Rectangular Pyramid Volume Calculator
This rectangular pyramid volume calculator works out the volume of a pyramid that has a rectangular base. Enter the base length, the base width and the vertical height, choose your unit, and it returns the volume along with the base area. A pyramid holds exactly one third of the box that would enclose it, so the volume is one third of the base area times the height. The base area for a rectangular base is just length times width. The calculator is unit agnostic, so measurements in metres give a volume in cubic metres and measurements in centimetres give cubic centimetres. Use it for geometry problems, packaging and display design, roof and hopper shapes, or any rectangular based pyramid where you need a quick, reliable volume. The vertical height is the perpendicular distance from the base up to the apex, not the slanted edge length. The formula, a worked example and the assumptions are all set out below so you can check the figure and see where it comes from.
The formula
The volume of any pyramid is one third of the base area times the perpendicular height. For a rectangular base the base area is length times width, so V = (1/3) l w h, where l and w are the base dimensions and h is the vertical height.
Worked example
A rectangular pyramid with a base of 6 by 4 and a height of 9 has a base area of 24 and a volume of (1/3) times 24 times 9 = 72. Enter those values above to confirm.
Frequently asked questions
What is the formula for a rectangular pyramid volume?
V = one third times base length times base width times height. The base area is length times width, then take a third of that times the height.
Is height the slant length or the vertical height?
Use the vertical (perpendicular) height from the base to the apex, not the slanted face or edge length.
Why one third?
A pyramid fills exactly one third of the prism or box with the same base and height. This holds for any pyramid, whatever the base shape.
Who this calculator is for
This calculator is for students, designers and makers who need the volume of a rectangular based pyramid.
What this calculator assumes
- The base is a rectangle of the length and width you enter.
- The height is the perpendicular height to the apex.
- The volume is in the cube of your chosen unit.
- Results are rounded for display.
Formula and sources
Related calculators
- Triangular Pyramid Volume Calculator: pyramid with a triangular base.
- Cylinder Volume Calculator: volume of a cylinder.
- Volume Calculator: volume of common solids.
- Cubic Metre Calculator: volume of a box.