# Conductance and conductivity

What is the relationship between conductance and conductivity? Is there any formula that can explain their relationship?

$$G=\sigma \frac A l$$
where $G$ is the conductance, $σ$ the conductivity, $A$ the cross-sectional area perpendicular to the direction of electric current, and $l$ the length of the conductor. This formula applies for any (geometrically) prismic or cylindrical conductor, including cuboids.
• @ΑλέξανδροςΖεγγ If your object is 2D or 1D (i.e. has zero thickness) there will be no actual material to conduct anything, so it would be 0. If you just have a very thin object with constant thickness then you can use formulas like $G = k\frac{\text{width}}{l}$ (where $k = \sigma \times \text{thickness}$) or $G = k \frac1{l}$ (where $k = \sigma A$), but really they are just the same formula with different arrangements of variables. At the end of the day you still have to either know the value of $A$ or experimentally measure the value of $k$. Feb 19 at 2:57
• Then do the $k$s in the two cases have a proper name? Feb 19 at 3:02
• @ΑλέξανδροςΖεγγ and if your object is 0D, it's essentially a point object. There isn't even a length to conduct across, and the formula boils down to something like $G = k$ where $k = \sigma \frac{A}{l}$, in which case we shouldn't bother about conductivity, since the whole formula literally say "conductance G equals constant k", which basically means that we're directly assigning a value to the conductance rather than calculating anything, and there may as well be no formula. Feb 19 at 3:06