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Closed Cone Surface from Radius, Circumference and Slant

Closed Cone Surface from Radius, Circumference and Slant. Convert compatible units, recover unknown dimensions and distinguish curved surfaces, bases and total measures.

  • Formula & worked example
  • Private in your browser
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

Example in initial displayed units: Radius (r) 3, Height (h) 4 gives Circumference (c) 18.849556, Slant height (l) 5, Surface area 75.398224.

C = 2πr; s² = r²+h²; A = πr(r+s)

Worked example

Enter these known values and leave the other values blank.

Radius (r)
3 cm
Height (h)
4 cm
Circumference (c)
18.85 cm
Slant height (l)
5 cm
Surface area
75.4 cm²

Assumptions and limitations

  • A right circular cone has perpendicular height h and slant length s. Total area includes one flat circular base; lateral area includes only the curved surface. Radius and height must be positive.
  • Select units before entering dimensions. Clear an unknown result before solving backward, and supply enough independent measurements. Display rounding does not represent measurement uncertainty.
  • Calculations use 64 significant digits and full-precision π. Original reference drawings explain dimensions and are not drawn to the entered scale.

Common questions

Does the cone surface result include the bottom disk?

Yes. The result adds πr² for the base to πrs for the curved side.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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