Math Calculators
Density Calculator

# Density Calculator

This volume calculator uses a density formula ρ = m/V to find densities of different substances and objects. It calculates the third one for two given values - density, mass, or volume of a substance.

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## Table of Contents

The density calculator will help you calculate the density of matter, mass, and volume. Because these parameters are interrelated, you can calculate one parameter by knowing the other two. For example, if you know an object's mass and volume, you can calculate its density. Or you can use the density calculator to determine an object's mass if you know its volume and density.

This calculator is incredibly convenient because you can use different measures to calculate density. You can use grams, kilograms, ounces, and pounds as mass measures in the density calculator. Milliliters, cubic centimeters, cubic meters, liters, cubic feet, and cubic inches can be used as volume measures.

## The Definition of Substance Density

The density of a substance is the mass contained in a unit of volume under normal conditions.

The world's most commonly used density units are the SI unit of kilograms per cubic meter (kg/m³) and the CGS unit of grams per cubic centimeter (g/cm³). One kg/m³ is equal to 1000 g/cm³.

In the U.S., traditionally, density is expressed in pounds per cubic foot.

One pound per cubic foot = 16.01846337395 kilograms per cubic meter. Accordingly, to convert the density of a substance from SI units to traditional U.S. units, divide the number by 16.01846337395 or simply by 16. And to convert the density of a substance from U.S. units to SI units, multiply your number by 16.

The Greek letter ρ is usually used to represent density. Sometimes the Latin letters D and d (from the Latin "densitas" or "density") are used in the density formula.

To find a substance's density, divide its mass by volume. The density ρ is calculated using the density formula:

$$ρ=\frac{m}{V}$$

Where V is the volume occupied by a substance of mass m.

Since density, mass, and volume are interrelated, knowing density and volume, we can calculate mass:

$$m=ρ V$$

And knowing the density and mass of the substance, we can calculate the volume:

$$V=\frac{m}{ρ}$$

## Densities of various substances

The densities of different substances and materials can vary significantly.

The density of the same substance in solid, liquid, and gaseous states is different. For example, the density of water is 1000 kg/m³, ice about 900 kg/m³, and water vapor 0.590 kg/m³.

The density depends on the temperature, the aggregate state of the substance, and external pressure. If the pressure increases, the molecules of the substance become denser; thereby the density is greater.

A change in the pressure or temperature of an object usually leads to a change in its density. When the temperature drops, the movement of molecules in the substance slows down, and because they slow down, they need less space. This leads to an increase in density. Conversely, an increase in temperature usually leads to a decrease in density.

This rule excludes water, cast iron, bronze, and some other substances that behave differently at specific temperatures.

Water has a maximum density at 4 °C, which is 997 kg/m³. The density of water is often rounded up to 1000 kg/m³ for ease of calculation. As the temperature rises or falls, the density of water will decrease. Ice doesn't sink on the surface of the water because it has a density of 916.7 kg/m³.

The reason for this property of ice is so-called hydrogen bonds. The ice crystal lattice looks like a honeycomb, with water molecules connected by hydrogen bonds in each of the six corners. The distance between the molecules of water in the solid state is greater than in the liquid form, where they move freely and can get closer together.

The density of water, bismuth, and silicon also decreases with solidification.

The density of matter determines what will float and what will sink. Objects less dense than water (less than 1 gm/cm³) will float on water, like Styrofoam or wood.

Materials with a high density, such as metal, concrete, or glass (greater than 1 gm/cm³), will sink in water because their density is higher than that of water.

An iron cannonball sinks in water because its density is greater than water's density. An iron ship floats in the ocean. Although iron is denser than water, most of the ship's interior is filled with air. And this reduces the overall density of the vessel. If the vessel were a solid block of iron, it would sink.

Objects submerged in salt water have a higher tendency to float than in clear or tap water; that is, they have greater buoyancy. This effect arises because of the buoyancy force that salt water has on objects due to its greater density.

## The Densities of solids

Solid matter kg/m³ g/cm³
Osmium 22 600 22.6
Iridium 22 400 22.4
Platinum 21 500 21.5
Gold 19 300 19.3
Lead 11 300 11.3
Silver 10 500 10.5
Copper 8900 8.9
Steel 7800 7.8
Tin 7300 7.3
Zinc 7100 7.1
Cast iron 7000 7.0
Aluminum 2700 2.7
Marble 2700 2.7
Glass 2500 2.5
Porcelain 2300 2.3
Concrete 2300 2.3
Brick 1800 1.8
Polyethylene 920 0.92
Paraffin 900 0.90
Oak 700 0.70
Pine 400 0.40
Cork 240 0.24

### Example

Imagine that you are a sculptor and are going to buy a marble block to make a small statue. You have found on sale a marble block with dimensions of 0.3 х 0.3 х 0.6 meters which suits you in terms of quality and price. How to calculate the weight of the block to understand how best to transport it?

Let's multiply the block's dimensions with each other to calculate the volume of the block.

0.3 × 0.3 × 0.6 = 0.054 m³

We know that marble's density is 2700 kg/m³. So we are looking for the mass of the block using the formula:

$$m=ρ V$$

That is 0.054 × 2700 = 145.8 kg. So, the marble block you like will weigh about 145.8 kilograms.

## The Densities of liquids

Liquid kg/m³ g/cm³
Mercury 13 600 13.60
Sulfuric acid 1 800 1.80
Honey 1 350 1.35
Seawater 1 030 1.03
Whole milk 1 030 1.03
Pure water 1 000 1.00
Sunflower oil 930 0.93
Machine oil 900 0.90
Kerosene 800 0.80
Alcohol 800 0.80
Oil 800 0.80
Acetone 790 0.79
Gasoline 710 0.71

## The Densities of gases

Gas kg/m³ g/cm³
Chlorine 3.210 0.00321
Carbon dioxide 1.980 0.00198
Oxygen 1.430 0.00143
Air 1.290 0.00129
Nitrogen 1.250 0.00125
Carbon monoxide 1.250 0.00125
Natural gas 0.800 0.0008
Water vapor 0.590 0.00059
Helium 0.180 0.00018
Hydrogen 0.090 0.00009

Knowing the density of carbon monoxide can come in handy in a fire that produces carbon monoxide, which is poisonous to humans. Carbon monoxide is slightly lighter than air, so it rises to the top of the room. So, if you are in the room during a fire, it is best to be as low and close to the floor as possible.

## The bulk food densities

Bulk materials kg/m³ g/cm³
Finely ground edible salt 1 200 1.2
Granulated sugar 850 0.85
Powdered sugar 800 0.8
Beans 800 0.8
Wheat 770 0.77
Grain corn 760 0.76
Brown sugar 720 0.72
Rice groats 690 0.69
Peeled peanuts 650 0.65
Cocoa powder 650 0.65
Dry walnuts 610 0.61
Wheat flour 590 0.59
Powdered milk 450 0.45
Roasted coffee beans 430 0.43
Coconut crumbs 350 0.35
Oatmeal 300 0.3

### Calculation example

You bought a pack of coffee beans weighing 900 grams. You have a convenient 1.5-liter coffee can at home. Will all this coffee fit in a jar? First, it is worth remembering that a liter contains 1000 cm³. Therefore, we have a jar of 1500 cm³.

Calculate the volume of coffee using its mass and knowledge of density.

$$V=\frac{m}{ρ}$$

The volume of coffee will be equal to:

$$\frac{900}{0.43}= 2093.023255814\ cm³$$

The existing jar is not enough for all the coffee you bought.

## Densities of bulk building materials:

Bulk materials kg/m³ g/cm³
The sand is wet 1920 1.92
Wet clay 1600 - 1820 1.6 - 1.82
Crushed gypsum 1600 1.6
Land, loam, wet 1600 1.6
Crushed stone 1600 1.6
Cement 1510 1.51
Gravel 1500 - 1700 1.5 - 1.7
Gypsum pieces 1290 - 1600 1.29 - 1.6
Sand dry 1200 - 1700 1.2 - 1.7
Land, loam, dry 1250 1.25
Dry clay 1070 - 1090 1.07 - 1.09
Asphalt crumb 720 0.72
Wood chips 210 0.21

The concept of bulk density is used to analyze bulk construction materials (sand, gravel, expanded clay, etc.). This indicator is essential for calculating the cost-effective use of various components of the construction mixture.

Bulk density is a variable value. Under certain conditions, a material of the same weight may occupy a different volume. Also, for the same volume, the mass may vary. The shallower the particles, the more densely they are arranged in a pile. Sand has the highest bulk density of construction materials. The larger the grains, the more voids there are between them. In addition to size, the shape of grains plays an important role. The best-compacted particles are those of regular form.

Knowing the bulk density is essential when you know the volume of the pit or ditch that needs to be filled, and you want to know the weight of the material that you need to buy for this purpose. Knowing the density also comes in handy when you have the material on sale in kilograms, and you need to know its volume. And information about bulk density will also be important if you want to correctly calculate the number of transport units required to transport the purchased material.

## Average matter density

Suppose a body has voids or is made of different substances (e.g., a ship, a soccer ball, a person). In that case, we speak of the average density of the body. It can also be calculated using the formula

$$ρ=\frac{m}{V}$$

For example, the average human body density ranges from 940-990 kg/m³ for a full inhalation to 1010-1070 kg/m³ for a full exhalation. Human body density is largely influenced by parameters such as the predominance of bone, muscle, or fat mass in the human body.

## Interesting natural examples of density

• Intergalactic medium has the lowest density in nature, namely 2×10⁻³¹kg/m³ to 5×10⁻³¹kg/m³.
• The average density of the Sun is about 1,410 kg/m³, about 1.4 times the density of water.
• The density of granite is 2,600 kg/m³.
• The average density of the Earth is 5 520 kg/m³.
• The density of iron is 7,874 kg/m³.
• The density of silver is 10,490 kg/m³.
• Gold has a density of 19,320 kg/m³.
• The densest substances at standard conditions are osmium (22,600 kg/m³), iridium (22 400 kg/m³) and platinum (21,500 kg/m³).
• The highest density in the Universe is in the black hole. The average density of a black hole depends on its mass. A black hole with a mass on the order of solar mass has a density of about 10¹⁹ kg/m³, exceeding the nuclear density of 2 × 10¹⁷ kg/m³. And a supermassive black hole with a mass of 10⁹ solar masses has an average density of about 20 kg/m³, much less than the density of water (1000 kg/m³).

## Density calculation

Several methods are used to measure the density of materials. Such methods include using:

• hydrometer (buoyancy method for liquids),
• hydrostatic balance (buoyancy method for liquids and solids),
• submerged body method (buoyancy method for fluids),
• pycnometer (for liquids and solids),
• air comparison pycnometer (for solids),
• oscillating densitometer (for fluids),
• fill-and-release (for solids).

You can calculate the density of a substance or the average density of an object at home by measuring the volume and mass of that substance or object.

First, determine the mass of the object using a scale.

Then determine the volume by measuring the dimensions or pouring it into a measuring vessel. This container can be anything from a measuring cup to a typical-sized bottle. If an object has a complex shape, you can measure the volume of water that the object displaces.

Divide the mass by the volume to calculate the density of the substance or object using the formula:

$$ρ=\frac{m}{V}$$

## The use of density properties in the industry

One known application of density is determining whether an object will float on water. If the density of an object is less than the density of water, it will float; if its density is less than the density of water, it will sink.

Ships can float because they have ballast tanks that hold air. These tanks provide a large volume of small mass, reducing the ship's density. The lower average density, along with the buoyant force the water exerts on the ship, allows the ship to float.

Oil floats on the surface of the water because it has less density than water. Although oil spills are harmful to the environment, oil's ability to float makes it easier to clean up.

The average density index reflects the physical condition of the materials. That's why the average density index determines how building materials behave under real-world conditions when exposed to moisture, positive and negative temperatures, and mechanical stress.

Using low-density materials in construction and mechanical engineering is environmentally and economically beneficial. For example, previously, the body of aircraft and rockets was made of aluminum and steel. Still, now it is made of less dense and, therefore, lighter titanium. This saves fuel and allows you to carry more cargo.

Information about the density of matter is also crucial for agriculture. If the density of the soil is high, it does not transmit heat well, and in winter, it freezes to a great depth. When plowed, such soil falls apart into large blocks, and plants do not grow well.

If soil density is low, the water quickly passes through such soil; that is, the moisture is not retained in the soil. And heavy rain can wash out the top most fertile layer of soil. So agronomists need to know the density of the soil to get a good crop.

## Legendary density measurement history

The story of density measurement begins with the story of Archimedes, who was tasked with determining whether a goldsmith had embezzled gold in making a crown for King Hiero the Second. The king suspected the crown was made of an alloy of gold and silver. At that time, scientists knew that gold was about twice as dense as silver. But to verify the composition of the crown, it was necessary to calculate its volume.

The crown could be squeezed into a cube, the volume of which could easily be calculated and compared to the mass and, based on the density, determine if it was gold. But the king would not have approved of such an approach.

From the rise of the water at its inlet, Archimedes noticed that he could calculate the volume of the gold crown by the volume of water displaced. After this discovery, he jumped out of the tub and ran naked through the streets, shouting, "Eureka! Eureka!" In Greek, "Εύρηκα!" meant, "I have found it."

Archimedes calculated the volume of water displaced by the crown and the volume of water displaced by a gold bar of the same mass as the crown. As a result of the experiment, the crown displaced more water. It turned out that it was made of a less dense and lighter material than pure gold. As a result, the jeweler was caught cheating.

This resulted in the term "eureka," which has become popular and is used to refer to a moment of enlightenment or insight.
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