pyramid volume calculator
Calculate a pyramid's volume in cubic feet, cubic yards, gallons, and liters from base length, base width, and height.
A pyramid narrows from a rectangular base to a single point at the top — useful for tapered piles, footings, and architectural forms with flat sides. Enter base length, base width, and height to get volume in cubic feet, cubic yards, gallons, and liters.
How this calculator works
Pyramid volume is one-third of the base area times the height.
Formula: Cubic feet = (1/3) × base length × base width × height. Cubic yards = ft³ ÷ 27. Gallons = ft³ × 7.48052. Liters = ft³ × 28.3168.
Worked example
A pyramid with a 6 ft × 6 ft base and 9 ft height:
- Cubic feet: (1/3) × 6 × 6 × 9 = 108.00 ft³
- Cubic yards: 108 ÷ 27 = 4.000 yd³
- Gallons: 108 × 7.48052 ≈ 807.9 gal
- Liters: 108 × 28.3168 ≈ 3058.2 L
Reference
| Base L×W × Height (ft) | Cubic feet |
|---|---|
| 4×4 × 6 | 32.00 ft³ |
| 6×6 × 9 | 108.00 ft³ |
| 10×10 × 12 | 400.00 ft³ |
How to measure
Measure the base length and width along the ground, and height straight up from the base’s center to the apex — not along a sloped edge. This applies to flat-sided material piles, tapered footings, and pyramidal architectural forms. For a round, cone-shaped pile instead, use the Cone Volume Calculator.
Frequently asked questions
What's the formula for pyramid volume?
Volume is one-third of the base area times the height: V = (1/3) × base length × base width × height. For a rectangular base, base area is simply length times width.
Why is a pyramid exactly one-third of a box with the same base and height?
Like a cone versus a cylinder, a pyramid tapers from its full base to a point, so it holds a third of what a box with matching base and height would. The 1/3 factor accounts for that taper.
Does this work for a square-based or rectangular-based pyramid?
Both — enter the base's length and width separately. For a square base, just enter the same value for both.
Where does a pyramid shape actually come up in a construction project?
Pyramidal spoil or material piles with a flat-sided rather than conical shape, tapered footings, and some architectural roof or monument forms are close matches for this shape.
Is the height measured along the slanted edge or straight up?
Straight up, from the center of the base to the apex — not along a sloped side. Measuring along a slanted edge will overstate the height and inflate the volume.
How does pyramid volume compare to a cone of similar footprint?
Both use the same one-third taper factor, but a cone's base is circular while a pyramid's is rectangular. For a similar footprint size, a square pyramid holds somewhat more than a cone inscribed within it, since a square covers more area than the circle inside it.
Estimates only. Verify quantities with your supplier before purchasing.