Density Calculator

Created by Davide Borchia
Last updated: Feb 18, 2023

Density describes the relationship between mass and volume: learn how to calculate and discover the values of some interesting materials with our density calculator.

Here you will learn:

  • What is density?
  • How to calculate density: formula and explanation?
  • Example of density: how to find the extremes of this quantity in the Universe.
  • Why do objects float?

What is density?

Density is an intensive property of matter, which means that its value doesn't depend on the size of the system. Density measures the mass per unit of volume. Notice how both mass and volume are extensive properties: calculating their ratio excludes the system's physical characteristics from the definition of density.

Density is, roughly speaking, a measure of how packed atoms (or subatomic particles) are. The bigger the space between them, the lower the density. This is why, intuitively, gases are far less dense than solid objects.

How to calculate density

To calculate density, you must know:

  • The mass of the object, mm; and
  • The volume of the object, VV.

The density formula is then:

d=mVd = \frac{m}{V}

Choose the appropriate measurement units: density is most often calculated in kilograms per cubic meter, but there may be situations where other units may be more convenient (grams per cubic centimeter comes to mind).

Density examples

The most commonly quoted example of density is water. A cubic meter of water, at 4 °C4\ \degree\text{C} has a mass of exactly 1,000 kg1,000\ \text{kg}. This is no coincidence: the kilogram's definition used a reference to water: in 1795, the weight of a liter of water was decided to correspond to a kilogram.

The densest material that can exist naturally on Earth is osmium, the element number 76. In its metallic state, at room temperature, a cubic meter of osmium weighs a staggering 22,750 kg22,750\ \text{kg}!

Moving away from our home planet, we find extremes examples of density:

  • The density of intergalactic medium: this mostly empty space between galaxies contains approximately one atom per square meter. Assuming this atom to be hydrogen, the most common in the Universe, the density of the medium would be 1.671027 kg/m31.67\cdot10^{-27}\ \text{kg}/\text{m}^3.
  • Staying closer to the Earth, we can consider the interstellar medium, which is eight orders of magnitude denser than the emptiness between galaxies. Said so, with a density of 21019 kg/m32\cdot10^{-19}\ \text{kg}/\text{m}^3, it's still mostly emptiness.
  • The density of the core of a neutron star lies at the other end of the spectrum. Those stellar remains contain the core of a sun compressed in the size of a city: with a diameter of a dozen of kilometers or so and masses comparable to the one of the Sun, they pack an impressive density of 4.81017 kg/m34.8\cdot10^{17}\ \text{kg}/\text{m}^3.
  • Denser? Black holes can be even denser, and the bigger, the better. However, they don't stop at all, reaching the point in which they break physics and create the singularity, a point in space with infinite density.

Why do objects float?

Our density calculator can tell you if a given material floats or sinks. In the bottom part of the calculator, select "non-metals" and then "wood (typical)". Wood's density is, on average, 700 kg700\ \text{kg} per cubic meter, which tells us that it easily floats.

Now, select "metals", "iron", and answer the question, "will it float?" With 7,870 kg7,870\ \text{kg} per cubic meter, iron sinks quickly. So how do boats float?

Let's ask Archimedes. The key of floating is in the displacement of water. If a body displaces a volume of water with mass greater than the one of the body itself, then the body will float: we talked in detail about this at our buoyancy calculator. Ships are mostly made of air, which greatly reduces their weight: hence, they float.

How to use our density calculator

Our density calculator will help you with two different questions:

  • How to find the density of a material (with the density formula)? Input the mass and volume of the object, and choose the desired measurement unit for the density.
  • Will a material float in water (at 4 °C4\ \degree\text{C}? Choose a material from two lists of presets (first a general type and then a more specific material), and discover their density — and if they float.

Try our density converter to focus more on the conversion between the measurement units of density rather than on the calculation themselves.

Davide Borchia
Calculate density
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Will it float in fresh water?
Nope, it's gonna sink.
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