### Table of contents

- Definition
- Formula
- Unit of measurement
- Example on how to calculate specific weight
- Specific weight of water
- Specific weight of air
- Specific weight calculator

### Definition

**Specific weight** is defined as the ratio between weight and volume. **Specific weight** can also be defined as the product between density and gravitational acceleration. **Specific weight**, unlike density, is not absolute, it depends on the value of the gravitational acceleration (g), which varies depending on altitude and latitude.

### Formula

\[\gamma = \frac{G}{V}=\frac{m \cdot g}{V} \tag{1}\]where:

G [N] – weight

V [m^{3}] – volume

m [kg] – mass

g [m/s^{2}] – gravitational acceleration

The density ρ [kg/m^{3}] is the ratio between mass (m) and volume (V):

Replacing the expression of the density (2) in the formula of specific weight (1), we get:

\[\gamma = \rho \cdot g \tag{3}\]### Unit of measurement

The **symbol used for specific weight** is the Greek letter *γ* (gamma). The **SI unit of measurement for specific weight** is [N/m^{3}].

The unit of measurement for specific weight can easily be demonstrated from equation (3). The unit of measurement for density is [kg/m^{3}]. The unit of measurement for gravitational acceleration is [m/s^{2}]. Multiplying them as per equation (3) gives:

We know that 1 N (Newton) is defined as:

\[N = \frac{kg \cdot m}{s^{2}} \tag{5}\]Replacing (5) in (4) gives the unit of measurement for specific weight as [N/m^{3}].

### Example on how to calculate specific weight

**Example 1**. The density of water at 10 °C is 999.75 kg/m^{3}. Knowing that gravitational acceleration is 9.81 m/s^{2}, calculate the **specific weight of water** at 10 °C.

Applying the formula of specific weight (3), we get:

\[\gamma = \rho \cdot g = 999.75 \cdot 9.81 = 9807.5475 \left [ \frac{N}{m^{3}} \right ] \]**Example 2**. The density of air at 20 °C is 1.2041 kg/m^{3}. Knowing that gravitational acceleration is 9.81 m/s^{2}, calculate the **specific weight of air** at 20 °C.

Applying the formula of specific weight (3), we get:

\[\gamma = \rho \cdot g = 1.2041 \cdot 9.81 = 11.812221 \left [ \frac{N}{m^{3}} \right ] \]**Example 3**. The density of mercury at 20 °C is 13600 kg/m^{3}. Knowing that gravitational acceleration is 9.81 m/s^{2}, calculate the **specific weight of mercury** at 20 °C.

Applying the formula of specific weight (3), we get:

\[\gamma = \rho \cdot g = 13600 \cdot 9.81 = 133416 \left [ \frac{N}{m^{3}} \right ] \]### Specific weight of water

Since water density varies with temperature, the **specific weight of water** will be function of temperature.

Water temperature [°F] | Water temperature [°C] | Water density [kg/m^{3}] | Specific weight of water [N/m^{3}] |

32 | 0 | 999.87 | 9808.7247 |

39.2 | 4 | 1000 | 9810 |

40 | 4.4 | 999.99 | 9809.9019 |

50 | 10 | 999.75 | 9807.5475 |

60 | 15.6 | 999.07 | 9800.8767 |

70 | 21 | 998.02 | 9790.5762 |

80 | 26.7 | 996.69 | 9777.5289 |

90 | 32.2 | 995.10 | 9761.931 |

100 | 37.8 | 993.18 | 9743.0958 |

120 | 48.9 | 988.70 | 9699.147 |

140 | 60 | 983.38 | 9646.9578 |

160 | 71.1 | 977.29 | 9587.2149 |

180 | 82.2 | 970.56 | 9521.1936 |

200 | 93.3 | 963.33 | 9450.2673 |

212 | 100 | 958.65 | 9404.3565 |

**Source**: U.S. Department of the Interior, Bureau of Reclamation, 1977, Ground Water Manual, from The Water Encyclopedia, Third Edition, Hydrologic Data and Internet Resources, Edited by Pedro Fierro, Jr. and Evan K. Nyler, 2007.

### Specific weight of air

Since air density varies with temperature, the **specific weight of air** will be function of temperature.

Air temperature [°C] | Air density [kg/m^{3}] | Specific weight of air [N/m^{3}] |

-25 | 1.4224 | 13.953744 |

-20 | 1.3943 | 13.678083 |

-15 | 1.3673 | 13.413213 |

-10 | 1.3413 | 13.158153 |

-5 | 1.3163 | 12.912903 |

0 | 1.2922 | 12.676482 |

5 | 1.2690 | 12.44889 |

10 | 1.2466 | 12.229146 |

15 | 1.2250 | 12.01725 |

20 | 1.2041 | 11.812221 |

25 | 1.1839 | 11.614059 |

30 | 1.1644 | 11.422764 |

35 | 1.1455 | 11.237355 |

**Source**: Wikipedia.

### Specific weight calculator

Density, ρ [kg/m^{3}] | Gravitational acceleration, g [m/s^{2}] |

Specific weight γ [N/m ^{3}] = |

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