# Volume of a sphere in n-dimension Calculator

## Calculates the volume and surface area of a sphere in n-dimensional space given the radius. | ||

n=1: V=2r (diameter), S=2 n=2: V=πr^2 (circle\ area), S=2πr (circumference) n=3: V=4/3*πr^3 (volume), S=4πr^2 (surface area) A sphere in 4-dimensional space or more is used by statistical mechanics, quantum mechanics, etc. |

[1-10] /10 | Disp-Num |

- Purpose of use
- Looking for a general formula for the surface of a "sphere" in an n-dimensional space, where n is "any" number. For one thing was wondering if there is a 4/3 power relationship for any particular value of n.

- Purpose of use
- Calculate the relative volume enclosed by the unit hypersphere of the [77x768] prompt Tensor for Stable Diffusion when inputs are treated as a flat 59136D space - in explanation of the vastness of the latent space whilst walking off the text-embedding manifold (random walks)
- Comment/Request
- Short simple and sweet, useful and quick. Very helpful - keep it up! Will likely come back to quickly check my working on mobile whilst doing other arithmetic afk. Thanks!

- Purpose of use
- Checking if the volume of a 1-d ball was indeed 2 (yes)

- Purpose of use
- Compare the volume of a 22 dimensional sphere with the fine structure constant. Close, but no cigar.
- Comment/Request
- The only place on the web that has a calculator for hyperdimensional spheres. Thanks for making it free!

- Purpose of use
- Research

- Purpose of use
- Writing my own code that will be able to calculate this. Checking my numerical results with this :)

- Purpose of use
- I was learning my alphabet today. and this helped me fill in the sphere for the full-stop
- Comment/Request
- I want more bugs on this page

- Purpose of use
- Keeping my mind sharp at 78 years old

- Purpose of use
- Calculate the dimensions of a hypothetical pile of soil

- Comment/Request
- Excellent Please include other formulae also

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