Sphere volume calculator
Enter the radius and the calculator works out the volume of the sphere and its surface area. Both formulas are shown with the numbers substituted in.
A sphere of radius 6 has a volume of 904.78.
Formula
r is the radius. The radius appears cubed, so a sphere twice as wide has eight times the volume.
How we got there
The surface area of a sphere is 4π r² — exactly four times the area of a circle of the same radius.
How to work out the volume of a sphere by hand
- Cube the radius
For a radius of 6: 6³ = 216.
- Multiply by 4 and by π
4 × π × 216 ≈ 2714.34.
- Divide by 3
2714.34 ÷ 3 ≈ 904.78. That is the volume.
Solid geometry before the exam? a lesson with a Mathema tutor
Frequently asked questions
Use V = 4π r³ ÷ 3. For a radius of 6 that is about 904.78.
The surface area is 4π r², so for a radius of 6 it is about 452.39.
Because the radius is cubed: 2³ = 8.
Unlock the Mathema lesson library
Leave your email and phone — we will take you through to the Mathema platform and open up the preparation library: problem sets, quizzes and lesson plans written by teachers.
Is geometry your weak spot?
Book a free introductory lesson with a Mathema tutor. 30 minutes online, no commitment — we find the gap and the plan to close it.