# Specific weight

### 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.

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### Formula

$\gamma = \frac{G}{V}=\frac{m \cdot g}{V} \tag{1}$

where:
G [N] – weight
V [m3] – volume
m [kg] – mass
g [m/s2] – gravitational acceleration

The density ρ [kg/m3] is the ratio between mass (m) and volume (V):

$\rho = \frac{m}{V} \tag{2}$

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

$\gamma = \rho \cdot g \tag{3}$

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### 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/m3].

The unit of measurement for specific weight can easily be demonstrated from equation (3). The unit of measurement for density is [kg/m3]. The unit of measurement for gravitational acceleration is [m/s2]. Multiplying them as per equation (3) gives:

$\frac{kg}{m^{3}} \cdot \frac{m}{s^{2}} = \frac{kg \cdot m}{m^{3} \cdot s^{2}} \tag{4}$

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/m3].

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### Example on how to calculate specific weight

Example 1. The density of water at 10 °C is 999.75 kg/m3. Knowing that gravitational acceleration is 9.81 m/s2, 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/m3. Knowing that gravitational acceleration is 9.81 m/s2, 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/m3. Knowing that gravitational acceleration is 9.81 m/s2, calculate the specific weight of mercury at 20 °C.

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

$\gamma = \rho \cdot g = 13600 \cdot 9.81 = 133416 \left [ \frac{N}{m^{3}} \right ]$

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### 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/m3] Specific weight of water [N/m3] 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.

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### 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/m3] Specific weight of air [N/m3] -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.

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### Specific weight calculator

 Density, ρ [kg/m3] Gravitational acceleration, g [m/s2] Specific weight γ [N/m3] =

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