Pyramid Volume Calculator
Created by: Emma Collins
Last updated:
The volume of a pyramid is one third of its base area times its height: V = ⅓ × B × h. For a square pyramid with a 6 m base and 8 m height, V = 6 × 6 × 8 ÷ 3 = 96 m³. Pick the base shape below and enter the dimensions in any unit.
Pyramid Volume Calculator
MathCalculate pyramid volumes for square, rectangular, and triangular bases
Square pyramid volume chart
Volume = side² × height ÷ 3, in cubic units of whatever length unit you use.
| Base side | Height | Base area | Volume |
|---|---|---|---|
| 2 | 3 | 4 | 4 |
| 3 | 4 | 9 | 12 |
| 4 | 6 | 16 | 32 |
| 5 | 5 | 25 | 41.67 |
| 6 | 8 | 36 | 96 |
| 8 | 10 | 64 | 213.33 |
| 10 | 12 | 100 | 400 |
| 12 | 15 | 144 | 720 |
| 20 | 30 | 400 | 4,000 |
Pyramid volume formulas
- Any pyramid: V = (1/3) × base area × height
- Square pyramid: V = s² × h ÷ 3
- Rectangular pyramid: V = l × w × h ÷ 3
- Triangular pyramid: V = (½ × b × t) × h ÷ 3, where b and t are the base and height of the triangle
The height is always the perpendicular height from the apex to the base, not the length of a sloping edge or face.
Worked examples
- Square pyramid, 4 ft base, 6 ft tall: 4 × 4 × 6 ÷ 3 = 32 ft³.
- Rectangular pyramid, 10 × 6 cm base, 9 cm tall: 10 × 6 × 9 ÷ 3 = 180 cm³.
- Triangular pyramid, triangle base 8 in and height 6 in, pyramid 10 in tall: base area = ½ × 8 × 6 = 24 in², so V = 24 × 10 ÷ 3 = 80 in³.
- From slant height: a square pyramid with 6 m sides and a 5 m slant height has vertical height √(25 − 9) = 4 m, so V = 36 × 4 ÷ 3 = 48 m³.
Frequently Asked Questions
What is the formula for the volume of a pyramid?
V = (1/3) × base area × height. For a square base with side s, V = s² × h ÷ 3. For a rectangular base, V = length × width × height ÷ 3. For a triangular base, V = (½ × base × triangle height) × pyramid height ÷ 3.
How do I calculate the volume of a square pyramid?
Square the side of the base, multiply by the height and divide by 3. A pyramid with a 6 m base and 8 m height has V = 6 × 6 × 8 ÷ 3 = 96 m³.
How do I find the volume of a rectangular pyramid?
Multiply the base length by the base width to get the base area, multiply by the height, then divide by 3. A 10 × 6 cm base with a 9 cm height gives 10 × 6 × 9 ÷ 3 = 180 cm³.
Why is a pyramid one third of a prism?
A pyramid’s cross-sections shrink steadily from the base to the tip, and adding them up (integrating) gives exactly one third of a prism with the same base and height. You can see it with three square pyramids that fit together to form a cube.
Should I use the slant height or the vertical height?
The vertical height, measured straight from the tip down to the center of the base. If you only know the slant height l of a square pyramid with side s, the vertical height is √(l² − (s/2)²).
What is the volume of the Great Pyramid of Giza?
Using its original dimensions of about 230.3 m per side and 146.6 m tall, V ≈ 230.3² × 146.6 ÷ 3 ≈ 2.59 million cubic meters.
Sources and References
- OpenStax Calculus Volume 1, section 6.2: Determining volumes by slicing. Derives the volume of a pyramid as one third of base area times height.