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

$$\large{ \gamma = \frac{ W_t }{ V_t } }$$

$$\large{ \gamma = \frac{ G_s \;+\; S \; e }{ 1 \;+\; e } \; \gamma_w }$$

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

Symbol 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 $$\large{dimensionless}$$