Density Calculator

What the density calculator does

Density is how much mass is packed into a given volume. This calculator links mass, volume, and density: enter any two and it finds the third. So you can get the density of an object from its mass and size, the mass from a density and volume, or the volume a given mass of material occupies.

Below is what density means, the equation behind it, why it decides whether things float, and a worked example.

How to use it

1. Choose what to find: density, mass, or volume.
2. Enter the other two, each with its own unit.
3. Press Calculate for the answer, shown across the relevant units, or Reset to clear it.

What density is

Density is mass divided by volume, a measure of how tightly matter is packed. It is why a small lump of lead feels heavy while a large block of foam feels light: the lead crams a lot of mass into little space, the foam very little into a lot. Density captures that, telling you the mass of each unit of volume rather than the total mass of the object.

Because it does not depend on how big the object is, density is a property of the material itself. A gold ring and a gold bar have the same density, even though the bar weighs far more, because density compares mass to volume rather than measuring either alone. This makes it one of the most useful ways to identify a material or check its purity, and it is listed for every substance in reference tables.

The equation it solves

Density, written with the Greek letter rho, is the mass m divided by the volume V:

ρ = m ÷ V

Rearranged, the same relationship gives the mass from a density and volume, m = ρ × V, and the volume a mass occupies, V = m ÷ ρ. The three are one statement read three ways.

Why things float or sink

Density is what decides whether something floats. An object placed in a fluid floats if it is less dense than the fluid and sinks if it is denser, regardless of its size. A huge log floats while a tiny pebble sinks, because what matters is density, not weight: the log is less dense than water and the pebble is more.

This is why water's density, 1000 kilograms per cubic metre, is such a useful benchmark. Anything less dense than that floats on water; anything more sinks. It also explains why a steel ship floats despite steel being far denser than water: the hull encloses a large volume of air, so the ship's overall density, averaged over that volume, is less than water's even though the metal itself is not. Density is always about mass spread over the whole volume.

Units and precision

The calculator works in SI units internally, converting your mass to kilograms and volume to cubic metres, then reports density across units including kilograms per cubic metre and grams per cubic centimetre. A handy fact ties two common units together: water's density is 1000 kg/m³, which is exactly 1 g/cm³, so densities in grams per cubic centimetre read directly as multiples of water. Results carry several figures, finer than most material measurements warrant.

A worked example

Suppose an object has a mass of 0.5 kg and occupies a volume of 0.00025 m³, that is 250 cubic centimetres.

Its density is ρ = 0.5 ÷ 0.00025 = 2,000 kg/m³, or 2 g/cm³. Since that is twice the density of water, the object would sink, and the figure is a clue to what it might be made of, in the range of light stone or glass.

Questions people ask

What is the formula for density?

Density is mass divided by volume, ρ = m/V. Knowing any two of density, mass, and volume gives the third.

What are the units of density?

The SI unit is kilograms per cubic metre. Grams per cubic centimetre is also common, and water conveniently has a density of 1 g/cm³, or 1000 kg/m³.

What determines whether something floats?

Its density compared with the fluid's. Less dense than the fluid and it floats; denser and it sinks. Size does not matter, only density.

Why does a steel ship float if steel is denser than water?

Because the hull encloses a large volume of air, so the ship's average density over its whole volume is less than water's, even though the steel itself is denser.

References

A quick note on where the physics comes from. Density as mass per unit volume, and its role in floating and sinking, are standard mechanics, set out in OpenStax's University Physics and in Georgia State University's HyperPhysics. The SI units follow the US National Institute of Standards and Technology.

1. OpenStax, University Physics Volume 1, Section 14.1, Fluids, Density, and Pressure. https://openstax.org/books/university-physics-volume-1/pages/14-1-fluids-density-and-pressure
2. HyperPhysics, Georgia State University, Density. http://hyperphysics.phy-astr.gsu.edu/hbase/permot.html
3. National Institute of Standards and Technology (NIST), Special Publication 811, Guide for the Use of the International System of Units (SI). https://www.nist.gov/pml/special-publication-811