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Hexagonal Pyramid Capacity from Base Edge or Apothem

Hexagonal Pyramid Capacity from Base Edge or Apothem. Use unit controls and documented positive geometric roots to compare base, lateral and total measures.

  • 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.

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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 edge (a) 2, Height (h) 4 gives Apothem (ap) 1.7320508, Slant height (l) 4.3588989, Base perimeter (P) 12, Base area (BA) 10.392305, Volume (V) 13.856406.

B = 3a apothem; V = BH/3; apothem = a√3/2

Worked example

Enter these known values and leave the other values blank.

Base edge (a)
2 cm
Height (h)
4 cm
Apothem (ap)
1.732 cm
Slant height (l)
4.359 cm
Base perimeter (P)
12 cm
Base area (BA)
10.392 cm²
Volume (V)
13.856 cm³

Assumptions and limitations

  • The base is a regular hexagon with six equal sides, and the apex lies above its center. The base apothem is a√3/2. Slant height reaches an edge midpoint, not a base vertex. Lateral area is the sum of six triangular face areas.
  • 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

Can I use base apothem as pyramid height?

No. Apothem lies inside the base plane, while perpendicular pyramid height extends from that plane to the apex.

References

The cubic international mile uses the cube of the exact 1609.344-meter mile, replacing a rounded reciprocal factor.

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