Free · 3D geometry calculators 📦

Right Cone Height from Radius, Slant or Volume

Calculate right cone height from radius, slant or volume with converted units, positive geometric inverses and explicit model limits.

  • Formula & worked example
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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

A right cone with radius 3 cm and perpendicular height 4 cm has slant length 5 cm and volume 12π cm³.

s² = r² + h²; V = πr²h/3

Worked example

Enter these known values and leave the other values blank.

Radius (r)
3 cm
Height (h)
4 cm
Slant height (s)
5 cm
Volume (V)
37.7 cm³

Assumptions and limitations

  • The apex is directly above the center of a circular base. Height is perpendicular to the base; slant height runs along the surface. Slant height must exceed radius.
  • Measurements must describe the same shape. Clear a quantity you want to infer instead of supplying conflicting measurements. Unit selectors are converted before the geometric relationships are applied.
  • Calculations use 64 significant digits with full-precision π; result formatting rounds the displayed value separately. These are ideal geometric models, without material allowances or measurement uncertainty.

Common questions

Can volume recover the height?

With a known positive radius, h = 3V/(πr²). With radius and slant length instead, h = √(s²−r²), using the positive root.

References

The US fluid ounce uses one 128th of the exact US liquid gallon, replacing the rounded captured reciprocal factor. Bookify replaces the captured rounded US gallon with the exact 3.785411784-liter definition.

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