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Sphere Calculator

Calculate volume, surface area, radius, diameter, and circumference from any known value

Input Values

How to Use the Sphere Calculator

  1. Select Input Type: Choose whether to calculate from radius, diameter, circumference, surface area, or volume
  2. Enter Value: Input the known measurement
  3. View Results: All properties are calculated instantly
  4. Copy Values: Click the copy button next to any result

Understanding Spheres

A sphere is a perfectly round 3D shape where every point on the surface is exactly the same distance (the radius) from the center. It's the 3D analogue of a circle and has the most symmetry of any 3D shape.

Key Properties:

  • All points on surface are equidistant from center
  • Every cross-section through center is a circle
  • Has infinite rotational symmetry
  • Smallest surface area for a given volume
  • No edges or vertices

Great Circles:

A great circle is any circle on the sphere whose center is the same as the sphere's center. The equator and meridians on Earth are examples of great circles. Great circles represent the shortest path between two points on a sphere.

Sphere Formulas

Basic Formulas

d = 2r
Diameter
C = 2πr
Great circle circumference
A = 4πr²
Surface area

Volume & Derived

V = (4/3)πr³
Volume
A_circle = πr²
Great circle area
A/V = 3/r
Surface to volume ratio

Practical Applications

Science & Nature

  • Planets and stars (approximately spherical)
  • Water droplets and bubbles
  • Atoms and molecules (models)
  • Cell biology (bacteria, pollen)
  • Weather balloons

Engineering

  • Storage tanks (pressure vessels)
  • Ball bearings
  • Domes and geodesic structures
  • Radar installations
  • Spherical valves

Sports & Recreation

  • Balls (basketball, soccer, tennis)
  • Marbles and bowling balls
  • Globes and planetariums
  • Exercise balls

Everyday Life

  • Light bulbs and ornaments
  • Eyeballs
  • Beads and pearls
  • Pills and capsules

Frequently Asked Questions

How do I calculate the volume of a sphere?

Use V = (4/3)πr³ where r is the radius. For example, a sphere with radius 5 has volume ≈ 523.6 cubic units.

How do I calculate the surface area?

Use A = 4πr². This equals exactly 4 times the area of a great circle (πr²).

Why is a sphere the most efficient shape?

A sphere has the smallest surface area for a given volume. This minimizes surface tension in bubbles and material use in tanks.

How do I find the radius from volume?

Use r = ∛(3V/(4π)). For V = 100, radius ≈ 2.88 units.