How to Develop a Cone - Cone Development

Updated on August 21, 2012

How to develop a cone or how to create a flat pattern of a cone can be achieved in a few easy geometrical steps. The geometrical method shown below does however have inaccuracy, so at the end of this hub I have included a mathematical formula to help produce an accurate conical development.

Figure 1
Figure 1

First of all you should draw your cone in elevation and plan as shown in Figure 1.

Divide your plan view up into equal segments. I have broken the plan view shown up into twelve (12) equal segments. (The accuracy of the development will increase with the number of segments that you break the plan view of the cone into.)

For twelve (12) equal divisions break the plan view up by drawing lines through the centre line at 30, 60 90 and 180 degrees.

We will use these divisions in a couple of steps but first we must lay out the initial overall cone development.

Figure 2
Figure 2

In Figure 2 I have shown the use of a drawing compass to get the true length of the cone side. You could use any computer aided drafting (CAD) method to obtain this length.

With Figure 3 as an example (shown below), take this true length of the cone side and scribe a full circle.

This is now your main development.

Figure 3
Figure 3

Now as in Figure 4 below, draw a horizontal line from the centre of this circle to intersect the outside diameter.

Figure 4
Figure 4
Figure 5
Figure 5

We now go back to our cone plan view and take one of the equal divisions we made earlier, as shown in Figure 5. You can do this using your compass or CAD program.

With this equal division on your compass and starting back at the horizontal line on your main development scribe the equal number of division. In my example I will scribe twelve (12) equal arcs along the circumference of the main development as shown in Figure 6.

Figure 6
Figure 6

Now finish this off by drawing a line from the last arc to the centre of the main development as shown in Figure 7.

Figure 7
Figure 7

An finally draw lines from every arc back to the center of the main development as shown in Figure 8. We can disregard the top half of the main development as the equal divisions form your full cone development.

Note: If this cone was to be cut out of steel these lines from the circumference to the center are actually called press lines.

You can check your work by printing out the development. Cut around the outline of the development and lightly folding each press line down. Join the two outside straight edges with sticky tape and there you have your cone! 

Figure 8
Figure 8

Finally I promised a mathematical formula to help produce a more accurate cone development. The inaccuracy occurs when you use a compass to break your cone base circle up into equal segments. You can check this buy measuring one of your arc lengths and multiplying this by the number of divisions. Compare this result with the formula for the circumference of a circle which equals Pi times by diameter. You will notice the calculated result is longer.

Now to help produce your accurate cone development use this formula:

Angle = (D1 x 360) / D2

Where:

  • Angle = the included angle between the outside lines of the main development
  • D1 = the diameter is of the base of the cone (see diagram below)
  • D2 = the diameter is of the developed cone, which you get from the elevation of your cone (see diagram below)

To use this formula, scribe your main development radius then draw your horizontal line. Then use the formula to calculate the included angle of the outside lines, grab a protractor (or use AutoCAD) and measure/draw this included angle out from the horizontal line.

The formula described in diagram...

Hope this helps, please drop me a comment if anything needs clarifying and I will certainly update this hub. Thanks!

Other drafting articles that you may like...

How to draw fast in AutoCAD, shows you how to improve your drafting productivity over time (by changing the way you enter commands) even with updates of AutoCAD where you get lost in the new user interface.

How to develop a Pyramid, follow similar easy steps on how to develop a flat pattern of a pyramid.

How to develop a truncated cone, follow similar steps on how to develop a truncated cone.

How to develop a Cylinder, follow easy steps to develop a flat pattern of a cylinder.

Questions & Answers

    Comments

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      • LeonJane profile imageAUTHOR

        LeonJane 

        2 months ago from Australia

        not as much as you

      • profile image

        Amrildo 

        6 months ago

        Who can give me an idea of developing a cone who intersections with a vertical plane

      • profile image

        Ishika 

        7 months ago

        Wriite in more briefly

      • profile image

        singh 

        9 months ago

        Very nice. I need eccentric cone sir.

      • profile image

        ibrahim 

        10 months ago

        am i going to use d normal circumference to divide what i need like if i need to let d cone be 8 on d circumference what should i do

      • profile image

        vinu 

        10 months ago

        Sir, how to marking eccentric cone

      • profile image

        Sathiaraj Ramakrishnan 

        11 months ago

        How to fabricate in eccentric reducer cone

      • profile image

        rohit agawane 

        11 months ago

        Sir how we devlope a cylinder with two different diameters?

        Shape like silencer which was used in conventional honda bikes

      • profile image

        D vamsi mohan 

        12 months ago

        if the sheet is above 25 mm thikness, how to calculate the development of cone. please sajest.

      • profile image

        pt 

        12 months ago

        Thank you, so helpful

      • profile image

        sanjay 

        23 months ago

        Dear SIr,

        I want to calculate the plate size of cone.Is any formula to make a cone development.Pls let me know.

      • profile image

        vishnu shelke 

        2 years ago

        sir i want to cone formula means i have square sheet & i want to made cone& cone size is big dia 580mm,small dia 250 mm & height is required 1000 mm so how i make cones from square sheet.

      • profile image

        menchie 

        2 years ago

        thanx for giving me an idea:))))

      • profile image

        mas 

        2 years ago

        Thank you, so helpful

      • profile image

        Prince Moralde 

        3 years ago

        hey man, thank you, this is great! but how can we close the cone or either the truncated cone if we are using plain or GI sheets to fabricate this components? think we should have additional measurements to do for the connection of each ends of the template? you got me? thanks, need your feed back..

      • profile image

        sambhaji 

        3 years ago

        Dear sir,

        How to make square to round development size? Any calculation, formula.

        Please give me information.

      • profile image

        ejaz aziz 

        3 years ago

        v get information quickly by yr way thanks

      • profile image

        Ishan 

        3 years ago

        I have to Get Cone from the Circular Plate - That Cone I have to place on Cylindrical Shell of diameter 1350mm. Now Can You tell me of What diameter of circular plate i should get so that after making it cone it comes to my actual size of 1350mm . ( Also how much be the Cut-off length, because only after Cut-off, It will form a Cone from Circular plate.)

      • profile image

        Nagavel.S 

        4 years ago

        Its very easy to develop the cone

      • profile image

        MILIND M. FROM MUMBAI 

        5 years ago

        Thanks sir.for your help

      • profile image

        Deven from india 

        5 years ago

        Thank u Leonjane

        I have used full of your developed cone development formula and drawing.

      • profile image

        mandar 

        5 years ago

        Thank you ..

      • profile image

        Tom Davis 

        5 years ago

        I use to have a software program that developed a flat cone layout nesting cone sections in the horizontal or vertical configurations. Input was cone inside diameters, cone height, thickness, end stock, distance to edge of plate and distance between cone plates. a new Windows is no longer compatible. Do you know of such software?

      • profile image

        anup 

        5 years ago

        how can i describe the geometrycal prove of volume of cone?

      • profile image

        Raja Kannan 

        5 years ago

        Very simple and to the dot. Excellent narration. On Cone frustum /cone development !!

      • profile image

        maneh 

        6 years ago

        how do we dovelope the partern of an oval

      • profile image

        Lynn 

        6 years ago

        When developing a cone whre the top and bottom is round do we use the same methode

      • profile image

        kishore kulkarni 

        6 years ago

        i want the development of 90degree miter i.e elbow please help me

      • profile image

        siva 

        6 years ago

        Dear SIr,

        I want to calculate the plate size of cone.Is any formula to make a cone development.Pls let me know.

      • LeonJane profile imageAUTHOR

        LeonJane 

        6 years ago from Australia

        Thanks PKR let me know how you go!

      • profile image

        manoj khaire 

        6 years ago

        Thanks.

      • profile image

        Masud Rana 

        6 years ago

        Man , i am grateful to you , in a word your cone development was the best and the easiest way to describe , you have given so simple method , which is just fabulous and your angle mathematical was simply the best to find the true development , my all development are giving me the right length since i've been using your method .

        thank you very much and all the best :)

      • profile image

        REXY PUTHUSSERY 

        6 years ago

        sir, how to make pattern for eccentric cone please send to mail for me, my id rexyputhussery@gmail.com

      • profile image

        nick 

        6 years ago

        how to development frustum cone

      • profile image

        mohamed mostafa 

        6 years ago

        thanks alooooooot

      • profile image

        ranjith 

        6 years ago

        Please explain me how to developed a cone.

        Top dia 12 inch,bottom dia 2" and slant height 10 inch.

        Waiting for your valuable reply

        regards/ranjith

      • profile image

        kisor 

        6 years ago

        thanks so much for good information

      • LeonJane profile imageAUTHOR

        LeonJane 

        6 years ago from Australia

        Thanks Santosh I have simplified the formula.

      • profile image

        prakash 

        6 years ago

        thanks

      • profile image

        dhirajredkr@yahoo.com 

        6 years ago

        dear sir,

        I am dheeraj redkar plz explain full detail of cone development strating to blank plate

        point (1) which of the diameter cutting layout

        (2) which formula equal part

        ex. 500dia & 60 height plz explain which cutting layout use plz help me this is my id dhirajredkar@yahoo.com

      • profile image

        vishal 

        6 years ago

        i like you.

      • profile image

        raja 

        7 years ago

        sir please mail me cone development excel sheet id kurubararaja@yahoo.in.

        it is very use full for lerners

      • LeonJane profile imageAUTHOR

        LeonJane 

        7 years ago from Australia

        Thanks guys, i'll try to answer your question Ajay in future hubs.

      • profile image

        Kumar 

        7 years ago

        Thank you for your needful help..........

      • profile image

        Ajay Patel 

        7 years ago

        Dear Sir,

        This is very useful, can u pl. explain how to do the development of Cone, one side flat i.e. one quadrant of smaller and bigger Dia is vertically in one line.

        Thanking you,

        Ajay Patel

      • LeonJane profile imageAUTHOR

        LeonJane 

        7 years ago from Australia

        Thanks Josh, glad this helped you! And cool that you made a spreadsheet from this.

      • profile image

        Josh 

        7 years ago

        Very nice postman. I went through everything, actually developed an Excel spreadsheet to spit out the numbers, and sure enough....It works! Tried it in autocad using calculated numbers and makes great templates. Printed a few different ones on paper, works perfectly! Thanks for the information again!

      • profile image

        Vicky 

        7 years ago

        Thank you So much Dear Leonjane, Very Wonderful and Elaborated Definition, These Explanation Like a Mother feeds Food to the small child,Thanks

      • LeonJane profile imageAUTHOR

        LeonJane 

        7 years ago from Australia

        Kannan, you need to tell me the height of the cone from the 230mm id to the 560mm id, then you can calculate the angle of the cone and the development with respect to the 5mm thickness of plate.

      • profile image

        kannan 

        7 years ago

        it was neat hub .and i have a doubt pls help me to find the angle for developing a cone in sheet of thickness is (say for ex:5 mm) and top id 230 mm and bottom id is 560mm and my mail id is kamal_august@yahoo.co.in .please explain me

      • profile image

        boobathi 

        7 years ago

        Thanks.

        Now am following same method.

        Its too big.Can you teach simple method., also MITRE BEND.

        many thanks once agin.

        -PK.

      • profile image

        Santosh 

        7 years ago

        imple is (D/d)*360!! why you add pi to both the sides?

      • LeonJane profile imageAUTHOR

        LeonJane 

        8 years ago from Australia

        Thanks for that techteddy, have updated with the correction of pi rather than Phi.

      • profile image

        techteddy 

        8 years ago

        Phi ? rather than pi?

      • LeonJane profile imageAUTHOR

        LeonJane 

        8 years ago from Australia

        Thanks cameron for your comment, I've tried to clarify the formula above with better descriptions, a diagram of the formula and a worked example. Hope this helps.

      • profile image

        cameron 

        8 years ago

        Hi there..

        i am having problems physically drawing the development of a cone. it keeps coming up short, like you have mentioned.. i have had a read through this information, and i see that the equation at the bottom keeps coming up with the same answer. 360. it doesn't matter what numbers you put in there. it still comes out with 360..

        the circumference of a circle is worked out by :

        pi x diameter = c

        so the equation ACTUALLY looks like this :

        ( PI x D ) X 360

        angle = -----------------

        PI x D

        so therefore you cancel out the PI x D on the top and bottom

        and you are left with angle = 360..

        can you please help me out here. i have asked many people about this and no one can give me an answer. my email is cambo@live.co.za if you would rather reach me there.

        thank you.

      • LeonJane profile imageAUTHOR

        LeonJane 

        8 years ago from Australia

        No worries mate, thanks Manoj Bala.

      • Waren E profile image

        Waren E 

        8 years ago from HAS LEFT THE BUILDING............

        Neat hub on drafting,I use AutoCad mostly,thanks for sharing LeonJane!

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