How this calculator works
A cone is narrower than the cylinder enclosing it, so a volume-and-height calculation includes a factor of three. Surface and lateral area modes solve their area equations for the radius before doubling it. Reverse modes recover height from a radius and another measurement. Height is always perpendicular to the base. The formulas assume the apex sits above the centre.
Formula
d = 2r; r² = 3V/(πh); r² = s² - h²; base = πr²; lateral = πr sqrt(r²+h²). For total area S and q=S/π, r = q/sqrt(h²+2q).
Worked example
Volume 12π m³ and height 4 m give r² = 3(12π)/(4π) = 9 m². The diameter is 6 m, the slant is 5 m and the total area is 24π m².
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Frequently asked questions
Can I use the cylinder formula?
No. For the same height and volume, a cone needs a radius √3 times as large as a cylinder.
Can the slant equal the height?
Only if the radius is zero. This tool requires a positive base.
Which surface area should I enter?
Choose lateral for the curved sheet alone, or total for that sheet plus the circular base.