Convert Density Units

Density Dimensional Analysis

Density is the amount of mass per unit volume of an object or substance.

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

Density = mass / volume
        = M¹ / L³
        = M¹ L⁻³

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

Understanding Density Units in Metric and US Systems

In the metric system, the International System of Units (SI) uses the kilogram per cubic meter (kg/m³) as the standard unit for expressing density. This unit represents the mass of a substance in kilograms divided by its volume in cubic meters. The kilogram is the base unit of mass in the metric system, and the cubic meter is the base unit of volume.

On the other hand, the US or imperial system employs different units for expressing density. The most common unit is the pound per cubic foot (lb/ft³ or pcf), which represents the mass of a substance in pounds divided by its volume in cubic feet. In this system, the pound is the base unit of mass, and the cubic foot is the base unit of volume.

How to Convert Density from Metric to US Units: kg/m³ to lb/ft³ (pcf)

From the dimensional analysis, we see that density depends on two fundamental units: mass and length.

The conversion factors for fundamental units were established at some point in history. The International Yard and Pound Agreement of 1959 standardized the conversion factors for the pound (lb) and the foot (ft) in relation to the metric system. According to this agreement:

lb = 0.45359237 kg
ft = 0.3048 m

By employing both conversion factors, we can derive a new factor for converting kg/m³ into lb/ft³:

lb/ft³ = 0.45359237 kg / (0.3048 m)³
       = 0.45359237 kg / (0.028316846592 m³)
       = 16.0184633739601396 kg/m³

A more useful way of seen this conversion is by using fractions. We can divide both sides of the equation by 16.018463... kg/m³:

(lb/ft³) / (16.0184633739601396 kg/m³) = 1

Now we can use the left side of the equation as a factor to multiply density measured in kg/m³ so metric density units cancel out, resulting in the US unit we're looking for.

Here's an example of how to convert the density of a 700 kg/m³ plank of wood into US units:

700 kg/m³ · conversion_factor
= 700 kg/m³ · (lb/ft³) / (16.0184633739601396 kg/m³) 
= 700 / 16.0184633739601396 lb/ft³
= 43.6995724033012284 lb/ft³

You probably don't need a precision of 18 digits. Rounding it to six decimals seems enough for most cases:

700 kg/m³ = 43.699572 lb/ft³

How to Convert Density from US Units to Metric: lb/ft³ (pcf) to kg/m³

Using the same procedure, we can convert lb/ft³ to kg/m³. We just have to invert the fraction to have in the denominator the units we need to cancel out:

(16.0184633739601396 kg/m³) / (lb/ft³) = 1

Here's how to convert the density of a plank of wood of 43 lb/ft³ into metric units:

43 lb/ft³ · conversion_factor
= 43 lb/ft³ · (16.0184633739601396 kg/m³) / (lb/ft³)
= 43 · 16.0184633739601396 kg/m³
= 688.793925080286002 kg/m³
= 688.793925 kg/m³

Common Density Values

Here you'll find a list of density references to effectively compare orders of magnitude.

Construction Materials Density

Density in Nature

Osmium is the densest element found on Earth.