cone volume calculator
Calculate a cone's volume in cubic feet, cubic yards, gallons, and liters from base diameter and height — for stockpiles, hoppers, and funnels.
A cone shape shows up anywhere material piles up naturally or funnels down to a point — gravel stockpiles, sand cones, hoppers, and conical tanks. Enter the base diameter and height to get volume in cubic feet, cubic yards, gallons, and liters.
How this calculator works
Cone volume is one-third of pi times the radius squared, times the height — exactly a third of a cylinder with the same base and height.
Formula: Cubic feet = (1/3) × π × (diameter ÷ 2)² × height. Cubic yards = ft³ ÷ 27. Gallons = ft³ × 7.48052. Liters = ft³ × 28.3168.
Worked example
A cone with a 6 ft base diameter and 8 ft height:
- Radius: 6 ÷ 2 = 3 ft
- Cubic feet: (1/3) × π × 3² × 8 ≈ 75.40 ft³
- Cubic yards: 75.40 ÷ 27 ≈ 2.793 yd³
- Gallons: 75.40 × 7.48052 ≈ 564.0 gal
- Liters: 75.40 × 28.3168 ≈ 2135.0 L
Reference
| Base diameter × Height (ft) | Cubic feet |
|---|---|
| 4 × 6 | 25.13 ft³ |
| 6 × 8 | 75.40 ft³ |
| 8 × 12 | 201.06 ft³ |
How to measure
Measure the base diameter as the footprint width where the pile meets the ground, and the height as the vertical distance straight up to the peak. This is the standard way to check a dumped gravel or sand delivery, size a hopper, or estimate a conical form. For a pile with a flattened top instead of a point, the Cylinder Volume Calculator or a frustum shape is a better fit.
Frequently asked questions
What's the formula for cone volume?
Volume is one-third of pi times the radius squared times the height: V = (1/3) × π × r² × h. It's exactly one-third of a cylinder with the same base and height.
Why is a cone exactly one-third of a cylinder?
A cone tapers from full width at the base to a point at the top, so on average it holds about a third of the material a same-sized cylinder would. The 1/3 factor in the formula captures that taper mathematically.
How do I estimate a gravel or sand pile's volume?
Loose material dumped from a truck or conveyor naturally forms a cone shape. Measure the base diameter (the footprint on the ground) and the height at the peak, and this calculator gives the volume — a quick way to sanity-check a delivered load.
Does this work for a cone-shaped hopper or funnel?
Yes — the same formula applies whether the cone points up (a pile) or down (a hopper). Just measure the diameter of the wide end and the vertical height to the point.
What if my pile isn't a perfect cone?
Real piles are rarely perfect; a lopsided or flattened pile holds somewhat less than the ideal cone. Treat this as an upper-bound estimate and expect actual volume to run a bit lower.
How is this different from the frustum calculator?
A cone comes to a full point. A frustum is a cone with the top sliced off flat — used for truncated piles or tapered forms that don't reach a point. Use the Frustum Volume Calculator when your shape has a flat top.
Estimates only. Verify quantities with your supplier before purchasing.