What this calculates
Choose what to find — density, mass or volume — enter the other two in any units, and this works out the third. It gives density in kg/m³, g/cm³ and lb/ft³, the mass in kilograms and volume in litres, and says whether the substance would float or sink in water.
The formula
Density
ρ = m ÷ VMass
m = ρ × VVolume
V = m ÷ ρρ (rho) is density, m is mass and V is volume. Every value is converted to SI — kilograms, cubic metres and kg/m³ — before the formula is applied, then back to the unit you chose.
Worked example
A litre of gold at 19.3 g/cm³ has a mass of 19,300 × 0.001 = 19.3 kg. A kilogram of ice at 917 kg/m³ takes up 1 ÷ 917 = 1.09 litres, and floats. Aluminium at 2,700 kg/m³ is 168.56 lb/ft³.
When to use it, and the mistakes to avoid
Use it for physics and chemistry homework, to work out how much a tank of liquid weighs, how much space a material takes up, or whether something will float.
The mistakes that cost the most:
- Mixing units. Grams with cubic metres gives a figure 1,000 times too small; convert first, or let the calculator do it.
- Confusing ml with m³. One cubic metre is a million millilitres.
- Dividing the wrong way. Density is mass ÷ volume, not volume ÷ mass.
- Forgetting temperature. Liquids and gases expand when warm, so their density falls.
- Using weight in newtons as mass. Density uses mass in kilograms.
FAQ
What is the formula for density?
Density is mass divided by volume: ρ = m ÷ V. Rearranged, mass = density × volume and volume = mass ÷ density, so any two give the third.
What is the density of water?
About 1,000 kg/m³, which is 1 g/cm³ or 1 kg per litre, or about 62.4 lb/ft³. It changes slightly with temperature and is greatest at about 4 °C.
How do I convert g/cm³ to kg/m³?
Multiply by 1,000. Gold at 19.3 g/cm³ is 19,300 kg/m³. A g/cm³ is also the same as a kg/L and a g/ml.
Why does ice float?
Ice is about 917 kg/m³, less dense than liquid water at about 1,000 kg/m³, so it floats. A kilogram of ice takes up about 1.09 litres, against 1 litre for a kilogram of water - which is why frozen pipes burst.
How do I tell if something will float?
Compare its density with the liquid's. In water, anything below about 1,000 kg/m³ floats and anything above sinks. The calculator tells you which, for whatever you enter.
What is the difference between density and weight?
Weight (or mass) is how much there is; density is how tightly packed it is. A kilogram of feathers and a kilogram of iron weigh the same, but the iron, at about 7,870 kg/m³, takes up a far smaller space.