Sphere Calculator (Volume & Surface Area)
Sphere Calculator (Volume & Surface Area)
A sphere is a perfectly round 3D shape where every point on the surface is the same distance from the center - balls, planets, and bubbles are all (approximately) spheres. Enter the radius (in whatever unit you like), and this calculator finds the volume, surface area, and diameter, along with a diagram and the full step-by-step working.
- V = 4/3πr³, so a sphere with radius 5 has a volume of 4/3 × π × 5³ ≈ 523.60 cubic units - notice the radius is cubed, so doubling the radius multiplies the volume by 8.
- SA = 4πr², exactly four times the area of the sphere's largest circular cross-section (πr²) - a sphere with radius 5 has a surface area of 4 × π × 5² ≈ 314.16 square units.
- A sphere encloses the most volume for the least surface area of any 3D shape - which is exactly why soap bubbles, water droplets, and planets naturally form spheres (surface tension and gravity both minimize surface area for a given volume).
How do I find the volume of a sphere?
Use V = 4/3πr³. A sphere with radius 5 has a volume of 4/3 × π × 5³ ≈ 523.60.
How do I find the surface area of a sphere?
Use SA = 4πr². A sphere with radius 5 has a surface area of 4 × π × 5² ≈ 314.16.
Sphere Calculator (Volume & Surface Area)
A sphere is a perfectly round 3D shape where every point on the surface is the same distance from the center - balls, planets, and bubbles are all (approximately) spheres. Enter the radius (in whatever unit you like), and this calculator finds the volume, surface area, and diameter, along with a diagram and the full step-by-step working.
- V = 4/3πr³, so a sphere with radius 5 has a volume of 4/3 × π × 5³ ≈ 523.60 cubic units - notice the radius is cubed, so doubling the radius multiplies the volume by 8.
- SA = 4πr², exactly four times the area of the sphere's largest circular cross-section (πr²) - a sphere with radius 5 has a surface area of 4 × π × 5² ≈ 314.16 square units.
- A sphere encloses the most volume for the least surface area of any 3D shape - which is exactly why soap bubbles, water droplets, and planets naturally form spheres (surface tension and gravity both minimize surface area for a given volume).
How do I find the volume of a sphere?
Use V = 4/3πr³. A sphere with radius 5 has a volume of 4/3 × π × 5³ ≈ 523.60.
How do I find the surface area of a sphere?
Use SA = 4πr². A sphere with radius 5 has a surface area of 4 × π × 5² ≈ 314.16.