What is the formula for the volume of a cone?

V = (1/3) × π × r² × H, where r is the base radius and H is the height (perpendicular distance from base to tip), both in feet.

How is the cone formula related to the cylinder formula?

A cone is exactly one-third the volume of a cylinder with the same base radius and height. That is why the formula has a 1/3 factor compared to the cylinder formula π × r² × H.

How do I calculate the volume of a sand or gravel pile?

Most piles are roughly conical. Measure the radius at the base (or circumference and divide by 2π) and the height. Use V = (1/3) × π × r² × H. Add 5–10% for irregularities.

What is the cubic feet of a 4-foot-radius cone, 6 feet tall?

V = (1/3) × π × 16 × 6 ≈ 100.53 ft³, or about 3.72 cubic yards.

Cubic Feet of a Cone Calculator — Free (1/3)πr²h Volume & Frustum Support

How to calculate cubic feet of a cone

A cone has a circular base and tapers smoothly to a single point. Its volume is exactly one-third of a cylinder with the same base and height. Measure the base radius and the perpendicular height (not the slant height), then apply the formula.

Cone

V = (1/3) × π × r² × H

= For r = 2 ft, H = 6 ft → (1/3) × 3.14159 × 4 × 6 ≈ 25.13 ft³

Use perpendicular height, not slant height

The H in the formula is the straight vertical distance from the base to the tip — not the diagonal length along the side of the cone. If you measured the slant, use the Pythagorean theorem to find the perpendicular height: H = √(slant² − r²).

Worked examples

Example 1: A pile of mulch, 8 ft across the base, 4 ft tall

Radius = 4 ft. V = (1/3) × π × 16 × 4 ≈ 67.02 ft³, or about 2.48 cubic yards.

Example 2: A conical funnel, 10-inch radius, 16 inches deep

r = 0.833 ft, H = 1.333 ft. V = (1/3) × π × 0.694 × 1.333 ≈ 0.97 ft³, or about 7.25 US gallons.

Example 3: A conical hopper, 3 ft radius, 5 ft deep

V = (1/3) × π × 9 × 5 ≈ 47.12 ft³, or 1.74 cubic yards.

Frustums (truncated cones)

A frustum is a cone with the tip cut off. For a frustum with bottom radius R, top radius r, and height H:

Frustum (truncated cone)

V = (1/3) × π × H × (R² + R·r + r²)

Common uses

Sand, gravel, and mulch piles (which form natural cones)
Funnels, conical hoppers, and grain spouts
Conical roofs, turrets, and architectural cones
Traffic cones, party hats, and ice cream cones
Volcanic cones and natural conical formations

Common mistakes to avoid

Forgetting the (1/3) coefficient. A cone holds one-third of a cylinder with the same base and height. Skipping the divide-by-3 triples the answer.
Using diameter instead of radius for the base. Half the diameter is the radius. Plugging diameter into r² quadruples the result.
Treating a frustum as a cone. If your shape has a flat top instead of a point, it is a frustum and needs the truncated-cone formula. Using the simple cone formula on a frustum underestimates the volume.

Expert tips

Do not forget the (1/3) factor. A cone holds exactly one-third of what a cylinder with the same base and height would hold. Skipping the divide-by-3 triples your answer.
For piles of mulch, sand, or gravel, the cone is an estimate.Real piles slump and spread. Use the cone formula on the dimensions you measure, then add 5–10% for typical settling. See the mulch and gravel calculators.
Measure base radius at the widest point. For a cone-shaped pile, the base diameter at ground level is the widest cross-section. Half of that is your radius.
Frustums (truncated cones) are different. A bucket or hopper with a flat top has both a top radius and bottom radius — the simple cone formula underestimates the volume. Use the frustum formula instead, covered above.