# Void Ratio

Written by Jerry Ratzlaff on . Posted in Geotechnical Engineering

Void ratio, abbreviated as e, a dimensionless number, is the ratio of the volume of voids to the volume of solids.

## Void Ratio formulas

 $$\large{ e = \frac {V_v} {V_s } }$$ $$\large{ e = \frac { V_v }{ V_t \;-\; V_v } }$$ $$\large{ e = \frac { n }{ 1 \;-\; n } }$$ $$\large{ e = \frac { w \; G_s }{ S } }$$ $$\large{ e = \left[ \frac { G_s \; \left( 1 \;+\; w \right) \; \gamma_w }{ Y } \right] \; -1 }$$

### Where:

 Units English Metric $$\large{ e }$$ = void ratio $$\large{dimensionless}$$ $$\large{ Y }$$ = bulk density $$\large{\frac{lbm}{ft^3}}$$ $$\large{\frac{kg}{m^3}}$$ $$\large{ S }$$ = degree of saturation (expressed as %) $$\large{dimensionless}$$ $$\large{ n }$$ = porosity $$\large{dimensionless}$$ $$\large{ G_s }$$ = specific gravity of soil $$\large{dimensionless}$$ $$\large{ V_t }$$ = total volume of soil $$\large{ft^3}$$ $$\large{m^3}$$ $$\large{ \gamma_w }$$  (Greek symbol gamma) = unit weight of water $$\large{lbf}$$ $$\large{N}$$ $$\large{ V_s }$$ = volume of solids $$\large{ft^3}$$ $$\large{m^3}$$ $$\large{ V_v}$$ = volume of voids $$\large{ft^3}$$ $$\large{m^3}$$ $$\large{ w }$$ = water content (% moisture contemt) $$\large{dimensionless}$$