Sphere Calculator

Calculate volume, surface area, and other properties of a sphere

Calculation Results

Enter sphere measurements to calculate all properties.

Sphere Diagram

r = 0 V = 0

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

r

Radius (r)
Distance from center to surface

d

Diameter (d)
d = 2r

V

Volume (V)
V = (4/3)πr³

S

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

1. What's the difference between a sphere and a circle?

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.

2. How do you find the radius if you know the volume?

Use the formula: r = ∛(3V / 4π) where V is volume.

3. Can a sphere have a negative radius?

No, radius is always a non-negative value. A radius of zero represents a single point.