How To Convert From Grams To Liters Using Density

Densities tell you how much mass occupies a certain amount of space, so if you need to find the amount of liters something will take up based on its mass, all you need is the density of the material in question. Anybody can do the calculation, provided you can find the specific density you need online. The formula you need is:

\(V=\frac{m}{\rho}\)

From there, convert from the "volume" unit you use for the density to liters, and you'll have your answer.

Imagine that you have two boxes containing different amounts of balls. The first has 10 balls in it, and the second has 15 balls in it, but both boxes are exactly the same size. If each box can hold a maximum of 20 balls, the first box is 50 percent full and the second one is 75 percent full, and you know the second one will be heavier than the first. The second box has a higher "density" than the first one because it has more mass crammed into the same amount of space. When scientists or engineers use density, they define it more precisely as the "mass (​m​) per unit of volume (​V​)." It has the symbol ​ρ​:

\(\rho=\frac{m}{V}\)

For the box example, if they were cubes with 1-meter-long sides and the balls weighed 1 kilogram each, the density of the first box would be 10 kg per cubic meter, and the second would be 15 kg per cubic meter. For real-world calculations, you'd be looking at something like water (​ρ​ = 1 gram per cubic centimeter) or lead (​ρ​ = 11.3 grams per cubic centimeter). There are many lists of common densities online (see Resources), so you can easily look it up for whatever you need.

Look up the density you need online (see Resources). For water, the density is 1 gram/cubic centimeter, or in symbols ​ρ​ = 1 g/cm³. If you have 500 g of water, you use the volume equation. To find the volume the water occupies. You can calculate this for water really easily:

\(V=\frac{500\text{ g}}{1\text{ g/cm}^3}=500\text{ cm}^3\)

Whereas 500 g of lead (​ρ​ = 11.3 g/cm³) occupies:

\(V=\frac{500\text{ g}}{11.3\text{ g/cm}^3}=44.2\text{ cm}^3\)

The same mass of lead occupies much less volume than water because it's much denser.

Now convert the volume in cm³ into liters, noting that 1 cm³ = 0.001 liter = 1 milliliter. Simply convert the cm³ directly into milliliters, and remember that there are 1,000 milliliters in 1 liter.

Using the previous examples, 500 g of water occupies 500 cm³ = 500 milliliters = 0.5 liters.

And 500 g of lead occupies 44.2 cm³ = 44.2 milliliters = 0.0442 liters.