# Unit Weight

Written by Jerry Ratzlaff on . Posted in Geotechnical Engineering

## Unit weight, abbreviated as $$\gamma$$, is the ratio of the total weight to the total volume.

## Unit Weight formulas

 $$\large{ \gamma = \frac{ W_t }{ V_t } }$$ $$\large{ \gamma = \frac{ G_s \;+\; S \; e }{ 1 \;+\; e } \; \gamma_w }$$ $$\large{ \gamma = \frac{ G_s \; \left( 1 \;+\; w \right) }{ 1 \;+\; e } \; \gamma_w }$$

### Where:

 Units English Metric $$\large{ \gamma }$$  (Greek symbol gamma) = unit weight $$\large{ \frac{lbm}{ft^3} }$$ $$\large{ \frac{N}{m^3} }$$ $$\large{ S }$$ = degree of saturation (expressed as %) $$\large{dimensionless}$$ $$\large{ G_s }$$ = specific gravity of soil $$\large{dimensionless}$$ $$\large{ V_t }$$ = total volume of soil $$\large{ft^3}$$ $$\large{m^3}$$ $$\large{ W_t }$$ = total weight of soil $$\large{lbf}$$ $$\large{N}$$ $$\large{ \gamma_w }$$  (Greek symbol gamma) = unit weight of water $$\large{ \frac{lbm}{ft^3} }$$ $$\large{ \frac{N}{m^3} }$$ $$\large{ e }$$ = void ratio $$\large{dimensionless}$$ 