Sphere Calculator
Calculate volume, surface area, and other properties of a sphere
Calculation Results
Enter sphere measurements to calculate all properties.
Radius (r): units
Diameter (d): units
Volume (V): cubic units
Surface Area (S): square units
Circumference (C): units
Sphere Diagram
Sphere Formulas
Key Properties
- Radius (r): Distance from center to surface
- Diameter (d): Twice the radius (d = 2r)
- Volume (V): Space contained within the sphere
- Surface Area (S): Total area of the sphere's surface
- Circumference (C): Perimeter of the great circle (C = 2πr)
Calculation Formulas
- Volume (V): V = (4/3)πr³
- Surface Area (S): S = 4πr²
- Diameter (d): d = 2r
- Circumference (C): C = 2πr = πd
Where: r = radius, d = diameter, π ≈ 3.14159
Example Calculation
For a sphere with:
Radius (r) = 5 units.Calculations:
- Diameter = 2 × 5 = 10 units
- Volume ≈ (4/3) × π × 5³ ≈ 523.6 units³
- Surface Area ≈ 4 × π × 5² ≈ 314.16 units²
- Circumference ≈ 2 × π × 5 ≈ 31.42 units
About Spheres
A sphere is a perfectly symmetrical three-dimensional shape where every point on its surface is equidistant from its center. It has no edges or vertices and is characterized by its radius (r).
Real-World Applications
- Astronomy: Planets and stars are approximately spherical
- Sports: Balls in basketball, soccer, and tennis
- Engineering: Ball bearings and pressure vessels
- Everyday Objects: Marbles, bubbles, and globes
Special Properties
- Minimal Surface Area: For a given volume, a sphere has the smallest possible surface area.
- Symmetry: All points on the surface are identical.
- No Edges or Corners: Smooth and continuous surface.
Sphere Components
Radius (r)
Distance from center to surface
Diameter (d)
d = 2r
Volume (V)
V = (4/3)πr³
Surface Area (S)
S = 4πr²
How to Use the Sphere Calculator
The Sphere Calculator helps compute various properties based on input values. Here's how to use it:
1. Select Calculation Method
Choose what measurements you know:
- Radius - Enter the radius
- Diameter - Enter the diameter
- Volume - To find the radius
- Surface Area - To find the radius
2. Enter Your Values
Input positive numbers in the appropriate fields:
Example 1: Radius = 5
Example 2: Volume = 523.6
3. Get Results
The calculator will compute all properties:
- Radius (r)
- Diameter (d)
- Volume (V)
- Surface Area (S)
- Circumference (C)
Practical Applications
- Calculate material needed for spherical structures
- Determine paint required for spherical objects
- Find storage capacity of spherical containers
- Solve physics problems involving spheres
Frequently Asked Questions
A circle is a two-dimensional shape, while a sphere is its three-dimensional counterpart. A sphere has volume, whereas a circle only has area.
Use the formula: r = ∛(3V / 4π) where V is volume.
No, radius is always a non-negative value. A radius of zero represents a single point.