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 article I have included a mathematical formula to help produce an accurate conical development.
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.
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.
Now as in Figure 4 below, draw a horizontal line from the centre of this circle to intersect the outside diameter.
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.
Now finish this off by drawing a line from the last arc to the centre of the main development as shown in 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!
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
- 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 article. 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.
Rodney Harris on July 30, 2020:
dayanand on January 03, 2020:
How to develop toriconical head from sheet metal
LeonJane (author) from Australia on May 02, 2018:
not as much as you
Amrildo on January 12, 2018:
Who can give me an idea of developing a cone who intersections with a vertical plane
Ishika on December 05, 2017:
Wriite in more briefly
singh on October 02, 2017:
Very nice. I need eccentric cone sir.
ibrahim on September 14, 2017:
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
vinu on September 05, 2017:
Sir, how to marking eccentric cone
Sathiaraj Ramakrishnan on August 10, 2017:
How to fabricate in eccentric reducer cone
rohit agawane on August 03, 2017:
Sir how we devlope a cylinder with two different diameters?
Shape like silencer which was used in conventional honda bikes
D vamsi mohan on July 14, 2017:
if the sheet is above 25 mm thikness, how to calculate the development of cone. please sajest.
pt on July 11, 2017:
Thank you, so helpful
sanjay on August 15, 2016:
I want to calculate the plate size of cone.Is any formula to make a cone development.Pls let me know.
vishnu shelke on November 25, 2015:
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.
menchie on November 10, 2015:
thanx for giving me an idea:))))
mas on October 05, 2015:
Thank you, so helpful
Prince Moralde on July 15, 2015:
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..
sambhaji on February 25, 2015:
How to make square to round development size? Any calculation, formula.
Please give me information.
ejaz aziz on November 03, 2014:
v get information quickly by yr way thanks
Ishan on September 15, 2014:
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.)
Nagavel.S on January 30, 2014:
Its very easy to develop the cone
MILIND M. FROM MUMBAI on July 07, 2013:
Thanks sir.for your help
Deven from india on June 15, 2013:
Thank u Leonjane
I have used full of your developed cone development formula and drawing.
mandar on January 16, 2013:
Thank you ..
Tom Davis on October 08, 2012:
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?
anup on September 08, 2012:
how can i describe the geometrycal prove of volume of cone?
Raja Kannan on August 15, 2012:
Very simple and to the dot. Excellent narration. On Cone frustum /cone development !!
maneh on June 22, 2012:
how do we dovelope the partern of an oval
Lynn on June 08, 2012:
When developing a cone whre the top and bottom is round do we use the same methode
kishore kulkarni on May 31, 2012:
i want the development of 90degree miter i.e elbow please help me
siva on May 12, 2012:
I want to calculate the plate size of cone.Is any formula to make a cone development.Pls let me know.
LeonJane (author) from Australia on April 29, 2012:
Thanks PKR let me know how you go!
manoj khaire on March 12, 2012:
Masud Rana on February 28, 2012:
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 :)
REXY PUTHUSSERY on February 28, 2012:
sir, how to make pattern for eccentric cone please send to mail for me, my id email@example.com
nick on February 11, 2012:
how to development frustum cone
mohamed mostafa on January 23, 2012:
ranjith on January 03, 2012:
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
kisor on October 26, 2011:
thanks so much for good information
LeonJane (author) from Australia on October 10, 2011:
Thanks Santosh I have simplified the formula.
prakash on September 20, 2011:
firstname.lastname@example.org on August 25, 2011:
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 email@example.com
vishal on July 27, 2011:
i like you.
raja on June 22, 2011:
sir please mail me cone development excel sheet id firstname.lastname@example.org.
it is very use full for lerners
LeonJane (author) from Australia on June 16, 2011:
Thanks guys, i'll try to answer your question Ajay in future hubs.
Kumar on June 06, 2011:
Thank you for your needful help..........
Ajay Patel on March 27, 2011:
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.
LeonJane (author) from Australia on March 01, 2011:
Thanks Josh, glad this helped you! And cool that you made a spreadsheet from this.
Josh on February 13, 2011:
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!
Vicky on December 03, 2010:
Thank you So much Dear Leonjane, Very Wonderful and Elaborated Definition, These Explanation Like a Mother feeds Food to the small child,Thanks
LeonJane (author) from Australia on October 10, 2010:
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.
kannan on October 10, 2010:
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 email@example.com .please explain me
boobathi on September 01, 2010:
Now am following same method.
Its too big.Can you teach simple method., also MITRE BEND.
many thanks once agin.
Santosh on August 28, 2010:
imple is (D/d)*360!! why you add pi to both the sides?
LeonJane (author) from Australia on April 17, 2010:
Thanks for that techteddy, have updated with the correction of pi rather than Phi.
techteddy on April 16, 2010:
Phi ? rather than pi?
LeonJane (author) from Australia on April 12, 2010:
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.
cameron on April 12, 2010:
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 firstname.lastname@example.org if you would rather reach me there.
LeonJane (author) from Australia on March 18, 2010:
No worries mate, thanks Manoj Bala.
Waren E from HAS LEFT THE BUILDING............ on September 24, 2009:
Neat hub on drafting,I use AutoCad mostly,thanks for sharing LeonJane!