Density, Unit Weight, and Specific Gravity

γ = ρ g SG = ρ / ρ_{w} = γ / γ_{w}

Mass density ρ is mass per volume. Unit weight γ = ρg. Specific gravity SG is the ratio of density (or unit weight) to that of water (ρw ≈ 1000 kg/m³, γw = 9.81 kN/m³ or 62.4 pcf). Used for concrete, soil solids Gs, and liquids.

$ρ$ (kg/m³): Mass density
$γ$ (kN/m³): Unit weight
$SG$: Specific gravity

Step-by-step solved example

Concrete ρ = 2400 kg/m³. Find γ and SG (g = 9.81 m/s², ρw = 1000 kg/m³).

SG compares a material density to water in the phase diagram sense.

1. Unit weight
γ = 2400×9.81 = 23 544 N/m³ = 23.5 kN/m³.
$γ = 23.5 kN / m^{3}$
2. SG
SG = 2400/1000 = 2.40.

Answer: γ = 23.5 kN/m³, SG = 2.40

10 practice questions

0/10 correct

1.γ equals

2.SG of water is

3.ρ = 7850 kg/m³ (steel). SG ≈

4.γw in pcf is about

5.If SG = 2.70 (quartz), ρ ≈

6.Unit weight of water in SI is nearest

7.A voidless material with Gs = 2.65 has dry unit weight

8.Mass of 2.0 m³ of concrete at 2400 kg/m³ is

9.SG is dimensionless because it is a

10.Apparent SG of an aggregate uses