# Density, Specific Weight and Specific Gravity

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

**Density** is defined as *mass per unit volume*. Mass is a property and the SI unit for density is [*kg/m*^{3}].

Density can be expressed as

ρ = m / V = 1 / ν

_{ }[1]where

ρ = density [kg/m^{3}], [slugs/ft^{3}]

m = mass [kg], [slugs]

V = volume [m^{3}], [ft^{3}]

ν = specific volume [m^{3}/kg], [ft^{3}/slug]

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

The Imperial (U.S.) units for density are *slugs/ft ^{3}* but

*pound-mass per cubic foot*-

*lb*is often used. Note that there is a difference between pound-force

_{m}/ft^{3}-*(lb*and pound-mass

_{f})*(lb*. Slugs can be multiplied with

_{m})*32.2*for a rough value in pound-mass

*(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/m
^{3}, 1.938 slugs/ft^{3}

See also **Unit converter - mass** and **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 be helpful for identification of substances.

Below on this page: Specific gravity (relative density), Specific gravity for gases, Specific weight, Calculation examples

Se also: Densities for some common materials

Water - Density, Specific Weight and Thermal Expantion Coefficient - variation with temperature at 1, 68 and 680 atm, SI and Imperial units

Air - Density, Specific Weight and Thermal Expantion Coefficient - variation with temperature and pressure, SI and Imperial units

How to measure density of liquid petroleum products

**Example 1: Density of a Golf ball**** Example 2: Using Density to Identify a Material Example 3: Density to Calculate Volume Mass**

**Specific Gravity (Relative Density) **- **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}[2]where

SG = Specific Gravity of the substance

ρ_{substance}= density of the fluid or substance [kg/m^{3}]

ρ_{H2O}= density of water - normally at temperature 4^{o}C [kg/m^{3}]

It is common to use the density of water at 4 ^{o}C (39^{o}F) as a reference since water at this point has its highest density of *1000 kg/m*^{3 }or *1.940 slugs/ft^{3}*.

Since Specific Gravity - SG - is dimensionless, it 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/m ^{3}*. Water is normally also used as reference when calculating the specific gravity for solids.

See also Thermophysical Properties of Water - Density, Freezing temperature, Boiling temperature, Latent heat of melting, Latent heat of evaporation, Critical temperature ...

#### Example 4: Specific Gravity of Iron

#### 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 (4^{o}C) | 1.00 |

Water, sea | 1.027 |

Wood, Oak | 0.77 |

**Specific Gravity of gases** 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.

SG = ρ

_{gas}/ ρ_{air}[3]where

SG = specific gravity of gas

ρ_{gas}= density of gas [kg/m^{3}]

ρ_{air}= density of air (normally at NTP - 1.204 [kg/m^{3}])

- NTP - Normal Temperature and Pressure - defined as 20
^{o}C (293.15 K, 68^{o}F) 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.

See also Thermophysical Properties of Air - density, viscosity, critical temperature and pressure, triple point, enthalpi and entropi, thermal conductivity and diffusicity,......

**Specific Weight** is defined as *weight per unit volume*. Weight is a **force**. The SI unit for specific weight is [N/m^{3}]. The imperial unit is [lb/ft^{3}].

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

γ = ρ a

_{g}[4]where

γ = specific weight (N/m^{3}], [lb/ft^{3}]

ρ = density [kg/m^{3}], [slugs/ft^{3}]

a_{g}= acceleration of gravity (9.807 [m/s^{2}], 32.174 [ft/s^{2}] under normal conditions)

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

**Example 5: Specific Weight of Water**

#### Specific Weight for Some common Materials

Product | Specific Weight - γ - | |
---|---|---|

Imperial Units(lb/ft^{3}) | SI Units(kN/m^{3}) | |

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 |

### Examples

**Example 1: 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} [m^{3}]

The density of the golf ball can then be calculated as

ρ = 45 [g] * 0.001 [kg/g] / 3.8 10^{-5 }[m^{3}] = 1184 [kg/m^{3}]

**Example 2: 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/m

^{3}]))= 18.5 10

^{-3}[kg] /23.4 10^{-6}[m^{3}] = 790 [kg/m^{3}]

If we look up the densities of some common liquids we find that ethyl alcohol - or ethanol - has a density of *789 kg/m ^{3}*. The liquid may be ethyl alcohol!

**Example 3: Density to Calculate Volume Mass**

The density of titanium is 4507 kg/m^{3}. The mass of 0.17 m^{3} volume titanium can be calculated as

m = 0.17 [m

^{3}] * 4507 [kg/m^{3}] = 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.

**Example 4: Specific Gravity of Iron**

The density of iron is 7850 kg/m^{3}. The specific gravity of iron related to water with density 1000 kg/m^{3} is

SG(iron) = 7850 [kg/m

^{3}] / 1000 [kg/m^{3}] = 7.85

**Example 5: Specific Weight of Water **

The density of water is 1000 kg/m3 at 4 °C (39 °F).

The specific weight in SI units is

γ = 1000 [kg/m^{3}] * 9.81 [m/s^{2}] = 9810 [N/m^{3}] = 9.81 [kN/m^{3}]

The density of water is 1.940 slugs/ft3 at 39 °F (4 °C).

The specific weight in Imperial units is

γ = 1.940 [slugs/ft^{3}] * 32.174 [ft/s^{2}] = 62.4 [lb/ft^{3}]

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