# Specific weight

The specific weight (also known as the unit weight) is the weight per unit volume of a material. The symbol of specific weight is γ (the Greek letter Gamma).

A commonly used value is the specific weight of water on Earth at 4°C, which is 9.807 kN/m3 or 62.43 lbf/ft3.[1]

The terms specific gravity, and less often specific weight, are also used for relative density.

## General formula

${\displaystyle \gamma =\rho \,g}$

where

${\displaystyle \gamma }$ is the specific weight of the material (weight per unit volume, typically N/m3 units)
${\displaystyle \rho }$ is the density of the material (mass per unit volume, typically kg/m3)
${\displaystyle g}$ is acceleration due to gravity (rate of change of velocity, given in m/s2, and on Earth usually given as 9.81 m/s2)

## Changes of specific weight

Unlike density, specific weight is not absolute. It depends upon the value of the gravitational acceleration, which varies with location. 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. [2]

## Uses

### 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/m3 or lbf/ft3). Specific weight can be used as a characteristic property of a fluid. [2]

### 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, which is the unit weight of a soil when void spaces of the soil contain both water and air.
${\displaystyle \gamma ={\frac {(1+w)G_{s}\gamma _{w}}{1+e}}}$

where

${\displaystyle \gamma }$ is the moist unit weight of the material
${\displaystyle \gamma _{w}}$ is the unit weight of water
w is the moisture content of the material
Gs is the specific gravity of the solid
e is the void ratio
• Dry unit weight, which is 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:

${\displaystyle \gamma _{d}={\frac {G_{s}\gamma _{w}}{1+e}}={\frac {\gamma }{1+w}}}$

where

${\displaystyle \gamma }$ is the moist unit weight of the material
${\displaystyle \gamma _{d}}$ is the dry unit weight of the material
${\displaystyle \gamma _{w}}$ is the unit weight of water
w is the moisture content of the material
Gs is the specific gravity of the solid
e is the void ratio
• Saturated unit weight, which is 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:

${\displaystyle \gamma _{s}={\frac {(G_{s}+e)\gamma _{w}}{1+e}}}$

where

${\displaystyle \gamma _{s}}$ is the saturated unit weight of the material
${\displaystyle \gamma _{w}}$ is the unit weight of water
w is the moisture content of the material
Gs is the specific gravity of the solid
e is the void ratio[3]
• Submerged unit weight, which is defined as the difference between the saturated unit weight and the unit weight of water. [4] It is often used in the calculation of the effective stress in a soil.

The formula for submerged unit weight is:

${\displaystyle \gamma ^{'}=\gamma _{s}-\gamma _{w}}$

where

${\displaystyle \gamma ^{'}}$ is the submerged unit weight of the material
${\displaystyle \gamma _{s}}$ is the saturated unit weight of the material
${\displaystyle \gamma _{w}}$ 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

Temperature(°C)Specific weight (kN/m3)
09.805
59.807
109.804
159.798
209.789
259.777
309.765
409.731
509.690
609.642
709.589
809.530
909.467
1009.399
Specific weight of water at standard sea-level atmospheric pressure (Metric units) [2]

Temperature(°F)Specific weight (lbf/ft3)
3262.42
4062.43
5062.41
6062.37
7062.30
8062.22
9062.11
10062.00
11061.86
12061.71
13061.55
14061.38
15061.20
16061.00
17060.80
18060.58
19060.36
20060.12
21259.83
Specific weight of water at standard sea-level atmospheric pressure (English units) [2]

## Specific weight of air

Temperature(°C)Specific weight (N/m3)
−4014.86
−2013.86
012.68
1012.24
2011.82
3011.43
4011.06
6010.4
809.81
1009.28
2007.33
Specific weight of air at standard sea-level atmospheric pressure (Metric units) [2]

Temperature(°F)Specific Weight (lbf/ft3)
−40
−200.0903
00.08637
100.08453
200.08277
300.08108
400.07945
500.0779
600.0764
700.07495
800.07357
900.07223
1000.07094
1200.06849
1400.0662
1600.06407
1800.06206
2000.06018
2500.05594
Specific weight of air at standard sea-level atmospheric pressure (English units) [2]