pyramid volume calculator
A pyramid volume calculator uses V = ⅓ × base length × base width × height. A 6 × 6 ft base and 9 ft height gives 108 ft³, 4.0 yd³, or about 807.9 gallons.
Pyramid volume calculator: cubic feet, yards, gallons, and liters
A pyramid volume calculator takes the area of the base and multiplies it by the height, then divides by three. In symbols, V = ⅓ × length × width × height. A pyramid with a 6 × 6 ft base and a 9 ft height holds 108 cubic feet, which is 4.0 cubic yards, or about 807.9 US gallons.
Enter the three measurements in feet and the result appears in four units, so you can order material by the yard or size a hollow form by the gallon.
The formula in plain words
Picture a cardboard box the same size as the pyramid’s base and the same height. Fill that box with sand. Now pour it into the pyramid. You would need three pyramids’ worth of sand to fill the box once. So the pyramid is one-third.
- Base area = length × width
- Cubic feet = ⅓ × base area × height
- Cubic yards = cubic feet ÷ 27
- Gallons = cubic feet × 7.48052
- Liters = gallons × 3.78541
Worked examples
- Pyramid, 6 ft × 6 ft base, 9 ft tall
- Base area: 6 × 6 = 36 ft²
- Cubic feet: ⅓ × 36 × 9 = 108 ft³
- Cubic yards: 108 ÷ 27 = 4.000 yd³
- Gallons: 108 × 7.48052 = 807.9 gal
- Liters: 3,058.2 L
- Flat-sided spoil pile, 10 ft × 8 ft base, 6 ft tall
- Base area: 10 × 8 = 80 ft²
- Cubic feet: ⅓ × 80 × 6 = 160 ft³
- Cubic yards: 5.926 yd³
- Gallons: 1,196.9 gal
Example 2 is a rectangular base, so the pyramid has two different sides. The same formula applies, and only the base area changes.
Pyramid volume by size
| Base (L × W) | Height | Cubic feet | Cubic yards |
|---|---|---|---|
| 4 × 4 ft | 6 ft | 32.0 | 1.185 |
| 6 × 6 ft | 9 ft | 108.0 | 4.000 |
| 10 × 8 ft | 6 ft | 160.0 | 5.926 |
| 10 × 10 ft | 12 ft | 400.0 | 14.815 |
How the height changes the answer
Volume is directly proportional to height. Double the height and the volume doubles. Double both base sides and the base area quadruples, so doubling the footprint but keeping the height gives four times the volume.
A 6 × 6 base at 9 ft is 108 ft³. At 18 ft it is 216 ft³. A 12 × 12 base at 9 ft is 432 ft³.
How to measure
- Base: Measure the length and width along the ground at the bottom edges.
- Height: Hold a plumb line from the apex and measure down to the base plane. Do not run the tape along the sloped face.
- Slant height: If that is all you can measure, use √(slant² − (half the base)²) to find the true height.
- Truncated tops: If the top is flat, treat it as a frustum, not a pyramid.
- Units: Convert inches to feet before entering.
Common mistakes
- Using the slant height as the height. That overstates volume, sometimes by a lot on steep pyramids.
- Forgetting the one-third. Without it the answer is three times too large.
- Using a pyramid for a round pile. A circular footprint is a cone.
- Treating a flat-topped pile as a point. The tip is missing, so the real volume is less. Use the frustum volume calculator.
- Not allowing for loose material. A real pile will settle and slump, so the geometry gives an upper estimate.
From volume to weight
The 6 × 6 × 9 ft pyramid is 4.0 yd³. If it is a pile of sand at 1.35 tons per cubic yard, that is 5.4 tons. If it is gravel at 1.4, it is 5.6 tons.
These are loose-pile numbers. A real flat-sided pile slumps at the corners and edges, so the true volume is a bit less than the geometry says. Compare your estimate to the delivery ticket if you have one.
Related calculators
For a round-based version, use the cone volume calculator. For a wedge with a constant triangular end, the triangular prism volume calculator is the right tool, and for a plain box, the volume calculator is the starting point.
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. A 6 × 6 ft base with a 9 ft height is 108 ft³.
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. Three identical pyramids can be fitted together to fill one such box.
Does this work for a square-based or rectangular-based pyramid?
Both. Enter the base's length and width separately. For a square base, enter the same value for both.
Where does a pyramid shape actually come up in a construction project?
Flat-sided material piles, tapered footings, and some architectural roof or monument forms are close matches. A pyramid roof such as a hipped square turret is another common example.
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 overstates the height and inflates the volume. If you only know the slant height of a face, subtract: height = √(slant² − (base ÷ 2)²) for a square base.
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. A square pyramid with a 6 ft side holds about 27 percent more than a cone with a 6 ft diameter at the same height, because the square covers more area than the circle.
Estimates only. Verify quantities with your supplier before purchasing.