Cone Flat Pattern Calculator (Sheet Metal, Paper, Lampshades)
Angle and radii of the flat piece that rolls up into a cone or a truncated cone — a funnel, a hopper, a lampshade or a paper hat — drawn to scale.
Results
Angle of the flat pattern
121.94
°
Outer radius of the pattern
442.8
mm
Inner radius of the pattern
177.1
mm
Slant length (side seam)
265.7
mm
Width of the pattern across its ends
774.4
mm
What this tool does
A cone unrolls into a slice of a circle and a truncated cone into a slice of a ring. The arc of that slice has to equal the circumference of the base, which fixes the angle: 360° × R ÷ outer radius. Draw the outer and inner arcs from the same centre, cut out the angle, add a seam allowance along one straight edge, and it closes into the shape. Use the diameters at the centre of the material thickness for sheet metal.
Formula
slant s = √(h² + (R − r)²) · outer radius = s × R ÷ (R − r) · angle = 360° × R ÷ outer radius
Variables
| Symbol | Meaning | Unit |
|---|---|---|
dl | Large diameter | mm |
ds | Small diameter (0 for a pointed cone) | mm |
h | Height | mm |
A | Angle of the flat pattern | ° |
RO | Outer radius of the pattern | mm |
RI | Inner radius of the pattern | mm |
SL | Slant length (side seam) | mm |
CH | Width of the pattern across its ends | mm |
Worked example
- Large diameter300 mm
- Small diameter (0 for a pointed cone)120 mm
- Height250 mm
- Angle of the flat pattern121.94 °
- Outer radius of the pattern442.8 mm
- Inner radius of the pattern177.1 mm
- Slant length (side seam)265.7 mm
- Width of the pattern across its ends774.4 mm
Limitations
- Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.
- Always order a little more material than the calculated quantity. Cuts, breakage and pattern matching create waste that depends on the shape of the job.