What is the formula for the cubic feet of a sphere?

V = (4/3) × π × r³, where r is the radius in feet. For r = 3 ft: (4/3) × π × 27 ≈ 113.10 ft³.

How do I find sphere volume from the diameter?

Divide the diameter by 2 to get the radius, cube it, multiply by π, then multiply by 4/3. For an 8-foot-diameter sphere: r = 4 ft, V ≈ 268.08 ft³.

Why is the sphere formula (4/3) π r³?

The factor 4/3 comes from integrating circular cross-sections of varying radius along the diameter. It can also be derived from the volume of a cone times 4 — Archimedes proved this around 250 BCE.

How many cubic feet is a 5-foot-diameter sphere?

Radius = 2.5 ft. V = (4/3) × π × 2.5³ = (4/3) × π × 15.625 ≈ 65.45 ft³, or about 489.5 US gallons of water.

Cubic Feet Sphere Calculator — Free (4/3)πr³ Volume from Radius (in ft³)

How to calculate cubic feet of a sphere

A sphere is a perfectly round 3D object — every point on the surface is equidistant from the center. The single measurement you need is the radius. Cube it, multiply by π, and multiply by 4/3 to get the volume.

Sphere

V = (4/3) × π × r³

= For r = 3 ft → (4/3) × 3.14159 × 27 ≈ 113.10 ft³

Diameter vs. radius

If you have the diameter (the distance across the sphere through the center), divide by 2 to get the radius before plugging into the formula.

Worked examples

Example 1: A 6-foot-diameter weather balloon

Radius = 3 ft. V = (4/3) × π × 27 ≈ 113.10 ft³.

Example 2: A 4-foot-diameter spherical propane tank

Radius = 2 ft. V = (4/3) × π × 8 ≈ 33.51 ft³ of internal capacity.

Example 3: A 12-inch ornamental ball

Radius = 6 in = 0.5 ft. V = (4/3) × π × 0.125 ≈ 0.524 ft³.

Hemispheres and partial spheres

For a hemisphere (half a sphere), the volume is exactly half the sphere formula: V = (2/3) × π × r³. For a spherical cap (a slice of a sphere), use V = (π × h² × (3r − h)) / 3, where h is the cap height.

Common uses

Spherical pressure vessels and gas tanks
Ornamental garden globes and gazing balls
Sports balls, weather balloons, and floats
Spherical bearings and ball joints
Geodesic domes (use a hemisphere)

Common mistakes to avoid

Using diameter instead of radius. Sphere volume uses radius cubed. Plugging diameter in gives 8× the correct answer.
Forgetting the 4/3 coefficient. The full formula is (4/3) × π × r³, not just π × r³.
Mixing units between radius and the answer. If you measure radius in inches, your answer comes out in cubic inches — divide by 1,728 for cubic feet.

Expert tips

Use radius, not diameter. Sphere volume scales with the cube of the radius. Putting diameter into r³ gives an answer 8× too large.
Small radius changes have big volume effects. A 10% larger radius means 33% more volume. When sizing balls, tanks, or domes, even small dimension tolerances matter.
For real-world objects, the formula is an approximation. Sports balls, fruit, and water droplets are not perfect spheres. The formula gets you close enough for shipping or storage; for precision work, use water displacement.
Round up for spherical containers. Capacity ratings on spherical tanks are usually nominal — actual usable volume is 90–95% of the geometric volume once you account for fill levels and outlets.