Cone Flat Pattern Calculator - Sheet Metal

Sheet Metal Cone Flat Pattern Calculator

Develop a cone or truncated-cone flat pattern from large diameter, small diameter, vertical height and seam allowance, with sector angle and pattern radii.

Inputs

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Large diameter (D1)

Large finished diameter of the frustum.

Small diameter (D2)

Small finished diameter. Use 0 for a full cone.

Vertical height (H)

Straight vertical height, not slant height.

Seam allowance

Straight seam allowance added as a simple slant-height strip for area estimating.

Results

Default result

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Pattern sector angle(theta)

103.45°

Pass

Also computed

Outer pattern radius(R1)530.37mm

Inner pattern radius(R2)265.18mm

Slant height(s)265.18mm

Large arc length957.56mm

Small arc length478.78mm

Pattern area190,450mm²

Method notes 3 notes

Slant height s = sqrt(H^2 + ((D1 - D2)/2)^2). Pattern radii are s*D1/(D1-D2) and s*D2/(D1-D2).
Sector angle comes from matching the developed outer arc to the finished large circumference: theta = 180*D1/R1 degrees.
This is a geometric flat-pattern screen. Thickness compensation, bend/stretch allowance, forming method, locks, hems, notch relief, grain direction and shop tooling are not included.

A cone flat pattern develops a conical frustum into a sector. Slant height is s = sqrt(H^2 + ((D1-D2)/2)^2), the outer pattern radius is R1 = s*D1/(D1-D2), and the sector angle is theta = 180*D1/R1 degrees so the flat arc matches the finished circumference. This calculator also returns inner radius, arc lengths and blank area with seam allowance.

How to use this calculator

Enter diameters. Use the large and small finished diameters. Use zero small diameter for a full cone.
Enter vertical height. Use straight vertical height, not slant height.
Add seam allowance. Enter a simple seam allowance for area estimating.
Lay out radii and angle. Use the outer radius, inner radius and sector angle for the developed pattern.

How it works

First calculate the slant height of the frustum:

s = sqrt(H^2 + ((D1 - D2) / 2)^2)

The developed radii come from extending the cone sides to the apex:

R1 = s x D1 / (D1 - D2)

R2 = s x D2 / (D1 - D2)

The sector angle makes the outer flat-pattern arc match the large circumference:

theta = 180 x D1 / R1

Worked example

Verified against the live calculator

A frustum with a 12 in large diameter, 6 in small diameter and 10 in height has a slant height of about 10.4 in. The developed pattern uses an outer radius near 20.9 in, an inner radius near 10.4 in and a sector angle near 103 degrees.

Frequently asked questions

How do you make a cone flat pattern?

Find the frustum slant height, extend the cone sides to the apex, then use the outer and inner developed radii. The sector angle is set so the outer arc length equals the large finished circumference.

What is the sector angle formula?

For a conical frustum, sector angle in degrees is 180 times the large diameter divided by the outer developed radius. That matches the flat pattern arc to the finished circumference.

Does this include sheet metal stretch or bend allowance?

No. It is a geometric development. Shop forming, thickness, neutral axis, lock seams, hems, notches and material stretch may require compensation.

Can I use this for a full cone?

Yes. Enter the small diameter as zero. A cylinder is not supported because a cylinder develops to a rectangle, not a cone sector.

Method & assumptions

Assumes a true right circular cone or conical frustum.
Seam allowance is added as a straight strip area estimate, not as a detailed lock, tab or hem pattern.
Does not compensate for thickness, neutral-axis shift, forming stretch, relief cuts, grain direction, shop tooling, welding shrinkage or rolling springback.
Use bend allowance, bend deduction and sheet metal gauge for adjacent fabrication checks.

Sheet Metal Cone Flat Pattern Calculator

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