Density Units: Where the Conversions Go Wrong

Mass over volume is the easy half. What throws an answer out by three orders of magnitude is the pair of units you happened to divide, and the mistake is nearly always one of two: a factor of 1,000 inside the metric system, or a factor of 16.02 on the way into pounds and cubic feet.

The three sets of units you will actually meet

Grams per cubic centimetre for anything lab-shaped or metallic. Kilograms per cubic metre for engineering and properly SI work. Pounds per cubic foot for US construction, freight and shipping quotes. Water anchors all three: 1 g/cm³, 1,000 kg/m³, 62.4 lb/ft³. If you are working on something denser than water and your answer in the third system comes out below 62, you have picked up the wrong unit somewhere.

The factor of 1,000 trap

A cubic metre holds 1,000,000 cubic centimetres, and a kilogram holds 1,000 grams. Divide one by the other and the conversion between g/cm³ and kg/m³ comes out at exactly 1,000. People instinctively reach for 100, because there are 100 centimetres in a metre, and end up with aluminium at 270 kg/m³, which would float. Going the other way, lb/ft³ to kg/m³ is a multiplication by 16.02.

How to use the density calculator

Enter any two of mass, volume and density and it solves for the third. Solving for mass is the more common job in practice: you know the material, you have the density from a table, and you want to know what the finished thing will weigh before you build it or ship it.

Where to find the inputs

Mass comes off a scale, and the unit shown on the scale matters more than the number does. Kitchen scales sold in the UK usually default to grams while the same model in the US defaults to ounces. Volume comes from either the dimensions or from displacement. For a rectangular block, multiply the three sides. For anything irregular, lower it into a measuring jug of water and read the rise, since 1 millilitre of displacement is exactly 1 cm³. A refresher on US and UK measurements is worth two minutes if your figures came from mixed sources, and the same care applies when you are converting mass between systems.

A worked example with a real container

Five US gallons of honey. Honey runs about 1.42 g/cm³. Five US gallons is 18.93 litres, which is 18,930 cm³. Multiply by 1.42 and you get 26,881 g, so 26.9 kg or roughly 59 lb before you count the bucket. That is why a five-gallon pail of honey is a two-person lift and a five-gallon pail of water, at 41.7 lb, is not.

Note the word US in that sentence. An imperial gallon is 4.546 litres against the US gallon's 3.785, a difference of 20%. Five imperial gallons of the same honey comes to 32.3 kg. When a figure crosses the Atlantic without its unit attached, check it before you build anything around it.

Common questions

Why is my answer out by a factor of 1,000? Almost always a mixed pair: grams divided by cubic metres, or kilograms divided by cubic centimetres. Convert both inputs into the same system before you divide, rather than trying to patch the answer afterwards by guessing at the factor.

Does temperature change density? Yes, and water does something odd. It is densest at about 4°C, at 1.000 g/cm³, and falls to roughly 0.997 at room temperature. Ice is 0.917, lighter than the liquid it came from, which is why icebergs float and why pipes burst rather than dent.

Is specific gravity the same thing? Nearly. Specific gravity is density divided by the density of water, so it is the same number you would write in g/cm³ with the units stripped off. Aluminium at 2.70 g/cm³ has a specific gravity of 2.70. It travels between unit systems unchanged, which is precisely why engineers use it.

How do I get the volume of an awkward shape? Displacement, as long as the object sinks and does not soak up water. Otherwise break it into shapes you can measure and add the volumes together. For anything porous you are measuring bulk density rather than material density, and the two can differ by a great deal.