Density, Specific Weight and Specific Gravity

An introduction and definition of density, specific weight and specific gravity - formulas with examples

Density

Density is defined as an objects mass per unit volume. Mass is a property.

• Mass and Weight - the Difference! - What is weight and what is mass? An explanation of the difference between weight and mass.

The density can be expressed as

ρ = m / V = 1 / v_g         (1)
where
ρ = density (kg/m³)
m = mass (kg)
V = volume (m³)
v_g = specific volume (m³/kg)

The SI units for density are kg/m³. The imperial (U.S.) units are lb/ft³ (slugs/ft³). While people often use pounds per cubic foot as a measure of density in the U.S., pounds are really a measure of force, not mass. Slugs are the correct measure of mass. You can multiply slugs by 32.2 for a rough value in pounds.
The higher the density, the tighter the particles are packed inside the substance. Density is a physical
property constant at a given temperature and density can help to identify a substance.

Relative Density  (Specific Gravity)

Relative density of a substance is the ratio of the substance to the density of water at 4^oC, i.e.

Substance	Relative density
Acetylene	0.0017
Air, dry	0.0013
Alcohol	0.82
Aluminum	2.72
Brass	8.48
Cadmium	8.57
Chromium	7.03
Copper	8.79
Carbon dioxide	0.00198
Carbon monoxide	0.00126
Cast iron	7.20
Hydrogen	0.00009
Lead	11.35
Mercury	13.59
Nickel	8.73
Nitrogen	0.00125
Nylon	1.12
Oxygen	0.00143
Paraffin	0.80
Petrol	0.72
PVC	1.36
Rubber	0.96
Steel	7.82
Tin	7.28
Zinc	7.12
Water (4oC)	1.00
Water, sea	1.02

Example - Use the Density to Identify the Material:

An unknown liquid substance has a mass of 18.5 g and occupies a volume of 23.4 ml. (milliliter).
The density can be calculated as

ρ = [(18.5 g) / (1000 g/kg)] / [(23.4 ml) / (1000 ml/l) (1000 l/m³)]
    = (18.5 10^-3 kg) / (23.4 10^-6 m³)
    = 790 (kg/m³)

If we look up densities of some common substances, we can find that ethyl alcohol, or ethanol, has a density of 790 kg/m³. The liquid may be ethyl alcohol!

Example - Use Density to Calculate the Mass of a Volume

The density of titanium is 4507 kg/m³. Calculate the mass of 0.17 m³ titanium!

m = (0.17 m³) (4507 kg/m³)
    = 766.2 (kg)

Specific Weight

Specific Weight is defined as weight per unit volume. Weight is a force.

• Mass and Weight - the difference! - What is weight and what is mass? An explanation of the difference between weight and mass.

Specific Weight can be expressed as

γ = ρ g         (2)
where
γ = specific weight (N/m³)
ρ = density (kg/m³)
g = acceleration of gravity (m/s²)

The SI-units of specific weight are N/m³. The imperial units are lb/ft³. The local acceleration g is under normal conditions 9.807 m/s² in SI-units and 32.174 ft/s² in imperial units.

Example - Specific Weight Water

Specific weight for water at 39 ^oF (4 ^oC) is 62.4 lb/ft³ (9.81 kN/m³) in imperial units. Specific weight in SI units can be calculated like

γ = (1000 kg/m³) (9.81 m/s²)
    = 9810 (N/m³)
    = 9.81 (kN/m³)

Example - Specific Weight Some other Materials

Product	Specific Weight - γ
	Imperial Units (lb/ft3)	SI Units (kN/m3)
Aluminium	172	27
Brass	540	84.5
Copper	570	89
Ethyl Alcohol	49.3	7.74
Gasoline	42.5	6.67
Glycerin	78.6	12.4
Mercury	847	133.7
SAE 20 Oil	57	8.95
Seawater	64	10.1
Stainless Steel	499 - 512	78 - 80
Water	62.4	9.81
Wrought Iron	474 - 499	74 - 78

Specific Gravity (Relative Density)

Specific Gravity Liquids

The Specific Gravity - SG - of a liquid is a dimensionless unit defined as the ratio of density of the liquid to the density of water at a specified temperature. Specific Gravity of a liquid can be expressed

SG = ρ / ρ_H2O         (3)
where
SG = specific gravity
ρ = density of fluid or substance (kg/m³)
ρ_H2O = density of water (kg/m³)

It is common to use the density of water at 4 ^oC (39^oF) as reference - at this point the density of water is at the highest - 1000 kg/m³ or 62.4 lb/ft³.

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Since Specific Weight is dimensionless it has the same value in the metric SI system as in the imperial English system (BG). At the reference point the Specific Gravity has same numerically value as density.

Example - Specific Gravity

If the density of iron is 7850 kg/m³, 7.85 grams per cubic centimeter (cm³), 7.85 kilograms per liter, or 7.85 metric tons per cubic meter - the specific gravity of iron is:

SG = (7850 kg/m³) / (1000 kg/m³)
    = 7.85

• water density is 1000 kg/m³

Specific Gravity Gases

The Specific Gravity - SG - of a gas is a dimensionless unit defined as the ratio of density of the gas to the density of air at a specified temperature and pressure. In general conditions according NTP - Normal Temperature and Pressure - defined as air at 20^oC (293.15 K, 68^oF) and 1 atm ( 101.325 kN/m2, 101.325 kPa, 14.7 psia, 0 psig, 30 in Hg, 760 torr), where density of air is 1.205 kg/m³ is used.

Specific Gravity of a gas can be expressed

SG = ρ / ρ_air         (3)
where
SG = specific gravity
ρ = density of gas or substance (kg/m³)
ρ_air = density of air (kg/m³)