Density, specific weight and specific gravity

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Density is defined as an objects mass per unit volume. Can be expressed by
rho = mass/Volume = 1/specific volume

where rho is density (kg/m^3)
mass (m) with the unit (kg)
Volume (V) with the unit (m^3)

Specific weight is defined as weight per unit volume. Weight = force. The equation is

gamma = rho * g

where gamma is specific weight with the unit (N/m^3)
rho is density (kg/m^3)
g is symbol for gravity acceleration (m/s²)

Specific gravity - SG
For liquid is a dimensionless unit defined as the ratio of density of the liquid to density of water at specified temperature.

SG = rho/rho H2O

where SG is specific gravity (N/m^3)
rho is density (kg/m^3)
rho of H2O is density of water (kg/m^3) , common to use the density of water at 4°C (39°F) = 1000 kg/m^3

for gas

SG = rho/rho O2

where SG is specific gravity (N/m^3)
rho is density (kg/m^3)
rho of O2 is density of air (kg/m^3) , common to use the density of water at 20°C (68°F), 1 atm = 1.205 kg/m^3

Source : engineeringtoolbox