Sphere Volume Calculator
Volume and surface area of a sphere from its radius.
Input sheet
DIY at your own risk. Calcora's calculators and guides are general estimates and information only — not professional, engineering, legal, or safety advice. Always verify local building codes and permit requirements, and hire a licensed pro for electrical, gas, plumbing, structural, or any work you're not fully comfortable doing yourself.
Balls, balloons, planets, and ball bearings are spheres, and both their volume and surface area follow from a single measurement: the radius.
How it works
Volume is 4/3 × pi × radius³; surface area is 4 × pi × radius².
Volume rises with the cube of the radius, so a sphere with twice the radius holds eight times as much. Surface area rises with the square of the radius, growing more slowly than volume as the sphere enlarges.
Both formulas hinge on pi (π ≈ 3.14159). The four-thirds factor in the volume comes from integrating the circular cross-sections that stack to form the sphere.
Volume = 4/3 × π × radius³; surface area = 4 × π × radius²
Worked examples
A sphere with a radius of 4. → ≈ 268.08 cubic units
4/3 × π × 4³ = 4/3 × π × 64 ≈ 268.08; surface area is 4 × π × 16 ≈ 201.06.
A ball with a radius of 3. → ≈ 113.10 cubic units
4/3 × π × 3³ = 4/3 × π × 27 = 36π ≈ 113.10.
Tips & gotchas
- If you measured the diameter, halve it for the radius before computing.
- Because volume scales with the cube of the radius, small radius errors balloon — measure carefully for precise results.
- As a sphere grows, its volume-to-surface ratio rises, which is why large animals lose body heat more slowly than small ones.
FAQ
Why does volume grow so much faster than surface area?
Volume depends on radius cubed while surface area depends on radius squared, so each added unit of radius adds more volume than surface.
How do I get the radius from the circumference of a great circle?
Divide the circumference by 2π. The radius equals circumference ÷ 6.2832.
Is a hemisphere just half the volume?
Yes for volume — half a sphere's volume. But its surface area is the curved half plus the flat circular base, not simply half the sphere's surface.
Related calculators
Percentage Calculator · Percent Change Calculator · Average (Mean) Calculator · Ratio Calculator · Exponent Calculator