Volume and surface elements in different co-ordinate systems
This page outlines the value of different volume and surface elements in several different co-ordinate systems.
System |
Volume |
Surface |
Cartesian |
dV = dx dy dz |
dS = dx dy |
Cylindrical |
dV = r dr dϕ dz |
dS = r dϕ dz |
Spherical |
dV = r2sin ϕ dr dϕ dθ |
dS = r2sin ϕ dϕ dθ |
These elements are computed according to following parametrizations:
Spherical coordinates:
x = rsin ϕ cos θ
y = rsin ϕ sin θ , ϕ ∈ (0,π), θ ∈ (0,2π)
z = rcos ϕ
Cylindrical coordinates:
x = rcos ϕ
y = rsin ϕ , ϕ ∈ (0,2π)
z = z
See also
- Line integral
- Volume integral
- Surface integral
- Spherical coordinates