Convert Specific Weight Units

Specific Weight Dimensional Analysis

Specific weight, also known as unit weight, is a fundamental quantity in the field of engineering. It represents the weight (force, not mass) present in a given volume.

To better understand the dimensional analysis of specific weight, we can start with the formula derived from its definition, to end up with a set of fundamental base units:

The dimensional analysis stems from the interrelation of two other quantities: force and volume.

specific weight = force / volume 
                = mass · acceleration / volume
                = M¹ · L¹T⁻² / L³ 
                = M¹L⁻²T⁻²

where M, L, and T represent the fundamental base units of mass, length, and time, respectively.

How to calculate Specific Weight?

The specific weight γ (gamma) of a material is equal to its densisty ρ (rho) times the gravity acceleration g:

γ = ρ · g

In Units Center, the gravity acceleration is assumed to be 9.80665 m/s² or ≈32.174049 ft/s² (see standard gravity on Wikipedia).

Specific Weight Conversion Factors

Specific weight can be expressed in various units depending on the system of measurement used. In the International System (SI) or metric system, it is typically measured in units of kN/m³ (kilonewton per cubic meter). In the Imperial system (US/British Customary units), it is typically measured in units of lbf/ft³ (pounds-force per cubic foot), often abbreviated as pcf.

To convert between these units, we can use conversion factors. The tables below provide some commonly used conversion factors for specific weight.

The first table shows the factors rounded to three significant figures for easy reference.

The following two tables show the factors in scientific notation with eight decimal places for greater precision.

How to Use the Specific Weight Conversion Factors

Using the conversion factors shown in the previous tables, you can easily convert units manually. Let's say you have a specific weight of 130 pcf (imperial unit), and want to convert it to the metric unit of kN/m³. If you just need a quick estimate, you can use the factors from the first tables. But, which one?

We have two options:

1. If we read it as 1 kN/m³ equals 6.37 pcf, you can go to the first column, find the row 1 kN/m³, and check the cell at the pcf column:

130 pcf · (1 kN/m³) / (6.37 pcf) 
= 130 / 6.37 kN/m³
= 20.4 kN/m³

2. If we read it as 1 pcf equals 0.157 kN/m³, you can go to the first column, find the row 1 pcf, and check the cell at the kN/m³ column:

130 pcf · (0.157 kN/m³) / (1 pcf) 
= 130 · 0.157 kN/m³ 
= 20.4 kN/m³

Similarly, you can apply the same process to use the more accurate conversion factors provided in the later tables.

Specific Weight Common Values

The specific weight of a material can vary depending on its density, which in turn depends on the material's composition and structure. The following table provides typical specific weights of some common materials used in construction and engineering.

Although concrete is typically thought of as a heavy and dense material, it is actually much less dense than steel. Nevertheless, concrete structures such as buildings and bridges are most of the time heavier than steel structures. That apparent contradiction is due to the resistance of each material. Compared to concrete, steel is much more resistant, so it requires less volume to build the same structure. This results in steel structures being more slender and lighter than concrete structures.

It's worth noting that the specific weight of some porous materials, such as the soils, can be affected by their moisture content. As a result, the values listed in the table may vary under certain circumstances, which should be taken into consideration when using them.

Difference between Specific Weight and Density

It's important to distinguish between specific weight and density since they are often confused with one another. Density measures the mass per unit volume of a material, and its SI unit is kg/m³. On the other hand, specific weight (or unit weight) is the weight per unit volume of a material, and its SI unit is N/m³.

To further illustrate the difference, let's consider a cubic meter of a material with a density of 200 kg/m³. On Earth, the acceleration due to gravity is approximately 9.80665 m/s², so we can calculate the specific weight as:

γ = ρ · g = 200 · 9.80665 = 1961.3300 N/m³

Now, if we were to take the same cubic meter of material to Mars, where the acceleration due to gravity is about 3.72076 m/s², the specific weight would be:

γ = ρ · g = 200 · 3.72076 = 744.1520 N/m³

Here we can clearly see that the specific weight on Earth is almost three times larger than on Mars. However, the density of the material hasn't changed, it's always 200 kg/m³.

Understanding the difference between specific weight and density is crucial in engineering applications such as designing structures.