Sphere Volume Calculator
Calculate sphere volume, surface area, and other properties from radius, diameter, circumference, or volume
Calculate Sphere Properties
Distance from center to surface
Sphere Properties
Real-World Examples
FIFA Soccer Ball (Size 5)
Basketball (Size 7)
Earth
Ping Pong Ball
Sphere Formulas
Volume
Surface Area
From Diameter
From Volume
Sphere Properties
Perfect Symmetry
All points on surface equidistant from center
Maximum Volume
Largest volume for given surface area
No Edges or Vertices
Smooth curved surface everywhere
Constant Curvature
Same curvature at every point
Quick Conversions
Understanding Sphere Volume
What is a Sphere?
A sphere is a perfectly round three-dimensional geometric object. Every point on its surface is exactly the same distance from its center. This distance is called the radius. A sphere is the 3D analog of a circle in 2D space.
Volume Formula Derivation
The sphere volume formula V = (4/3)πr³ can be derived using calculus by integrating circular cross-sections. As you move from the bottom to the top of a sphere, each horizontal slice is a circle with varying radius, and integrating these gives the total volume.
Practical Applications
- •Engineering: Tank and container design
- •Medicine: Calculating medication dosages in spherical pills
- •Sports: Ball specifications and regulations
- •Astronomy: Planetary and stellar volume calculations
- •Architecture: Dome and spherical structure design
Spherical Cap Applications:
Useful for calculating partial volumes in tanks, domes, and spherical containers that are not completely full.
Key Mathematical Relationships
Volume to Surface Area
V/A = r/3
Ratio depends only on radius
Hemisphere
V = (2/3)πr³
Half of sphere volume
Scaling
If r × k, then V × k³
Volume scales with cube of radius