frustum volume calculator
Calculate the volume of a frustum — a cone or pyramid with the tip cut off — in cubic feet, cubic yards, gallons, and liters.
A frustum is what’s left when you slice the pointed top off a cone — a tapered shape with a narrow end and a wide end. This calculator finds its volume in cubic feet, cubic yards, gallons, and liters from the two diameters and the height.
How this calculator works
The frustum formula extends the cone formula to account for both the top and bottom radii, not just one.
Formula: Cubic feet = (π × height ÷ 3) × (R² + R×r + r²), where R is the bottom radius and r is the top radius, both in feet.
Worked example
A frustum with a 4 ft top diameter, 8 ft bottom diameter, and 6 ft height:
- Bottom radius (R): 8 ÷ 2 = 4 ft; top radius (r): 4 ÷ 2 = 2 ft
- Cubic feet: (π × 6 ÷ 3) × (4² + 4×2 + 2²) = 2π × 28 ≈ 175.93 ft³
- Cubic yards: 175.93 ÷ 27 ≈ 6.516 yd³
- Gallons: 175.93 × 7.48 ≈ 1,316.0 gal
- Liters: 1,316.0 × 3.785 ≈ 4,981.8 L
Reference
| Top × Bottom × Height | Cubic feet |
|---|---|
| 2 × 4 × 3 ft | 21.99 ft³ |
| 4 × 8 × 6 ft | 175.93 ft³ |
| 6 × 12 × 8 ft | 527.79 ft³ |
How to measure
Measure the diameter across the flat top, the diameter across the flat bottom, and the vertical distance between the two — not the slanted side. For a flat-topped stockpile that hasn’t been measured yet, the Stockpile Volume Calculator walks through estimating pile dimensions directly.
Frequently asked questions
What is a frustum, in plain terms?
It's a cone with the pointed top sliced off flat, leaving two different-sized circular ends — a narrower top and a wider bottom (or vice versa). A bucket, a lampshade, a hopper, and a flat-topped gravel pile are all frustum shapes.
What if the top diameter is zero?
Then it's a full cone, not a frustum, and the formula still works — it just reduces to the standard cone volume formula since the top circle shrinks to a point.
What if the top and bottom diameters are equal?
Then it's a plain cylinder, and the frustum formula reduces to that as well. A frustum calculator covers cylinders and cones as special cases.
Where do frustum shapes show up in construction?
Flat-topped stockpiles of gravel or sand, tapered concrete footings, hoppers and chutes, tapered retaining wall sections, and truncated silos are all frustums. Anywhere material naturally settles into a cone but doesn't come to a sharp point.
Does the height need to be vertical?
Yes — use the perpendicular (vertical) height between the two flat ends, not the slanted side length. Measuring along the slope will overstate the height and the volume.
Estimates only. Verify quantities with your supplier before purchasing.