Pyramid Volume Calculator
Find the volume of a rectangular-base pyramid.
Results update as you type.
How it works
A pyramid is a solid with a polygonal base that tapers to a single apex, and this calculator finds the volume of a pyramid with a rectangular base from its length, width, and height. You enter the base dimensions and the perpendicular height from the base to the apex, and it returns the volume and the base area. The volume formula is one third of the base area times the height, a beautiful result that means a pyramid holds exactly one third as much as a prism or box with the same base and height. This one-third factor applies to every pyramid and cone, whatever the base shape, provided the height is measured straight up from the base plane to the apex, not along a slanted edge. Pyramids are among the oldest engineered structures, and the volume calculation matters for estimating material in construction, for tent and roof design, for packaging, and in mathematics education. Be sure to use the vertical height, the perpendicular distance from the base to the tip, rather than the slant height along a face, which would give a wrong, larger answer. Enter the base length, base width, and height to compute the pyramid's volume.
Volume = (1/3)·length·width·height
The volume of a pyramid is one third of the base area times the perpendicular height. For a rectangular base, the base area is length times width, so the volume is one third of length times width times height. The one-third factor holds for any pyramid or cone regardless of base shape, as long as the height is measured perpendicular to the base.
Source:Solid geometry
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter base length, base width and height.
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Volume updates instantly as you type — no button to press.
Frequently asked questions
How do you find the volume of a pyramid?
Multiply the base area by the height, then divide by three. For a rectangular base, the base area is length times width, so the volume is one third of length times width times height. A pyramid holds exactly one third the volume of a box with the same base and height, which this calculator computes directly.
Why is there a factor of one third?
Any pyramid or cone occupies exactly one third of the prism or cylinder that shares its base and height. This can be shown by calculus or by dissection arguments dating back to ancient Greek mathematics. The one-third factor is universal for pointed solids, which is why it appears in both the pyramid and cone volume formulas.
Should I use the slant height or the vertical height?
Always use the vertical height, the perpendicular distance from the base plane straight up to the apex. The slant height, measured along a triangular face, is longer and belongs in surface-area calculations, not volume. Using the slant height here would overstate the volume, so make sure your height is the true perpendicular one.
Does this work for a square pyramid?
Yes. A square pyramid is just a rectangular pyramid whose base length equals its base width. Enter the same value for both length and width, and the calculator gives the correct volume. The formula handles any rectangular base, from a long thin one to a perfect square, with the same one-third rule.
What units does the volume use?
The volume comes out in cubic units of whatever length unit you enter. If length, width, and height are in metres, the volume is in cubic metres; if in feet, it is in cubic feet. Keep all three inputs in the same unit, and the result will be in the corresponding cubic unit.