Density, Specific Weight and Specific Gravity

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

Density

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

• What is weight and what is mass? - the difference between weight and mass

Density can be expressed as

ρ = m / V
   = 1 / ν         (1)
where
ρ = density (kg/m³, slugs/ft³)
m = mass (kg, slugs)
V = volume (m³, ft³)
ν = specific volume (m³/kg, ft³/slug)

The SI units for density are kg/m³ - the Imperial (U.S.) units are slugs/ft³.
Pounds per cubic foot - lb/ft³ - is often used as a measure of density in the US, but 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 (lb_m).

• 1 slug = 32.174 lb_m = 14.594 kg 
• 1 kg = 2.2046 lb_m = 6.8521x10^-2 slugs
• density of water: 1000 kg/m³, 1.938 slugs/ft³
• Unit converter - mass
• Unit converter - density

On atomic level - particles are packed tighter inside a substance with higher density. Density is a physical property - constant at a given temperature and pressure - and may helpful for identification of substances.

• densities and properties for some common materials

• density of water at different temperatures - SI and Imperial units

Example - Density of a Golf ball

A golf ball has a diameter of 42 mm and a mass of 45 g. The volume of the golf ball can be calculated as

V = (4 / 3) π ((42 mm) (0.001 m/mm) / 2)³

   = 3.8 10^-5 m³

The density of the golf ball can then be calculated as

ρ = (45 g) (0.001 kg/g) / (3.8 10^-5 m³)

   = 1184 kg/m³

Example - Using Density to Identify a Material

An unknown liquid substance has a mass of 18.5 g and occupies a volume of 23.4 ml (milliliter).
The density of the substance 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 liquids, we find that ethyl alcohol - or ethanol - has a density of 789 kg/m³. The liquid may be ethyl alcohol!

Example - Density to Calculate Volume Mass

The density of titanium is 4507 kg/m³. The mass of 0.17 m³ volume titanium can be calculated as

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

Note! - be aware that there is a difference between "bulk density" and actual "solid or material density". This may not be clear in the description of products. Always double check values with other sources before important calculations.

Specific Weight

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

• What is weight and what is mass? - the difference between weight and mass

Specific Weight (or force per unit volume) can be expressed as

γ = ρ a_g         (2)
where
γ = specific weight (N/m³, lb/ft³)
ρ = density (kg/m³, slugs/ft³)
a_g = acceleration of gravity (9.807 m/s², 32.174 ft/s²)

The SI units for specific weight are N/m³. The imperial units are lb/ft³.
Local acceleration of gravity - a_g - is (under normal conditions) 9.807 m/s² in SI units and 32.174 ft/s² in imperial units.

Example - Specific Weight of Water

The density of water is 1000 kg/m³ at 4 ^oC (39 ^oF). The specific weight in SI units is

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

The density of water is 1.940 slugs/ft³ at 39 ^oF (4 ^oC). The specific weight in Imperial units is

γ = (1.940 slugs/ft³) (32.174 ft/s²)
    = 62.4 (lb/ft³)

Specific Weight for Some common Materials

Product	Specific Weight - γ -
	Imperial Units (lb/ft3)	SI Units (kN/m3)
Aluminum	172	27
Brass	540	84.5
Carbon tetrachloride	99.4	15.6
Copper	570	89
Ethyl Alcohol	49.3	7.74
Gasoline	42.5	6.67
Glycerin	78.6	12.4
Kerosene	50	7.9
Mercury	847	133.7
SAE 20 Motor Oil	57	8.95
Seawater	63.9	10.03
Stainless Steel	499 - 512	78 - 80
Water	62.4	9.81
Wrought Iron	474 - 499	74 - 78

• Material Properties

Specific Gravity (Relative Density)

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

SG = ρ_substance / ρ_H2O         (3)
where
SG = Specific Gravity of the substance
ρ_substance = density of the fluid or substance (kg/m³)
ρ_H2O = density of water - normally at temperature 4 ^oC (kg/m³)

It is common to use the density of water at 4 ^oC (39^oF) as a reference since water at this point has its highest density of 1000 kg/m³ or 1.940 slugs/ft³.
Specific Gravity - SG -  is dimensionless and has the same value in the SI system and the imperial English system (BG). SG of a fluid has the same numerical value as its density expressed in g/mL or Mg/m³. Water is normally also used as reference when calculating the specific gravity for solids.

• Thermal Properties of Water - Density, Freezing temperature, Boiling temperature, Latent heat of melting, Latent heat of evaporation, Critical temperature ...

Specific Gravity for some common Materials

Substance	Specific Gravity - SG -
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	1.027

Example - Specific Gravity of Iron

The density of iron is 7850 kg/m³. The specific gravity of iron related to water with density 1000 kg/m³ is

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

Specific Gravity for Gases

The Specific Gravity of a gas is normally calculated with reference to air - and defined as the ratio of the density of the gas to the density of the air - at a specified temperature and pressure.
The Specific Gravity can be calculated as

SG = ρ_gas / ρ_air         (3)
where
SG = specific gravity of gas
ρ_gas = density of gas (kg/m³)
ρ_air = density of air (normally at NTP - 1.205 kg/m³)

• NTP - Normal Temperature and Pressure - defined as 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)

Molecular weights can be used to calculate Specific Gravity if the densities of the gas and the air are evaluated at the same pressure and temperature.

Related Topics

• Basics - The SI-system, unit converters, physical constants, drawing scales and more
• Fluid Mechanics - The study of fluids - liquids and gases. Involves velocity, pressure, density and temperature as functions of space and time
• Mechanics - Forces, acceleration, displacement, vectors, motion, momentum, energy of objects and more
• Beams and Columns - Deflection and stress, moment of inertia, section modulus and technical information of beams and columns
• Material Properties - Material properties for gases, fluids and solids - densities, specific heats, viscosities and more
• Statics - Loads - force and torque, beams and columns

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