Sphere Volume Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/5/2026
The volume of a sphere is calculated with (4⁄3) × π × radius³, and its surface area with 4 × π × radius². For a sphere with a 3 cm radius, the volume is about 113.10 cm³ and the surface area about 113.10 cm² (a numeric coincidence specific to this exact radius, not a general equality).
Explanation
A sphere is the set of points at a constant distance (the radius) from a center, in three dimensions — the equivalent of a circle, but in space rather than on a plane. Its volume, the space it occupies, is calculated with (4⁄3) × π × r³. Its surface area, the size of its outer shell, is calculated with 4 × π × r². These two formulas only coincide numerically for a radius of exactly 3 (as in the example below): this isn't a general property of spheres, only of this particular case, where the volume in cm³ and the area in cm² happen to share the same numeric value because of the units chosen. For the two-dimensional version of this same shape, see our circle area and circumference calculator; for another common solid, our cylinder volume calculator.
Example: a sphere with a 3 cm radius
Inputs
Radius: 3 cm.
Calculation
Volume: (4⁄3) × π × 3³ = (4⁄3) × π × 27 = 36π ≈ 113.10 cm³. Surface area: 4 × π × 3² = 4 × π × 9 = 36π ≈ 113.10 cm².
Result
A sphere with a 3 cm radius has a volume of about 113.10 cm³ and a surface area of about 113.10 cm².
Frequently asked questions
What's the difference between a sphere and a ball?
In strict mathematical terms, a sphere is only the shell (the hollow outer surface), while a ball is the solid volume it encloses. In everyday language, "sphere" is often used for both interchangeably — this calculator gives the solid volume and the shell's surface area.
Why do the volume and area coincide for a radius of 3?
It's a numeric coincidence: the formulas (4⁄3)πr³ and 4πr² become equal precisely when r = 3, because (4⁄3) × 3³ = 4 × 3². For any other radius, the two values normally differ (see the example with a 1 cm radius, where the volume is much smaller than the area).
How do I calculate the volume from the diameter?
Divide the diameter by 2 to get the radius, then use the usual formula. For example, a 6 cm diameter corresponds to a 3 cm radius.