How this calculator works
Cutting a straight line along the cone and flattening the curved surface produces a circular sector. Its arc must wrap exactly once around the circular base. The ratio r/l therefore gives the fraction of a full disk needed. The reverse radius mode solves a quadratic in r² from the known curved area and vertical height. Dimensions describe ideal surfaces with no seam or overlap allowance.
Formula
l=√(r²+h²); lateral L=πrl; sector angle θ=2πr/l; base B=πr²; total=L+B; volume=Bh/3.
Worked example
Radius 3 m and vertical height 4 m give slant height 5 m. The curved area is 15π m². Its flat pattern is a sector of radius 5 m and angle 216°, with arc length 6π m.
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Frequently asked questions
Does lateral area include the circular base?
It includes only the curved sheet. Add πr² for the closed cone total.
Is the sector radius the vertical height?
The sector radius is the slant height from apex to rim. The vertical height is shorter.
Can I use this for an off-centre apex?
No. An oblique cone does not unroll to this simple circular sector.