# 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 6dgt10dgt14dgt18dgt22dgt26dgt30dgt34dgt38dgt42dgt46dgt50dgt 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. $\normal Sphere\ in\ n-dimensional\ space\\(1)\ volume:\hspace{50} V={\large\frac{\pi^{\normal\frac{n}{2}}r^n}{\Gamma({\large\frac{n}{2}}+1)}}\\(2)\ surface\ area:\hspace{10} S={\large\frac{dV}{dr}}={\large\frac{2\pi^{\normal\frac{n}{2}}r^{n-1}}{\Gamma({\large\frac{n}{2}})}}\\$

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