Density Calculator

This density calculator will calculate the density from mass and volume of a material but can also be used in reverse. Enter two out of three values (mass, volume or density), leave one field blank and the calculator will do the rest for you. As units are automatically converted during calculation, you can enter values in grams and milliliters to get the density in g/cm3, or use kg, m3 and kg/m3.

What is Density?

Density is the mass contained in a given volume. It indicates how tightly packed matter is within an object. A small lead weight feels heavy when you pick it up because lead has a high density. Conversely, a large foam pad feels light because it has a lower density.

Density is a property of the material itself and not of any particular object. A gold ring and a gold bar have very different masses and volumes but since they are made from the same material, they have the same density. For this reason, density can be used to identify materials.

Formula for density:

Density is the value obtained by dividing mass by volume. The Greek letter rho (ρ) represents density.

In this case ρ is for density, m is for mass and V is for volume. As these three quantities are connected by the same relationship, you can rearrange the formula to calculate either mass or volume.

The SI unit of density is kilograms per cubic meter. However, for everyday solids and liquids, grams per cubic centimeter is more practical and intuitive. Since the value for water is approximately 1, this allows you to see how a material's density compares to that of water by looking at its value in this unit.

How to use this calculator:

Enter two of the known values and leave the third field blank. To calculate Density enter Mass and Volume; to calculate Mass enter Density and Volume; to calculate Volume enter Mass and Density.

If you fill in two fields, the calculator will calculate the third value and show the density as a result, also giving information about relative density and whether an object would float or sink in water. No mode selection is required. By leaving one field blank, you tell the calculator what to calculate. If you change the unit of any element, the other values are automatically recalculated.

Arrangement of formula for density, mass and volume.

This table shows the same relationships in three different ways, each of which may account for certain missing quantities.

Example calculation:

Suppose a block of metal has a mass of 965 grams and a volume of 50 cubic meters. The density is obtained by dividing the mass by the volume.

Calculating in the opposite direction is just as easy.

If you know that a piece of copper has a density of 19.3 grams per cubic centimeter and a volume of 50 cubic centimeters, then its mass is the product of the density and volume, which is the result of multiplying 19.3 by 50, or 965 grams. To use this calculator, simply enter the two known values and read off the third result.

Specific gravity and buoyancy:

Specific gravity, also known as relative density, is the value obtained by dividing the density of a material by that of water. Since the density of water is approximately 1000 kilograms per cubic meter or 1 gram per cubic centimeter, a relative weight greater than one means that the material is denser than water while a value less than one means it is lighter than water.

This single value can predict buoyancy. If the density of a solid is less than that of the surrounding liquid, it will float; if it's greater, it will sink. Since ice has a relative density of about 0.92, it floats on water. This explains why icebergs are only partially above the surface of the water. Iron, with a relative density of about 7.9, sinks like a rock.

This concept can be traced back to Archimedes in ancient Syracuse. He was asked by a person to check the purity of a crown without melting it. He stepped into a bathtub filled with water and observed how the water overflowed, realizing that the volume of displaced water is equal to the volume of the object. By dividing the mass by this volume, one gets the density. The density of gold is higher than that of possible cheap metals added by an unscrupulous jeweler. This story is the origin of the exclamation "Eureka".

Density of common materials:

The density of a pure material is constant at any given temperature, so these reference values can be used to check results or identify samples. The values are expressed in kilograms per cubic meter. To convert them into grams per cubic centimeter, divide by 1000.

Density units:

As density can be expressed in different units this is a common source of error with such problems. Calculation tools will convert between these units but it is also helpful to understand their relationships. Each row shows the value of a particular unit converted into kilograms per cubic meter.

Density changes with temperature and pressure

Density is not constant. When a material is heated it usually expands, so the same mass takes up more volume and the density decreases. In solids and liquids the changes are less than in gases. This explains why hot air rises above cold air.

The effect of pressure is the opposite. When a material is compressed into a smaller volume, its density increases. Gases are easily compressed so their densities vary greatly with pressure, while solids and liquids change very little in density. Water is an important exception to this rule: between 0 and 4 degrees Celsius, water actually becomes denser when it warms up. This explains why lakes freeze from the top down.

Density applications

Density plays a crucial role in many fields of science and everyday life. Geologists use it to identify minerals, while jewelers use it to check if gold is real. Engineers consider density along with strength when selecting lighter yet sturdy materials for airplanes. In the shipbuilding industry, density is used to make steel hulls floatable. A ship floats when its average density (including the hull and air inside) is less than that of water.

In the kitchen, density explains why oil floats on top of vinegar and why fresh eggs sink while rotten ones float. In medicine and brewing, hydrometers are used to measure relative densities in order to determine the amount of dissolved sugar or salt in liquids. Density is important whenever you want to compare how much an object weighs with respect to its size.

Tips for accurate results:

Measure the mass and volume carefully. Even a small error in either value will directly affect the density. For solids of irregular shape, you can determine the volume by displacement method. Place an object into a graduated cylinder filled with water and read off the increase in water level. Be sure to use consistent units or convert them using a calculator. Also note that this result is the average density for the entire object. So for hollow or porous objects, it will be less than the solid material contained within.