What is a triangular pyramid?
A triangular pyramid is a solid with a triangular base and three triangular faces meeting at a single apex. When all four faces are equal it is called a regular tetrahedron, but the general formula below works for any triangular base and apex position. This calculator returns the enclosed volume in cubic units.
How to use this calculator
Enter three measurements: the base of the triangular base (b), the height of that triangle (h), and the perpendicular height of the pyramid from the base to the apex (H). All measurements must use the same length unit. The result is reported in cubic units, and the area of the triangular base is shown as an intermediate value.
The formula explained
The volume of any pyramid equals one-third of the base area multiplied by the perpendicular height: $$V = \frac{1}{3} \cdot A_{\text{base}} \cdot H$$ For a triangular base, the area is \(A_{\text{base}} = \frac{b \cdot h}{2}\). Combining the two gives $$V = \frac{1}{3} \cdot \frac{b \cdot h}{2} \cdot H$$ The one-third factor reflects that a pyramid fills exactly one-third of the prism with the same base and height.
Worked example
Suppose the triangular base has \(b = 6\) and \(h = 4\), so its area is $$\frac{6 \times 4}{2} = 12 \text{ square units}$$ If the pyramid height is \(H = 9\), then $$V = \frac{1}{3} \times 12 \times 9 = 36 \text{ cubic units}$$
FAQ
Is the pyramid height the same as the slant height? No. \(H\) is the perpendicular distance from the apex straight down to the plane of the base, not the sloped edge length.
Does the apex have to be centered? No. The volume depends only on the base area and the perpendicular height, regardless of where the apex sits horizontally.
What units does it return? If lengths are in centimetres the volume is in cubic centimetres; the tool simply reports "cubic units" since it is unit-agnostic.
