What Is a Rectangular Pyramid Volume Calculator?
A rectangular pyramid is a three-dimensional solid with a rectangular base and four triangular faces that meet at a single apex. This calculator finds its volume instantly from three measurements: the length and width of the base and the perpendicular height from the base to the apex. It works with any consistent unit — centimeters, meters, inches, or feet — and returns the result in the corresponding cubic units.
How to Use It
Enter the base length (l), the base width (w), and the vertical height (h). All three values must use the same unit of measurement. Click calculate and the tool returns the volume in cubic units, along with the base area for reference. Make sure the height is the perpendicular distance from the base to the tip, not the slant height along a face.
The Formula Explained
The volume of any pyramid is one-third of its base area times its height: \(V = \frac{1}{3} \cdot A \cdot h\). For a rectangular pyramid the base area \(A\) is simply length times width, so the full formula becomes:
$$V = \frac{1}{3} \cdot l \cdot w \cdot h$$
The one-third factor reflects that a pyramid fills exactly one third of the prism (box) that shares the same base and height.
Worked Example
Suppose a pyramid has a base 6 units long and 4 units wide, with a height of 9 units. First find the base area: \(6 \times 4 = 24\) square units. Then apply the formula: $$V = \frac{1}{3} \times 24 \times 9 = \frac{1}{3} \times 216 = 72 \text{ cubic units.}$$
FAQ
Does this work for square pyramids? Yes. A square pyramid is a special case where length equals width — just enter the same value for both.
What height should I use? Use the vertical (perpendicular) height from the center of the base to the apex, not the slant height measured along a triangular face.
What units does it return? Whatever unit you input, the result is in cubic units of that unit (e.g., centimeters in gives cubic centimeters out).
