Volume and surface elements in different co-ordinate systems

This page outlines the value of different volume and surface elements in several different coordinate systems.

Note that in the surface area elements dS, the radius r is not a variable but a constant evaluated at the particular value, hence the absence of the dr differential term.

These elements are computed according to following parametrizations:

Spherical coordinates::$\{x\}=r\; ,\; sin\; heta\; ,\; cosvarphi\; quad$:$\{y\}=r\; ,\; sin\; heta\; ,\; sinvarphi\; quad\; ,\; heta\; in\; left(0,pi\; ight),,\; varphiin\; left(0,2pi\; ight)\; quad$:$\{z\}=r\; ,\; cos\; heta\; quad$

Cylindrical coordinates:

:$x\; =\; ho\; cos\; varphiquad$:$y\; =\; ho\; sin\; varphi\; quad\; ,\; varphiin\; left(0,2pi\; ight)\; quad$:$z\; =\; z\; quad$

See also

* Line integral
* Volume integral
* Surface integral
* Spherical coordinates