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Taper Calculator

taper calculator

Table of Content


Taper calculator helps you determine the right measurements for tapering a workpiece and also provides you with the angle of the taper. It helps in figuring out the proper way to shape one end of a workpiece to make it look like a frustum cone. This way, you can easily and accurately determine the dimensions needed for your machining projects.

What does the taper mean?

In machining, tapering refers to the process of gradually reducing the dimensions of a workpiece from one end with respect to its length.

There are two ends to a taper, and they are different in size. It is similar to a conical frustum. The larger end of the shape is the major section, and we call its width the major diameter \(D_l)\. On the flip side, the smaller end is the minor section and its width is known as minor diameter \(D_s)\.

Tapers are commonly used in drill chucks, arbors, nails, bolts, and screws.


Imagine shaping an object like a piece of metal or wood, so that it goes from wide to narrow in a smooth way like a frustum or truncated cone. This process is called tapering, and it’s commonly done in manufacturing to create different shapes or designs.

How to use this taper calculator?

  • First, enter the values of the major diameter, minor diameter, and length of the taper into the required field
  • Tap Calculate button
  • The calculator will show you the results of taper calculations, including the taper angle as well.

How to calculate taper?

To calculate, follow these steps:

  1. Measure how much bigger the wide end (major diameter) is compared to the narrow end (minor diameter).
  2. Divide that difference by the length of the tapered part.
  3. To get the taper for the whole foot, multiply the taper per inch by 12.

To calculate the measurements of the taper, we need the taper formula which we have given below.

Taper Formula:

$$ T = \frac{{D_l - D_s}}{{L}} $$


  • T is the taper
  • \(D_l\) is the major diameter
  • \(D_s\) is the minor diameter, and
  • L is the length of the taper


Let's say \(D_l\) =8 inches, \(D_s\) =4 inches, and L=12 inches:

Add these values into the taper equation:

\(T = \frac{{8 - 4}}{{12}}\)

Now, start calculating:

\(T = \frac{{4}}{{12}}\)

Finally, divide this to get the results:

\(T = 0.3333 \, \text{inches}\)

So, the taper (T) in this example is approximately 0.3333.

To calculate the angle of the taper you need to follow the taper angle formula, which is as follows:

\(TA = \arctan(0.5 \times \text{Taper})\)

Now, put the values into the equation:

\(TA = \arctan(0.5 \times 0.3333)\)

\(TA = \arctan(0.16665)\)

\(TA \approx 9.516^\circ\)

So, the angle (TA) for the given taper value is approximately \(9.516^\circ\)

Types of taper:

There are several types of tapers in machining and manufacturing, each serves a specific purpose. Here are some common types of tapers:

  • Morse Taper: Used in machine tool spindles and tool shanks for secure and self-releasing connections.
  • Jacobs Taper: Commonly found in drill chucks to provide a secure grip on drill bits.
  • Jarno Taper: Used in machine tools especially in Europe, for securing cutting tools.
  • Brown & Sharpe Taper: Utilized in milling machines and machining centers for tool holding.
  • Standard Taper: Often employed in taper turning on lathes for creating conical shapes.
  • Pipe Taper: Common in plumbing applications for joining pipes, such as NPT (National Pipe Taper) threads.
  • Center Taper: Used in lathe tailstocks and spindles for centering workpieces.
  • Tapered Roller Bearing: Utilized in wheel bearings and other applications for radial and axial load support.

These tapers come in different designs and are used for various things like shaping, securing, or connecting parts in many types of manufacturing.

How many degrees is a taper per foot?

There are some factors that influence how the specific part is threaded. Typically, a taper of 3 inches per foot equals 7.125 degrees. Likewise, for a taper of 1.5 inches per foot, it equals 3.576 degrees.

Alan Walker

Studies mathematics sciences, and Technology. Tech geek and a content writer. Wikipedia addict who wants to know everything. Loves traveling, nature, reading. Math and Technology have done their part, and now it's the time for us to get benefits.

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