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Pyramid Volume Calculator
Last updated: June 17, 2026
A pyramid volume calculator computes the space enclosed by a pyramid with a rectangular or square base. The volume is calculated as one-third of the product of the base area (length * width) and the perpendicular height. This tool is useful for students and architects studying 3D geometry and structural space.
Calculate the volume of a square or rectangular pyramid using the base length, base width, and height.
Quick Answer
Find the volume of a pyramid. Enter the base length, base width, and height to compute the volume instantly.
For a square base, keep length and width equal. · e.g. 6
Width of the rectangular or square base. · e.g. 6
Perpendicular height from base center to apex. · e.g. 8
Volume (V)
96 units³
Square Base Pyramid
Examples
Square Pyramid
length = 6 · width = 6 · height = 8 — Volume = 96 units³
Rectangular Pyramid
length = 5 · width = 8 · height = 9 — Volume = 120 units³
How it works
Volume Formula
The volume of a pyramid is computed using the base area and the perpendicular height:
Volume = (1/3) × l × w × h
Where:
- l is the length of the base
- w is the width of the base
- h is the height of the pyramid
Disclaimer
For educational purposes. Verify results for critical applications.
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Frequently asked questions
The volume of a pyramid is one-third of the base area multiplied by the height. Formula: Volume = (1/3) × base_length × base_width × height.
For a square pyramid, the length and width of the base are equal (l = w). The formula simplifies to: Volume = (1/3) × base_side² × height.
If you have a prism and a pyramid with the exact same base and height, the pyramid will hold exactly one-third of the volume of the prism. This can be visualized by dividing a cube into three identical pyramids.
Yes. Cavalieri's principle states that if two solids have the same height and base area, and their cross-sections at any height have the same area, they have the same volume. This means the standard formula works even if the apex is not centered.
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