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Conical Frustum Closed Surface and Slant Length

Conical Frustum Closed Surface and Slant Length. Use unit controls and documented positive geometric roots to compare base, lateral 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: Base radius (R) 3, Top radius (r) 1, Height (H) 4 gives Slant height (S) 4.472136, Surface area of the frustum 87.614444.

A = π(R²+r²+(R+r)s); s² = H²+(R−r)²

Worked example

Enter these known values and leave the other values blank.

Base radius (R)
3 cm
Top radius (r)
1 cm
Height (H)
4 cm
Slant height (S)
4.472 cm
Surface area of the frustum
87.614 cm²

Assumptions and limitations

  • Total surface includes both circular ends. The base radius is strictly larger than the top radius; a zero top radius is the retained cone boundary. Equal radii and swapped radii are excluded in this workflow. Perpendicular height is positive.
  • Select compatible units and enough independent dimensions. Clear unknown values before solving backward. Numeric precision and display rounding do not quantify uncertainty in measured inputs.
  • Arithmetic uses 64 significant digits. Original reference diagrams explain the dimensions and do not follow entered proportions.

Common questions

Does the frustum surface include both end disks?

Yes. Add πR² and πr² to the curved-side area π(R+r)s.

References

Require physical dimensions and real positive inverse geometry; distinguish dependent measurements and cross-section consistency. The international acre is exactly 43560 square international feet; Bookify replaces the rounded captured area factor.

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