Sphere Calculator

Calculate sphere volume, surface area, diameter, and circumference from radius.

By Konstantin Iakovlev · Updated September 2026 · Source: Khan Academy

Volume

523.5988

Surface Area

314.1593

Properties

Diameter10.0000
Circumference31.4159
V = 4/3 πr³523.5988
SA = 4πr²314.1593

Use the Sphere Calculator above to calculate your results. Enter your values and see instant results — all calculations run in your browser.

Disclaimer: This calculator is for informational purposes only. Results are estimates based on the information you provide and the assumptions described on this page.

How It Works

Give the calculator a radius and it returns the volume, surface area, diameter, and circumference of the sphere in one pass. Engineers, architects, and astronomers all lean on these quantities. Volume in particular drives the design of spherical storage tanks, since a sphere encloses the most volume for a given surface area.

The four outputs follow directly from classical geometry. For radius 'r', the diameter (d) equals 2r and the circumference (C) of the great circle is 2πr. Surface area (A) works out to 4πr², and volume (V) to (4/3)πr³. Every result carries a high-precision value of Pi (π ≈ 3.1415926535) so accuracy doesn't drift.

Watch the input itself: the most frequent error is feeding in a diameter where a radius belongs, which doubles every dimension downstream. Units travel through untouched, so a radius in meters yields volume in cubic meters and surface area in square meters. And because rounding too early quietly compounds, hold onto enough significant figures for whatever your application demands.

Example: Calculating for a Spherical Hydrogen Storage Tank

  1. 1 Input Radius: Let's say we're designing a spherical hydrogen storage tank with a radius of 5 meters.
  2. 2 Calculations: Using the provided radius (r = 5 m), the calculator shows Diameter = 2 × 5 = 10.0000 m, Circumference = 2 × π × 5 = 31.4159 m, Surface Area = 4 × π × 5² = 314.1593 m² and Volume = (4/3) × π × 5³ = 523.5988 m³.
  3. 3 Results: For a spherical tank with a 5-meter radius, the diameter is 10 meters, the great circle circumference is approximately 31.42 meters, the surface area is about 314.16 square meters, and the volume is roughly 523.60 cubic meters.
  4. 4 Context: Hydrogen gas at 0 °C and 1 atmosphere has a density of about 0.08988 kg per cubic meter (NIST Chemistry WebBook), so at that pressure the 523.60 m³ tank would hold only about 47.06 kg. That low density is why hydrogen is stored in high-pressure tanks (350–700 bar) or as a cryogenic liquid (U.S. Department of Energy).

Source: Khan Academy · Last updated: September 2026

Frequently Asked Questions

How do you calculate the volume of a sphere?
Volume equals (4/3)πr³. For a sphere with radius 6, volume is (4/3) x π x 216 = 904.78 cubic units.
How do you find the surface area of a sphere?
Surface area equals 4πr². For a sphere with radius 5, surface area is 4 x π x 25 = 314.16 square units.
How do you find the radius of a sphere from volume?
Radius equals the cube root of (3V / 4π). For a volume of 500 cubic inches, radius = cube root of (1500 / 4π) = cube root of (119.37) = 4.92 inches.

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