Density Calculator

Introduction

Density is an important physical property of any material, be it solids, liquids, or gases. Density is the mass per unit volume and measures how tightly matter is packed together. The density calculator will help you calculate the density using the mass and volume of the object.

The SI unit of density is kilogram per cubic meter (kg/m^3). Usually, for different types of materials, different units are used, like g/cm^3, which is the centimeter-gram-seconds (cgs) unit used for solids, g/ml for liquids, and g/L for gases.

How to use the Density Calculator?

Using the density calculator, you can calculate the material’s density by inputting the object’s mass and volume.

The variables in the density calculator include

Mass (m): The mass of the object

Volume (v): The volume occupied by the object

Density (ρ): The density of the object as calculated by the formula

ρ = \normalsize \dfrac{m}{v}

What is Density?

Density is a measure of how closely or loosely packed are the molecules of a material. It is defined as its mass per unit volume and denoted by the rho(ρ) symbol.

The principle of density was discovered by a Greek mathematician, Archimedes, around 250 B.C., when the king of Syracuse tasked Archimedes to determine if his crown was made of pure gold or if the goldsmith was cheating him by adding silver to the crown.

Archimedes was not allowed to damage the crown or melt it to determine if silver was added, so he had to devise another way.

One day, while bathing, he had an idea when he noticed that the amount of water that spilled out of the bathtub was equal to the volume his body occupied. It is said that Archimedes ran through the streets of Sicily crying “Eureka” when he discovered this concept.

He knew that Gold was denser than Silver, so if a crown made of a mixture of gold and silver were to be submerged in water, more water would spill over compared to when a crown of the same mass made of pure gold is submerged into the water because in the first case, the volume would be more.

When Archimedes carried out this experiment, it turned out that the goldsmith’s crown displaced more water per gram than a crown made of pure gold, so the Craftsman was indeed cheating the king.

The Result

A homogenous material, like iron, aluminum, gold, etc., will have the same density throughout, so any two objects made up of the same homogeneous material will have the same density, irrespective of the object’s mass and volume.

Some materials won’t have the same density throughout and will vary. For example, in the Earth’s atmosphere, the higher the altitude, the less dense the atmosphere, and if we were to go beneath the surface, the density increases as we go along.

How is Density Calculated?

Density is given by the ratio of mass to volume of the object. We can calculate the density by using the following formula.

\rho = \dfrac{m}{v}

Where,

m → mass of the object

v → volume of the object

Examples

Given an object with a mass of 5 kg and a volume of 0.5 m^3. What is the density of the object?

The density of the object can be calculated by using the following formula

\begin{aligned} \rho &= \dfrac{m}{v} \\[10pt] &= \dfrac{5}{0.5} \\[10pt] & = 10 \; kg/m^3 \end{aligned}

The density of the object is 10 kg/cubic meter.

FAQ

What is the relationship between density, mass, and volume?

Density is directly proportional to mass and inversely proportional to volume; if the mass of an object increases, so does its density. So, if the object’s volume increases, the density decreases.

What is the density of water?

The density of water varies with temperature. At 4 Celsius (39 F), The density of water is approximately 1 g/cm^3 or 1000 kg/m^3. At room temperature, the density of water is around 0.997 g/cm^3 or 997 kg/m^3.

How does temperature affect the density of a substance?

For most substances, the density decreases as the temperature increases. This is due to the thermal expansion of the substance. Some exceptions to this phenomenon are substances like water, and ice is less dense than water, so it floats on water.

How does pressure affect the density of a gas?

The density of a gas is directly proportional to pressure as the density increases as the pressure increases, and as the density decreases, the pressure decreases. This is due to the behavior of gas molecules.

What is relative density?

Relative density, also known as specific gravity (SG), is the ratio of the density of a substance to the density of a reference substance, typically water. The name specific gravity may be misleading, and it is not related to gravity in any manner.

How does density relate to buoyancy?

Density plays a crucial role in buoyancy; objects denser than the fluid they are in will sink, and objects less dense than the fluid they are in will float.

Can the density of an object change?

The density of an object is directly proportional to mass and inversely proportional to volume. If the volume of an object changes by either compression or expansion, the volume will change, and hence the density will also change.

How is density used in everyday life?

Density is used in everyday applications, such as determining whether an object will float or sink, measuring the purity of liquids, and determining the composition of substances in geology, chemistry, and industry.