Sphere Volume Calculator: (4/3)πr³ Step by Step

Sphere Volume Calculator

Enter the radius of a sphere; the tool applies the standard formula V = (4/3)πr³ and reports the volume. Use it to check geometry homework, compare with real-world sizes, and see how small changes in radius sharply change volume (because volume scales with r³).

Radius (r)

Non-negative number; use the same length unit you want for volume cubed (e.g. m → m³).

How it works

Enter the radius of a sphere; the tool applies the standard formula V = (4/3)πr³ and reports the volume. Use it to check geometry homework, compare with real-world sizes, and see how small changes in radius sharply change volume (because volume scales with r³).

The Formula

Volume of a sphere (radius r):
V = (4/3)πr³

Radius must be non-negative. Units of volume match the cube of your radius units (e.g. cm → cm³, inches → in³).

Worked Example

Example: radius 3 cm
If r = 3 cm, then V = (4/3)π(3)³ = (4/3)π·27 = 36π ≈ 113.10 cm³. Doubling the radius to 6 cm multiplies the volume by 8 (since 2³ = 8), giving about 904.78 cm³.

Tips, Assumptions & Limitations

Volume grows with the cube of the radius: if r doubles, V is 8 times larger.
Keep units consistent: if r is in feet, V is in cubic feet.
For a diameter d, use r = d/2 before applying the formula.

FAQ

Use V = (4/3)πr³ where r is the radius. If you only know the diameter d, first set r = d/2, then substitute into the formula.

The volume is expressed in cubic units matching your radius. For example, radius in centimetres gives cubic centimetres; radius in inches gives cubic inches.

The formula assumes a perfect sphere. Real objects are approximations; the result is an ideal mathematical model for study and estimation.

Volume depends on r³, so increasing r increases V much faster than the radius itself. That is why a slightly larger sphere holds disproportionately more space inside.