Fabrication Layout Development of Rectangular to Round by Geometrical & Numerical Method using Example

In this post we will learn how to layout of Rectangular to Round transition by using Geometrical or Graphical and Numerical Method using one practical Example.

Rectangular to round development is widely used in fabrication for converting shape of equipment from rectangular to round so that we can easily connect round connection for rectangular section. This layout development should be made by utilizing Triangular method of development.

We will discuss in Detail of fabrication layout of Rectangular to Round development in various aspect also with considering Maximum utilization Metal Plate so that we can minimize our scrap, hence our profitability can be increase by using this approach of the fabrication.

We are consistently saying in each part that always use mean Dimensions while making layout Development so that our final size should be come in within tolerance of fabrication and it will not expand while rolling and bending of this layout plate. So we are assuming that you had taken your dimension precisely so that you will get perfect solution.

Geometrical or Graphical Method for Layout Development of Rectangular to Round Transition:

Steps for Geometrical or Graphical Layout Development:

1. Draw Top View and elevation view of rectangular to round transition.

2. Divide the Circle in to equal parts as shown in figure

3. Connects divided point from point B to point 1’, 2’, 3’, 4’ as shown in figure.

4. Taking Height reference mark the point A-3’,A-2’,A-4’,A-1’ etc as shown in figure to from the triangle and note hypotenuse of the triangle.

5. Marks the points using the distance measure from Step no 4. And arc distance for each divided part.

6. By connecting vortex A,B,C,D,S and points 1’,2’,3’,4’ etc shown in figure.

7. Mark out Cutting profile of transition piece and cut out profile and use it for further processing.

By using this process of geometrical layout we will get all dimension and using this we can layout required shape. This method is most useful while lay-outing on AutoCad Tool.

Numerical method for layout Development of Rectangular to Round Transition Shape:

W = Width of rectangular section;
L = Length of Rectangular section;
D = Diameter of Circular section;
H = height of Section;
N = No of part to Divide Circle;


α= 360 / N ;

Arc Distance = pi*D/N ; 1’-2’=2’-3’=3’-4’ = Arc Distance ;

1’-S = √{ (W/2-R)2 + H2};

1’-D = √{ (L/2 – R*sin(0))2 +(W/2 –R*cos(0))2+H2) } ;

2’-D = √{ (L/2 – R*sin(𝛼))2 +(W/2 –R*cos(α))2+H2) } ;

3’-D = √{ (L/2 – R*sin(2𝛼))2 +(W/2 –R*cos(2α))2+H2) } ;

4’-D = √{ (L/2 – R*sin(3𝛼))2 +(W/2 –R*cos(4α))2+H2) } ;

1’-D=4’-C ; 2’-D = 3’- C ; 3’-D=2’-C ; 4’-D=1’-C;

Similarly all corresponding dimension are calculate used in layouts. And using all this calculated Values we can layout rectangular to Round transition Piece.

From above Method and above calculated Values We can layout Rectangular to Round Shape by easy and simple way this method is useful for learning Basics of layout and know the mathematical and graphical concept behind this development.

Example for Layout development of Rectangular to Round Transition Shape Using Numerical Method:

Draw Transition layout for the Rectangular to round having rectangular Size as 500 mm x 600 mm and Height 1000 mm and round at top having Diameter 400 mm; by dividing circle in 12 parts.


N=12 ;

L = 500 ;

W = 600 ;

H = 1000 ;

r = d/2 = 400/2= 200 mm;

α= 360 / N ; α= 360 / 12 = 30 degree;

Arc Distance = pi*400/*12 = 104.71 mm ;

1’-D = √{ (500/2 – 200*sin(0))2 +(600/2 –200*cos(0))2+10002) } = 1035.6 mm ;

2’-D = √{ (500/2 – 200*sin(30))2 +(600/2 –200*cos(30))2+10002) } = 1019.1 mm;

3’-D = √{ (500/2 – 200*sin(2*30))2 +(600/2 –200*cos(2*30))2+10002) } = 1022.6 mm;

4’-D = √{ (500/2 – 200*sin(3*30))2 +(600/2 –200*cos(3*30))2+10002) } = 1045.22 mm;

1’-S = √{(600/2 – 200)2 + (1000)2} = 1004.9 mm = 1005 mm;

From using all the above value we can marking the layout as shown in above layout figure of an example. Cutting out our profile from the plate and by pressing on the marking points we get desired shape of rectangular to round section.

please share this post and application for those who are in field of fabrication and also give your suggestion making new tools ease of fabrication methods.

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