Specific weight (also called weight density and denoted by γ) of a fluid is defined as the weight of the fluid per unit volume:

γ = W / V

Its SI unit is therefore newton per cubic metre (N/m³). It represents how heavy a unit volume of the fluid is, and it links directly to mass density ρ through the acceleration due to gravity:

γ = ρ × g

where ρ is in kg/m³ and g ≈ 9.81 m/s². For water, taking ρ = 1000 kg/m³, this gives γ ≈ 1000 × 9.81 = 9810 N/m³. Because specific weight depends on g, it varies slightly with location, unlike density, which is a property of the fluid alone. So the correct definition is the weight of fluid per unit volume.

• The weight of fluid per unit mass would give W/m = g, which is simply the acceleration due to gravity, not specific weight; this describes the ratio that yields g, not a fluid property.
• The weight of fluid per unit pressure has no standard physical meaning as a fluid property and does not correspond to any recognised definition.
• The weight of fluid per unit force is dimensionless (force divided by force) and is likewise not a meaningful definition of specific weight.

Hence specific weight is correctly defined as the weight of fluid per unit volume.