Pyramid Volume Calculator – Rectangular, Square, and Any Base Area
Compute the volume of a pyramid from base length and width, square base side, or a known base area and height. Supports metric and imperial units and shows the formula \(V = \tfrac{1}{3} A_{\text{base}} h\) step by step.
1. Pyramid volume calculator
Choose the description that best matches your pyramid, select the unit for all linear dimensions, then enter the base dimensions and the vertical height.
All lengths and height must use this unit.
The calculator will return volume in cubic of the selected unit (e.g. cm³) and also convert to m³ and liters when possible.
Volume (main)
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Volume (m³)
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Cubic meters
Approx. liters
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Using 1 m³ = 1000 L
Volume of a pyramid – general formula
A pyramid is a solid with a polygonal base and a point (the apex) that is not in the plane of the base. All lateral edges connect the apex to the vertices of the base. The key fact – valid for all pyramids – is that the volume is one third of the volume of a prism with the same base and height:
Special cases: rectangular and square pyramids
For common pyramids used in exercises and engineering sketches, the base is rectangular or square. In those cases it is convenient to express the base area in terms of the side lengths:
- Rectangular base with length \(L\) and width \(W\): \[ A_{\text{base}} = L \cdot W \quad\Rightarrow\quad V = \frac{1}{3} L W h. \]
- Square base with side \(s\): \[ A_{\text{base}} = s^2 \quad\Rightarrow\quad V = \frac{1}{3} s^2 h. \]
The calculator lets you work either with the side lengths or directly with the base area \(A_{\text{base}}\), which is useful if the base is a triangle, regular polygon or any other shape for which you already know the area.
Height vs slant height
In right pyramids you may encounter the slant height \(l\): the distance from the apex to the midpoint of a base edge along a lateral face. It is related to the vertical height, but they are not the same:
Units of measurement for pyramid volume
If the base dimensions and height are expressed in a unit of length (meters, centimeters, inches, feet…), the volume is expressed in the corresponding cubic unit:
- m → m³
- cm → cm³
- mm → mm³
- in → in³
- ft → ft³
- yd → yd³
The calculator also converts to cubic meters and liters using the exact relation \(1 \text{ m}^3 = 1000 \text{ L}\). This is convenient when a pyramid-shaped container is used to hold liquids or granular material.
FAQ – Pyramid volume
Why is the volume of a pyramid one third of the corresponding prism?
A classical way to see this is by dissection or Cavalieri’s principle. For example, you can partition a cube into three congruent pyramids with the same base area and height. Since the three pyramids exactly fill the cube, each must have one third of the cube’s volume. The same reasoning extends to general pyramids and cones by comparing cross-sectional areas at each height.
Does the position of the apex above the base centre matter?
The general formula \(V = \tfrac{1}{3} A_{\text{base}} h\) does not require the apex to lie directly above the centre of the base. It only requires the height \(h\) to be measured perpendicularly from the base to the apex. The shape can be a right pyramid (apex above the centre) or oblique; the volume formula is the same.
What happens to the volume if I double all linear dimensions?
Volume scales with the cube of the linear scale factor. If you multiply all linear dimensions of a pyramid (base lengths and height) by a factor \(k\), the volume is multiplied by \(k^3\). For example, doubling all lengths (k = 2) multiplies the volume by 8.
Is a cone a special case of a pyramid?
Yes. From a volume point of view, a right circular cone can be treated as a pyramid whose base is a circle of radius \(r\). The base area is \(A_{\text{base}} = \pi r^2\), so the same formula gives \(V = \tfrac{1}{3} \pi r^2 h\).