Free · Algebra and geometric relations

Pyramid Volume from a Triangular Base

Compute volume from perpendicular pyramid height and several descriptions of its triangular base.

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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

For the worked example, Volume = 18.

V=Bh/3; triangular B=base×altitude/2

Worked example

Enter these known values and leave the other values blank.

Do you know the area of the pyramid's base?
1
Pyramid base area (A)
6 cm²
Pyramid height (H)
9 cm
Volume
18 cm³

Assumptions and limitations

  • Pyramid height is perpendicular to the base plane.
  • Base data must form a strict triangle; ASA angles are positive with sum below 180 degrees.
  • ASA angle inverses use cotangent addition and recover an interior angle from 0 to 180 degrees. A missing angle stays incomplete until side, area and the other angle are known.
  • Bookify validates the real geometric or algebraic domain and inverse branches omitted or approximated by this capture. The ASA constant-π inverse is replaced by cotangent addition, with every original equation pinned.

Common questions

How do I use this relation?

Choose the relevant mode and enter independent known quantities. Leave a missing value empty where the control permits an inverse.

What do the displayed numbers mean?

The result follows the stated mathematical model. All dimensions must use consistent units; available unit selectors handle conversions.

References

The captured ASA inverse angle returned the constant π, which fabricates a flat triangle. The identity cot α + cot β = a²/(2B) recovers the unique interior angle through atan2, including obtuse triangles. Bookify validates the real geometric or algebraic domain and inverse branches omitted or approximated by this capture. The international acre is exactly 43560 square international feet; Bookify replaces the rounded captured area factor. The cubic international mile uses the cube of the exact 1609.344-meter mile, replacing a rounded reciprocal factor.

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