Density in plain terms
Density is how much mass is packed into a given space. A brick and a sponge can be the same size, but the brick is far denser. It is written as mass divided by volume, often with the Greek letter ρ (rho), and it explains why some things float and others sink.
This density calculator works three ways. Give it mass and volume to get density, or give it density and one of the others to get the missing value. Mix units freely: grams with cubic inches, pounds with litres. The conversions use exact definitions.
How to use it
- Choose what you want to find: density, mass or volume.
- Type the two values you know and pick their units.
- Pick the unit you want the answer in.
- Read the answer, the same result in other units, and whether it is denser than water.
To measure the volume of an odd shaped solid, lower it into a measuring jug of water and read how far the level rises. That rise is its volume in millilitres, which are the same as cubic centimetres.
The density formula
density = mass ÷ volume (ρ = m ÷ V)
mass = density × volume
volume = mass ÷ densityA handy way to remember it is a triangle with m on top and ρ and V underneath: cover the one you want and the other two show how to get it. Keep the units matched; grams with cubic centimetres give g/cm³, and kilograms with cubic metres give kg/m³.
Worked example: 500 g in 400 cm³
- Density: 500 g ÷ 400 cm³ = 1.25 g/cm³
- In kg/m³: 1.25 × 1,000 = 1,250 kg/m³
- In lb/ft³: 1.25 × 62.428 = 78.035 lb/ft³
The object has a density of 1.25 g/cm³, or 1,250 kg/m³, or 78.035 lb/ft³. That is more than water, so it sinks. The other modes run the same formula backwards: 2 litres of a material at 7.85 g/cm³ has a mass of 15.7 kg.
Density unit conversions
| Unit | 1 g/cm³ equals |
|---|---|
| kg/m³ | 1,000 |
| g/L | 1,000 |
| g/mL | 1 |
| lb/ft³ | 62.428 |
| lb/in³ | 0.0361273 |
| lb per US gallon | 8.3454 |
Water is close to 1 g/cm³, which is why the gram was first defined from it. Specific gravity is a material’s density divided by the density of water, so in g/cm³ the two numbers are nearly the same. Anything under about 1 floats on fresh water.
Where density matters
- Building and landscaping: turning a volume of gravel, sand or concrete into a weight for delivery. See the gravel calculator.
- Cooking and mixing: a cup of flour weighs far less than a cup of honey.
- Shipping: carriers compare weight with size to set a price, so a large light parcel can cost as much as a small heavy one.
- Science lessons: identifying a metal by measuring its mass and volume.
Frequently asked questions
How do I calculate density?
Divide the mass by the volume. An object with a mass of 200 grams and a volume of 50 cubic centimetres has a density of 4 g/cm³. Choose Density above, type both values with their units, and the calculator gives the answer in g/cm³, kg/m³, lb/ft³ and more.
How do I convert g/cm³ to kg/m³?
Multiply by 1,000. A cubic metre holds a million cubic centimetres, and a kilogram is a thousand grams, so the two factors leave 1,000. For example, 2.7 g/cm³ is 2,700 kg/m³. Going the other way, divide kg/m³ by 1,000 to get g/cm³.
How do I find mass from density and volume?
Multiply the density by the volume, after making the units match. A 2 litre block of a material with a density of 7.85 g/cm³ has a mass of 7.85 × 2,000 cm³ = 15,700 g, or 15.7 kg. Choose Mass above to do this in any units.
Why do things float?
An object floats when it is less dense than the liquid around it, because it pushes aside its own weight of liquid before it is fully under. Fresh water is close to 1 g/cm³, so anything less dense floats. Salt water is a little denser, which is why swimmers float more easily in the sea.
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