Types of Taper in Mechanical & How to Calculate Taper Ratio

Hello friends, Today in this topic we are going to discuss what is a taper and how many types of taper are there? 

At the end of this topic we will also know that how to calculate a taper ratio and taper angle?

Taper means short or thin towards one end. It also means a gradual decrease in the width or thickness of a long object. 

A taper is also defined as the uniform change of the diameter of a workpiece on its axis.

Taper provides a method to quickly and precisely align machine parts.

Tools such as twist drill bits, lathe centers, and reamers are easier to hold because of the taper.

For making these types of tools uses different types of cutting tool materials as per requirement, because every material has its own mechanical properties.

These tools are mostly used in drilling machine and lathe machine.

Tapers are also used in many more application like used in bearing as a taper roller bearing.

The taper is made into a lathe machine using the taper turning method.

Types of taper in mechanical can be categorised according to their class, sizes and uses which we will be know further in detail.

So let’s get start to know,

What is Taper?

The continuous or uniform increasing or decreasing in diameter of a cylindrical work piece is called a taper.

Taper is also called Taper conicity. 

Its works on the principle of trigonometry. 

Clearly see in figure taper with dimension


D = Larger diameter of the taper

d = Smaller diameter of the taper

L = Length of the taper

Types of taper

Before knowing the types of taper, we need to know about the methods of Specified taper so that we can understand the types of taper very well.

Methods of Specified Taper

Taper can be specified into following ways
  • Taper in Degree
  • Taper in Inch
  • Taper in Foot
  • Taper in Metric
  • Standard Taper Number
  • Taper by Symbol

Taper in Degree

In this method the taper is expressed in degree.

Like 60°, 3°,30°, etc.

Taper in Inch

In inch systems tapers are expressed in a taper per inch.

Like 0.0208".

Taper in Foot

In foot systems tapers are expressed in a taper per foot.

Like 5/8'.

Taper in Metric

Metric tapers are represented in the ratio of 1 mm per unit length.

For example in a 1: 20 taper the diameter will change 1 mm per 20 mm length.

Standard Taper Number

According to standard taper numbers taper can be specified as their standard number

For Example, Morse taper specified in MT 0 to MT 7.

Taper by Symbol

In this method taper is expressed by a symbol for example taper is denoted by K.

Types of Taper

Taper can be classified into three categories
  • According to Class
  • According to Use
  • According to Size

According to Class

According to class there are two types of taper
  1. Self Holding Taper
  2. Quic Releasing Taper

Self Holding Taper

In this type of taper, the taper angle is kept less than 3°.

In that taper does not require any other locking device to hold the assembled component.

It is also called slow taper.

Quick Releasing Taper

In this type of taper, taper angle is kept more than 18 °. 

Due to the high Taper Angle, they require a locking device to clamp. 

They have Taper ratio 7:24.

According to Use

According to uses are two types of taper
  1. Internal Taper
  2. External Taper

Internal Taper

The taper given on the inner surface of a cylindrical job or a workpiece is called an internal taper.

External Taper

The taper given on the outer surface of a cylindrical job or a workpiece is called an external taper.

According to Size

According to size there are following types of taper
  1. Morse Taper
  2. Metric Taper
  3. Jarno Taper
  4. Brown and Sharpe Taper
  5. Standard Pin Taper
  6. Jacobs Taper

Morse Taper

Morse Taper is a self holding type taper and it is available in a 8 size from MT 0 to MT 7.

The taper ratio of morse taper is found 1:10 and its included angle available in 3° or 5/8 inch/foot.

Morse taper mostly used in lathe machine  ds nose spindle, drill shank, arbor, etc.

Metric Taper

Metric Taper is a self holding and quick releasing type taper on which 7 sizes available in self holding and 4 sizes available in quick releasing.

Where, MT O to MT 6 sizes in self holding type and 30°,40°,45°,50° are quick releasing type.

Metric taper mostly used in lathe machine's nos spindle surfaces.

Jarno Taper

Jarno taper is an also self holding type of taper and available in 20 sizes from 01 to 20.

Taper ratio of jarno taper is 1:20 and its included angle available in 0.6 inch/foot.

It is mostly used in die marking machine.

Brown and Sharpe Taper

Brown and Sharpe taper is a self holding and quick releasing type  taper on which 18 sizes available in self holding and 09 sizes available in quick releasing.

BS 1 to BS 18 sizes in self holding type and 4 to 12 are quick releasing type.

Taper ratio of jarno taper is 1:20 and its included angle of BS 10 is 0.5161 inch/foot.

And all other types tapers including angle are 1/2 inch/foot.

Brown and Sharpe taper is used in spindle and arbor of milling machine.

Standard Pin Taper

Standard pin taper is a self holding type taper.

Taper ratio of standard pin taper is 1:50 in metric and 1:48 in British. 

Its included angle is 1/4 inch/foot.

Standard pin taper used in clamp devices, tapered pin, etc.

Jacobs Taper

Jacobs taper mostly used in drill press chuck, arbor, etc.

How to Calculate a Taper Ratio and Taper Angle?

For calculating taper ratio there are following formula applied


Taper Ratio

K = D-d/L



K = Taper Ratio

D = Larger diameter of the taper

d = Smaller diameter of the taper

L = Length of the taper


Taper Angle

Tan θ = D-d/2L

θ = tan-1 (D-d/2L)



D = Larger diameter of the taper

d = Smaller diameter of the taper

L = Length of the taper


For Example,

If the large diameter and small diameter of the taper is 40 mm and 30 mm respectively.

And total length of the taper is 20 mm. Then calculate taper ratio and taper angle?

types of taper in mechanical


Taper Ratio = (40 – 30)/20

                   =  10/20

                   =  1/2


That means taper ratio is 1:2


Taper Angle


tan θ = (40-30)/(2*20)


     θ = tan-1(10/40)

         = 14.03°



So friends here I discussed types of taper according to their class, size and uses in briefly. And also known how to calculate taper ratio and taper angle?

I hope you clearly understand all aspects related to taper.


Thank You.

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