# Volume of a sphere in n-dimension Calculator

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

 dimension n n=1,2,3,... radius r 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit volume V surface area S
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.

Volume of a sphere in n-dimension
 [1-10] /10 Disp-Num5103050100200
[1]  2022/12/28 01:41   60 years old level or over / Others / Very /
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.
[2]  2022/11/15 22:28   20 years old level / Self-employed people / Very /
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!
[3]  2022/01/19 10:52   Under 20 years old / High-school/ University/ Grad student / Useful /
Purpose of use
Checking if the volume of a 1-d ball was indeed 2 (yes)
[4]  2021/12/09 12:43   50 years old level / An office worker / A public employee / Very /
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!
[5]  2019/06/26 06:35   20 years old level / High-school/ University/ Grad student / Useful /
Purpose of use
Research
[6]  2015/10/15 22:40   Under 20 years old / High-school/ University/ Grad student / Very /
Purpose of use
Writing my own code that will be able to calculate this. Checking my numerical results with this :)
[7]  2014/11/07 02:21   60 years old level or over / Elementary school/ Junior high-school student / Very /
Purpose of use
I was learning my alphabet today. and this helped me fill in the sphere for the full-stop
Comment/Request
[8]  2014/09/20 16:06   60 years old level or over / An engineer / Very /
Purpose of use
Keeping my mind sharp at 78 years old
[9]  2013/04/24 17:32   50 years old level / An office worker / A public employee / Very /
Purpose of use
Calculate the dimensions of a hypothetical pile of soil
[10]  2009/10/05 07:15   50 level / Self-employed people / Very /
Comment/Request
Excellent Please include other formulae also

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