Mass

• Mass is not completely understood, so it is defined in two very different ways: inertial mass measures how strongly an object resists acceleration while gravitational mass measures how strongly an object attracts other things to itself. It isn't clear why these two different types of mass are the same, but experiments confirm that they are. Strictly speaking, a scale measures weight, but converting weight to mass is straightforward.
  
  

Volume

• Volume measures the spatial size of an object. Although the formula used to calculate volume depends on the object's shape and can be very complicated, thinking of it as width times height times length gives a basic idea. Measuring an object's volume can sometimes be easier than calculating it. Putting an object into a large container of water and measuring the rise in water level can quickly solve the problem, no matter the shape of the object.
  
  

Density

• Density is calculated by dividing an object's mass by its volume. Density is less intuitive than mass or volume, but if you have ever picked up an object and found it much lighter or heavier than you expected, that's because its density is not what you thought. Density usually can't be measured directly, and must be calculated after mass and volume have been determined. Density is sometimes used to describe other quantities divided by volume, such as energy density.
  
  

Function

• Since knowing something's density is no better than knowing its mass and volume, density may seem unimportant, but it is convenient for scientists and engineers. In some situations, density is constant while mass and volume change. Writing the equations that describe these situations using density instead of mass and volume makes the subsequent calculations easier. One famous example of this is when calculating an object's moment of inertia.
  
  

History

• One of the most famous examples of calculating density is the story of Archimedes and the golden crown. Archimedes was asked by the king to determine if his new crown was made of pure gold, but without damaging the crown in any way. Archimedes realized that by submerging the crown in water, he could determine its volume and therefore it density. If the density was less than that of pure gold, it would be proven a fraud.