# Relative Density

Written by Jerry Ratzlaff on . Posted in Dimensionless Numbers

Relative density, abbreviated as RD or $$D_r$$, a dimensionless number, is the density or ratio of any substance relative to another substance.  It sometimes may be called just gravity or specific gravity.  Traditionally, specific gravity is used to compare the density of a substance relative to air (SG=1) or water (also SG=1).

## relative density formulas

$$\large{ D_r = \frac{\rho_s}{\rho_r} }$$

$$\large{ D_r = \frac{ e_{max} \;-\; e }{ e_{max} \;-\; e_{min} } }$$     (soil)

Symbol English Metric
$$\large{ D_r }$$ = relative density $$\large{dimensionless}$$
$$\large{ \rho_r }$$   (Greek symbol rho) = reference density $$\large{\frac{lbm}{ft^3}}$$ $$\large{\frac{kg}{m^3}}$$
$$\large{ \rho_s }$$   (Greek symbol rho) = substance density $$\large{\frac{lbm}{ft^3}}$$ $$\large{\frac{kg}{m^3}}$$
$$\large{ e }$$ = void ratio $$\large{dimensionless}$$
$$\large{ e_{min} }$$ = void ratio of the soil at its densest condition $$\large{dimensionless}$$