliper with a vernier caliper scale? vernier caliper least count formula 

We will use this vernier caliper as an example of 0.1 mm (1/10 mm = ten divisions).

Reading the measurement on a caliper gaugeHow to read the vernier caliper caliper

In the auxiliary vernier scale we can see that:

  • The zero of the vernier exceeds the mark on the main scale of 15 mm
  • The zero of the vernier does not reach the 16 mm mark

Therefore, the measurement will be between 15 and 16 mm, it can also be observed that:

  • The mark of the vernier that best fits some mark of the rule is that of 8
  • Both the 7 and 9 marks are slightly off

Then: if we add the offset of the vernier (0.8 mm) to the measurement of the main scale (15 mm), we obtain that the measurement is 15.8 mm.

And indeed: you can see with the naked eye how the vernier zero mark is much closer to 16 mm than to 15 mm. This additional verification ensures that the interpretation of the measurement is correct.

How to keep a vernier caliper

For the correct conservation of the caliper, you should clean the gauge when you have finished using it, especially in the case that it has been stained with grease, coolant, or other cutting/coolant liquids.

In addition, periodically you should apply a thin sheet of oil or petroleum jelly on its guides and dry the excess with an absorbent paper. And, of course, keep it in its case.

caliper sleeveStore the caliper gauge in its case when you are done using it

Regarding the use, you must avoid that the caliber suffers blows or that it falls to the ground. Also, you should never measure with the ends of the outer tips, but with their flat surface. You should also not use the inside tips as a compass.

And another thing you should never do is measure the part with the lathe running. Doing such a thing will quickly wear down the gauge’s reference surface and also expose you to an accident.

Measurement errors with the vernier caliper

When measuring with a caliper, the precision will be higher or lower, depending on several factors. Measurement errors can be mainly due to two causes:

  • Human error: it can be an error in the interpretation of the measurement (reading error) or a measurement error (misuse of the instrument).
  • Gauge error

The gauge may have different measurement errors. For example, wear on the guides can tilt the movable jaw, distorting the measurement. Another possibility is that the reference faces are already worn or lacking in flatness, parallelism defects, and so on.

The brake screw can also alter the measurement if the friction against the screed accidentally displaces the movable jaw.

As for human errors, the most common are the following. Applying excessive force to the measurement can deform the gauge ruler and alter the measurement.

Not laying the gauge perfectly flat is another common mistake, as is using the tips of the outdoor tweezers, rather than their flat part. In addition, applying a force defect can also alter the measurement, as can the misuse of the adjusting screw.

The above are errors related to how to measure. Another type of human error is misreading the measurement indicated by the vernier scale.

Lighting conditions, the surface condition of the gauge ruler and its finish (glossy or matte), as well as the graduation of the operator’s sight are three factors that influence the interpretation of the gauge reading.

For example, for the same measurement, two people may consider that the vernier mark that best matches the main scale is not the same.

The parallax effect is one of the factors that can introduce a measurement error. This consists of a poor appreciation of the position of the auxiliary scale over the main one and occurs when the gauge is not viewed perpendicularly.

The parallax effect also occurs in analog clocks. If we look at the minute hand not perpendicular to the dial, but at an angle, it will give us the impression that the hand points to another number. And that’s why you have to face the front to read a vernier caliper.

It is also important to keep the Abbe principle in mind. This principle says that only that whose axis coincides in a linear way with the instrument used for the measurement can be accurately measured. vernier caliper least count formula 

That is, in the caliper the axis of the instrument is that of the main scale, however, the measurement is made with the calipers, which do not coincide with the axis but are separated from it.

This means that if there is play in the slide with respect to the fixed rule, a measurement error will occur. In fact, this is one of the shortcomings of some cheap calipers.

Another error related to the Abbe principle is the application of excessive force by the user who measures with the caliper.

In this case, it may happen that as a result of the pressure exerted, the rule bends and alters the measurement (let’s think of a carpenter sergeant: when tightening the screw, the rectangular section slide locks on the plate and this is how the pressure is exerted ). vernier caliper least count formula 

The Abbe principle does not distort, however, the measurement with the horseshoe micrometer, since in this case the axis of the piece and the instrument do coincide, that is, they are parallel.

It is also important that the piece being measured and the caliper are at the same temperature, otherwise, the measurement will be altered due to the different degrees of expansion of the materials.

In conclusion, although the reading and interpretation of the measurement are correct, and without a doubt, it will be in a digital caliper, the measurement may not be perfect due to the state of wear of the caliper, and lack of parallelism, etc.

How to check that a caliper gauge measures correctly

There are two quick checks you can do to check the status of your gauge.

First, when it is closed there should be no passage of light between the fixed and mobile openings. Second, to check the measurement you can use reference gauges or calipers.

These parts are machined with high precision, allowing you to find out if the gauge is measuring well or not. You can also compare the measurement with a micrometer or with another gauge.

Principle of operation of a gauge

Why does the caliper work? We have already seen that the principle of operation of this apparatus is based on the Vernier scale, but what does this scale consist of?

The vernier or vernier scale is printed or embossed on the gauge slide. On this scale, each of the divisions is less than one millimeter. Depending on the appreciation of the gauge, they will be 0.95 mm (if the gauge appreciates 0.05 mm) or 0.98 mm (if it is 0.02 mm).

This implies that if we open the jaw of the instrument at 0.05 mm, the second line of the vernier scale will coincide with the second line of the main scale. If we open it 0.10 mm, the third will do it, and so on.

This accumulation of fractions of 0.05 mm is what allows us to know how much the decimal part of the piece measures. To make it easier to read, the vernier caliper manufacturers add a couple of details:

  • Print the vernier scale in fractions of a millimeter
  • Proportionally increase the size of the vernier so that the scale divisions are larger (without affecting the measurement)

Advantages and disadvantages of the caliper versus the micrometer

The arc micrometer is a more precise measuring instrument than a caliper, however, the caliper has three advantages:

  • Vernier calipers are cheaper than micrometers
  • The caliper can cover a greater range of measurements while the micrometer is very limited (several sets of instruments are required to be able to measure the same range of parts as with the caliper)
  • The universal gauge can measure outside, inside and grooves, while the conventional micrometer is only for outside

Parts of a Vernier vernier caliper least count formula 

Because there are different types of Vernier we can find some variations in terms of its parts, since some may have faces or digital meters.

These differences are minimal and do not affect the main structure. Broadly speaking, this instrument is made up of two graduated rulers, a pair of jaws, a stem, and a safety device.

vernier parts

As for the material, they are generally made of hardened stainless steel (Stainless hardened in English), because it has a great resistance to wear and deformation.

  • Jaws
  • Depth probe
  • Vernier
  • Graduated scales
  • Sure
  • Driving

Jaws vernier caliper least count formula 

The jaws are one of the most important parts since they are used to reference how long or wide an object is, that is, when you want to measure an object, it is placed inside the jaws, and with the help of the scales, you know how much actually measured.

Vernier jaws

Stem or depth probe

This instrument has a small shank that protrudes when the movable part is slid, this protrusion is used to measure depth surfaces such as holes.

Vernier stem

Vernier vernier caliper least count formula 

The Vernier is an auxiliary rule that allows us to have greater precision since it allows measurements of up to two decimal points, that is, 0.01 or 0.05 depending on the type of Vernier.

Nonio vernier

Scales or graduated rulers

It is located in the fixed part of the Vernier and like any other rule, it has the same structure since on one side we find the measurements in inches and on the other in millimeters.



It is a screw that is responsible for fixing the mobile part of the Vernier. This can be of great help since it helps us to save the measurements we take in places that are difficult to access to the eye or to be able to move without missing any detail.



The main function of this part is to help the user to operate the tool with greater freedom, depending on the Vernier there may be slight variations such as a rotating wheel, a fixed semicircle or an impeller with safety included where you have to press to be able to slide.

Vernier impeller

Types of Vernier

This tool in most versions has the main structure, which is a Vernier, a graduated scale, and the jaws, but it is those small variations that make a Vernier change type.

  • Universal
  • Button
  • Cover
  • Swing arm
  • Double
  • For lefties
  • Long Vernier
  • Deep
  • Type CM and M
  • With uneven tips
  • Digital

Standard Universal Vernier types of vernier caliper

It is the simplest and most common that we can find, it is used in practically any situation, that is, it is for general use.

types of vernier caliper: Universal vernier

Button Vernier types of vernier caliper

This type makes a modification in the way of fixing the moving part since it eliminates the screw and in turn, incorporates the fixing system together with the impeller. To be able to slide the impeller has to be pressed and to fix it is simply released.

types of vernier caliper: Button Vernier

Dial Vernier types of vernier caliper

In this version, the Vernier is completely removed and a dial that resembles an old clock is incorporated. This modification makes it possible to speed up the reading process since it has a needle that indicates the measurement. One of its great disadvantages is that we can only have a single system, either in inches or centimeters.

types of vernier caliper: Dial Vernier

Vernier with narrow tips

It has practically the same uses as a universal one, only with the only difference that it has outdoor jaws in the form of blades to access narrow places.

types of vernier caliper: Vernier blades

Vernier for gears vernier caliper least count formula 

This model is very different from the others because it has a square shape, thanks to the fact that it has two different rulers, it can be used to measure the thickness and height of the gear teeth.

types of vernier caliper: Vernier gears

Vernier for grooves vernier caliper least count formula 

It has long and large jaws with protrusions that go outwards, they are mainly used to measure interiors in grooves with great depths.

types of vernier caliper: Vernier grooves

Left handed Vernier

It is practically an inverted Vernier to facilitate use by people who use their left hand as their main hand.

v: Left handed Vernier

Long Vernier vernier caliper least count formula 

As its name indicates, it is an instrument that allows measurements of greater length, within this type we can find 30, 50, and even up to 100 cm long.

types of vernier caliper: Long Vernier

Depth Vernier vernier caliper least count formula 

The operation of this Vernier is slightly different, since the graduated ruler works as a stem to measure depths, it is practically the tool that undergoes the most modifications because the depth probe is removed and the jaws are exchanged for a mobile base that It serves as a support to make the measurement.

types of vernier caliper: Depth Vernier

Vernier type M and type CM

The type M is basically the one we all know with two pairs of chamfered jaws, one for exteriors or others for interiors.

Universal vernier

The CM type is a bit more special since it only has one pair of jaws, but it is designed in such a way that it can be measured inside and outside.

Vernier CM

Vernier with uneven tips

It has a fixing screw in one of the jaws that are used to move it, this function is mainly used for the measurement of pieces with different levels.

Vernier uneven tips

Digital Vernier vernier caliper least count formula 

It is the most modern instrument and easiest to use since it is enough to put the piece in the jaws and the measurements taken are automatically reflected on a small screen. Because this model is easy to lose its calibration, One of the great disadvantages of this model is that it loses its calibration and you have to recalibrate with the zero position button.

Digital VernierHow is the Vernier used?

To measure an object, it must be placed in between the jaws and then closed until the piece is slightly tightened. The next step that must be done is to verify if the 0 of the Vernier scale coincides with a number, if it does not exactly match that data is taken and it is searched for which number exactly matches any line of the rule, once it is found they are added the data as explained by the video. types of vernier caliper

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