Conical Frustum Flat Pattern Calculator
Find the ideal planar sector for laying out a conical frustum from larger/smaller radii and axial height. This is a geometric development for a thin, developable surface.
Method, example, and limits
Formula: Slant s = √(H² + (R−r)²); pattern radii are sR/(R−r) and sr/(R−r); sector angle α = 360°·R/(outer pattern radius).
Inputs and units: R is the larger end radius, r the smaller end radius, and H the axial height. Pattern radii and slant height share the input unit.
Worked example: For R = 50 mm, r = 20 mm, H = 40 mm, slant height is 50 mm, pattern radii are 83.333 mm and 33.333 mm, and sector angle is 216°.
Result meaning: The sector's inner and outer radii are distances from the developed cone apex; its 216° arc lengths reproduce the two circular end circumferences.
Assumptions: The side is a right circular conical frustum with straight generators. R must exceed r, so a cylinder (R = r) is outside this annular-sector formula.
Limits: The ideal pattern excludes seam allowance, kerf, material thickness, springback, flange, and forming distortion. For a full cone with r = 0, inner pattern radius is zero.
Creator & reviewers
Creator persona
- Casey RowanUnits, conversions & measurement
Reviewer personas
- Devon ShawFormula & assumptions review
- Sage MitchellClarity & usability review