Unit Weight

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	\(\large{dimensionless}\)