How to use the cone development layout calculator
The flat pattern for a truncated cone is the difference between two circular sectors. Start with the slant height, the hypotenuse of a triangle whose legs are the vertical height and half the difference of the diameters: √(h² + ((D − d)/2)²). The outer layout radius measured from the imaginary apex is slant × D ÷ (D − d), and the inner radius is that value minus the slant height.
The sector angle follows from the requirement that the outer arc equal the bottom circumference, giving angle = 180° × D ÷ R. Shallow cones approach 360 degrees while tall cones produce a narrow wedge. To lay it out, strike both radii from one center point with a beam compass, then open the sector to the calculated angle and draw the two radial lines. On large plates, stepping off the chord length is more accurate than measuring the arc.
Entering a plate thickness shifts the layout to the mean line. If the drawing gives inside diameters, enter 0 for thickness and use the inside dimensions directly. In the shop, add the seam root gap, cutting kerf, and the flat unrolled ends left by the bending rolls, and use the developed area figure for material takeoff. Heavy plate and alloys with high springback should be confirmed with a trial form before cutting production material.
Frequently Asked Questions
Rolling keeps the mid-thickness line at its original length while the outside stretches. Laying out on the mean line is what makes the finished part match the drawing, so when dimensions are given to the outside surface, subtract one plate thickness from each diameter before developing.
It means a very shallow cone. As the height approaches zero the development becomes a full ring, and as the height grows the sector angle shrinks into a narrow wedge.