Pyramid Volume Calculator
Square-base pyramid: Volume = (1/3) × Base Area × Height
Same Rule as a Cone, Squared-Off Base
A square-base pyramid follows the same one-third relationship as a cone: its volume is exactly one-third of the prism that shares its base and height. Only the base-area formula changes — a square side squared instead of a circle's πr².
The Formula
Base Area = Side²
Volume = (1/3) × Base Area × Height
Volume = (1/3) × Base Area × Height
Worked Example
For a pyramid with base side 6 and height 10:
| Step | Calculation | Result |
|---|---|---|
| Base area | 6² | 36 |
| Volume | (1/3) × 36 × 10 | 120 |
Where This Matters
- Architecture and monuments — estimating the material volume of pyramidal roofs, spires, or structures.
- Excavation and grading — a pyramidal stockpile or excavation pit's volume follows the same formula.
- Packaging design — calculating the internal capacity of a pyramid-shaped container.
How to Use This Calculator
- Enter the Base Side Length of the square base.
- Enter the pyramid's Height.
- Select Calculate to get the volume.
Related Calculations
For a pyramid with a non-square base, use the general Prism Volume Calculator logic with your own base area, or compare to a cone with the Cone Volume Calculator.