Characteristics of Density

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Regardless of the extent of your background in the physical sciences, you have almost surely come across the term "density" at some point in your online, television, book or other media travels. You perhaps know that "dense" means "thick" in both literal and metaphorical senses: That friend who never quite "gets" basic jokes or repeatedly tries to "sweeten" his coffee with table salt might be described as such.

In physics, however, density has a specific definition. The density equation is simple: Take the ​mass​ of an object (the SI, or système internationale, unit is the kilogram or kg) whose matter is evenly distributed and ​divide this​ ​value​ by the total ​volume​ of the object (the SI unit in this case being the cubic meter or m3, although often liter or L is used) and ​density​ is the result. For historical reasons, this quantity is often denoted by the Greek letter rho or ​ρ​.

The density formula is therefore

ρ = \frac{m}{V}

"Heavy" vs. Dense

In everyday language, when someone offers the claim "Lead is heavier than mist" or the like, we typically assume that the speaker is talking about a similar "amount," or volume, of each. Strictly speaking, though, if "heavy" implies "massive" or "weighty," and the claim that some unspecified amount of one substance is more massive than an unspecified amount of a different substance is inane. 1,000 liters of air, for example, is heavier than a cubic micrometer of gold.

The Density of Water: a Benchmark

By definition, one liter (1 L) of water at a temperature of 4 degrees Celsius (4 °C) has a mass of a kilogram (1 kg). This is convenient because everyone handles water just about every day, and most people therefore have a decent sense of how "heavy" it is compared to other substances, including metals.

Note that calculating density is meaningless without the proper matching of the units in the numerator and the denominator. That is, if you use kg for mass, you must use m3 for volume. An equivalent unit, grams per milliliter, or g/mL, is more commonly encountered in both scientific and lay contexts. A mL is equivalent to a cubic centimeter or cm3, so this can also be written g / cm3.