# Units for volume and density

I am a bit confused with using the appropriate units. I have two values for density and volume which contain units of:

Density $\rho$ = kg m^-3

Volume v = m^3

One thing i am confused here is why density is per meters negative cubed and volume is per meters positive cubed?

What is the difference between the two ? I am trying to visualize this in my mind in a physical aspect to understand why this is the case but don't fully understand it.

• Units for volume are not kg m$^3$, just m$^3$. The reason for the negative sign is that density is inversely related to volume. – HDE 226868 Jan 8 '16 at 1:14
• Oops sorry that was a typo for volume. – WDUK Jan 8 '16 at 1:15
• @HDE226868 wikipedia states: Density is kg/m3 which is a postive cubed.. – WDUK Jan 8 '16 at 1:21
• I expanded that into an answer, addressing your comment. – HDE 226868 Jan 8 '16 at 1:24

The units of density you give there are kg$\cdot$m-3. This is equivalent to a different formulation: kg/m3. We now have a positive exponent, because we're treating the total units as a fraction: kilograms over cubic meters.
This leads to a better conceptual interpretation. If our density is $x$ kg/m3, then in every m3 - a cubic meter - there are $x$ kilograms of matter.
• So how would a positive exponent be read if negatives mean per something ? – WDUK Jan 8 '16 at 1:26