Construction Converter

Calculating Volumes or Mass Through Densities

When working within the context of construction or engineering, we often stumble upon conversion problems between volume and mass, which are always tied to the concept of density. 

Density is a value that is always expressed as MASS / VOLUME.

Calculating Density Manually

Working with density is not difficult, as the unit of density in question is directly the expression of the formula we need, to calculate it.

The general formula requires us to know the volume (V) and the mass (M) in order to calculate the density (D).

D=\frac{M}{V}

Working With Construction Material

The most common usage for this formula can be when working with construction material. The densities of individual materials can be easily found online, on the packaging of the material, they can be requested from the seller of the material, or, simply, they can be found in our calculator directly from a menu that offers a wide array of material choices with their densities.

We often need to know the mass of our construction material, especially when built on fragile ground, where heavy loads could cause issues.

This often requires knowing the dimensions of our construction, then knowing the material we are planning to use, and finally, being able to calculate the mass of that material, based on the density.

Some commonly used construction materials, including their densities, are as follows:

The exact densities of material can differ across the globe, as local regulations and laws may permit different additives and safety requirements for the material itself.

Worked-our Example

We can calculate by having two of the three values: mass, volume, or density.

EXAMPLE 1

A 4,000-pound pile of a specific material fits perfectly into a container with a volume of 40 ft³. What is the density of this material?

We substitute M = 4,000 lb, and V = 40 ft³ into the formula.

D=\frac{M}{V}=\frac{4,000}{40}

=100 lb/ft^3

We use a unit of lb/ft³ since we have our mass in pounds and volume in ft³. That is about 1,600 kg/m³.

EXAMPLE 2

A 2.7-ton (US short ton) pile of sand has been delivered. What volume will this pile take up, assuming a density of 90 lb/ft³ (about 1,440 kg/m³)?

We will convert 2.7 tons = 5,400 lb (1 US ton = 2,000 lb).

We substitute M = 5,400 lb and D = 90 lb/ft³ into the formula.

D=\frac{M}{V}

90 = \frac{5,400}{V}

90V = 5,400

V = 60

This means, that the volume of this pile of sand is 60 ft³ (about 2.22 yd³, or 1.7 m³).

EXAMPLE 3

How heavy are 250 ft³ of a material with a density of 75 lb/ft³ (about 1,200 kg/m³)?

We substitute V = 250 ft³ and D = 75 lb/ft³ into the formula.

D=\frac{M}{V}

75=\frac{M}{250}

18,750 = M

Hence, the weight of this material is 18,750 lb (about 9.4 US tons, or 8,505 kg).