# Specific weight

The specific weight, also known as the unit weight (symbol γ, the Greek letter gamma), is a volume-specific quantity defined as the weight W divided by the volume V of a material: $\gamma =W/V$ Equivalently, it may also be formulated as the product of density, ρ, and gravity acceleration, g: $\gamma =\rho \,g$ Its unit of measurement in the International System of Units (SI) is newton per cubic metre (N/m$^3$), with base units of kg ⋅ m$^{−2}$ ⋅ s$^{−2}$. A commonly used value is the specific weight of water on Earth at 4 °C (39 °F), which is 9.807 kilonewtons per cubic metre or 62.43 pounds-force per cubic foot.

## Discussion

The density of a material is defined as mass divided by volume, typically expressed in units of kg/m$^3$. Unlike density, specific weight is not a fixed property of a material, as it depends on the value of the gravitational acceleration, which varies with location (e.g., Earth's gravity). For simplicity, the standard gravity (a constant) is often assumed, usually taken as 9.81 m/s$^2$.
Pressure may also affect values, depending upon the bulk modulus of the material, but generally, at moderate pressures, has a less significant effect than the other factors.

## Applications
### Fluid mechanics

In fluid mechanics, specific weight represents the force exerted by gravity on a unit volume of a fluid. For this reason, units are expressed as force per unit volume (e.g., N/m$^3$ or lbf/ft$^3$). Specific weight can be used as a characteristic property of a fluid.

### Soil mechanics

Specific weight is often used as a property of soil to solve earthwork problems.
In soil mechanics, specific weight may refer to:

#### Moist unit weight

    The unit weight of a soil when void spaces of the soil contain both water and air. $\gamma ={\frac {(1+w)G_{s}\gamma _{w}}{1+e}}$ where
   * γ is the moist unit weight of the material
   * γ$_w$ is the unit weight of water
   * w is the moisture content of the material
   * G$_s$ is the specific gravity of the solid
   * e is the void ratio

#### Dry unit weight

    The unit weight of a soil when all void spaces of the soil are completely filled with air, with no water. The formula for dry unit weight is: $\gamma _{d}={\frac {G_{s}\gamma _{w}}{1+e}}={\frac {\gamma }{1+w}}$ where
   * γ is the moist unit weight of the material
   * γ$_d$ is the dry unit weight of the material
   * γ$_w$ is the unit weight of water
   * w is the moisture content of the material
   * G$_s$ is the specific gravity of the solid
   * e is the void ratio

#### Saturated unit weight

    The unit weight of a soil when all void spaces of the soil are completely filled with water, with no air. The formula for saturated unit weight is: $\gamma _{s}={\frac {(G_{s}+e)\gamma _{w}}{1+e}}$ where
   * γ$_s$ is the saturated unit weight of the material
   * γ$_w$ is the unit weight of water
   * G$_s$ is the specific gravity of the solid
   * e is the void ratio

#### Submerged unit weight

    The difference between the saturated unit weight and the unit weight of water. It is often used in the calculation of the effective stress in a soil. The formula for submerged unit weight is: $\gamma '=\gamma _{s}-\gamma _{w}$ where
   * γ′ is the submerged unit weight of the material
   * γ$_s$ is the saturated unit weight of the material
   * γ$_w$ is the unit weight of water

### Civil and mechanical engineering

Specific weight can be used in civil engineering and mechanical engineering to determine the weight of a structure designed to carry certain loads while remaining intact and remaining within limits regarding deformation.

## Specific weight of water

Specific weight of water at standard sea-level atmospheric pressure (Metric units) :
| Temperature(°C) | Specific weight (kN/m$^3$) |
| 0 | 9.805 |
| 5 | 9.807 |
| 10 | 9.804 |
| 15 | 9.798 |
| 20 | 9.789 |
| 25 | 9.777 |
| 30 | 9.765 |
| 40 | 9.731 |
| 50 | 9.690 |
| 60 | 9.642 |
| 70 | 9.589 |
| 80 | 9.530 |
| 90 | 9.467 |
| 100 | 9.399 |
Specific weight of water at standard sea-level atmospheric pressure (English units) :
| Temperature(°F) | Specific weight (lbf/ft$^3$) |
| 32 | 62.42 |
| 40 | 62.43 |
| 50 | 62.41 |
| 60 | 62.37 |
| 70 | 62.30 |
| 80 | 62.22 |
| 90 | 62.11 |
| 100 | 62.00 |
| 110 | 61.86 |
| 120 | 61.71 |
| 130 | 61.55 |
| 140 | 61.38 |
| 150 | 61.20 |
| 160 | 61.00 |
| 170 | 60.80 |
| 180 | 60.58 |
| 190 | 60.36 |
| 200 | 60.12 |
| 212 | 59.83 |

## Specific weight of air

Specific weight of air at standard sea-level atmospheric pressure (Metric units) :
| Temperature(°C) | Specific weight (N/m$^3$) |
| −40 | 14.86 |
| −20 | 13.86 |
| 0 | 12.68 |
| 10 | 12.24 |
| 20 | 11.82 |
| 30 | 11.43 |
| 40 | 11.06 |
| 60 | 10.4 |
| 80 | 9.81 |
| 100 | 9.28 |
| 200 | 7.33 |
Specific weight of air at standard sea-level atmospheric pressure (English units) :
| Temperature(°F) | Specific Weight (lbf/ft$^3$) |
| −40 | |
| −20 | 0.0903 |
| 0 | 0.08637 |
| 10 | 0.08453 |
| 20 | 0.08277 |
| 30 | 0.08108 |
| 40 | 0.07945 |
| 50 | 0.0779 |
| 60 | 0.0764 |
| 70 | 0.07495 |
| 80 | 0.07357 |
| 90 | 0.07223 |
| 100 | 0.07094 |
| 120 | 0.06849 |
| 140 | 0.0662 |
| 160 | 0.06407 |
| 180 | 0.06206 |
| 200 | 0.06018 |
| 250 | 0.05594 |