# How to calculate density

• calculate a single variable (density, mass or volume) from the density equation
• calculate specific gravity of an object, and
• determine whether an object will float or sink given its density and the density of its surroundings.

Density is the mass of an object divided by its volume. Density often has units of grams per cubic centimeter (g/cm3). Remember, grams is a mass and cubic centimeters is a volume (the same volume as 1 milliliter). A box with more particles in it will be more dense than the same box with fewer particles Hide

Density is a fundamental concept in the sciences; you will see it throughout your studies. It is used quite often in identifying rocks and minerals since the density of substances rarely changes significantly. For example, gold will always have a density of 19.3 g/cm3; if a mineral has a density other than that, it isn't gold.

You probably have an intuitive feeling for density in the materials you use often. For example, sponges are low in density; they have a low mass per unit volume. You are not surprised when a large sponge is easy to lift. In contrast, iron is dense. If you pick up an iron skillet, you expect it to be heavy.

Students, and even teachers, often confuse mass and density. The words heavy and light on their own refer to mass, and not density. A very large sponge may weigh a lot (have a high mass), but its density is low because it still weighs very little per unit of volume. For density, you also need to consider the size, or volume, of the object.

## How do I determine density?

Density is not something that is directly measured. Typically if you want to know the density of something you will weigh it and then measure its volume.

Hide You collect a boulder and take it back to the lab, where you weigh it and find its mass to be 1000 g. You then determine the volume is 400 cm3. What is your boulder's density? Hide Density is mass divided by volume, In this case the mass is 1000g and the volume is 400 cm3, so you divide 1000g by 400 cm3 to get 2.5 g/cm3.

Another tricky thing about density is that you can't add densities. If I have a rock that is made up of two minerals, one with a density of 2.8 g/cm3, and one with a density of 3.

5 g/cm3, the rock will have a density between 3.5 and 2.8 g/cm3, not a density of 6.3 g/cm3.

This is because both the mass and the volume of the two minerals will be added, and so when they are divided to get the density the result will be between the two.

Typical densities for gasses are on the order of thousandths of grams per cubic centimeter. Liquids often have densities of about 1.0 g/cm3, and indeed, fresh water has a density of 1.0 g/cm3. Rocks often have a density around 3 g/cm3, and metals often have densities above 6 or 7 g/cm3.

### How do I calculate specific gravity?

To calculate the specific gravity (SG) of an object, you compare the object's density to the density of water:

## Calculating the Density of an Object

By Steven Holzner

In physics, density is the ratio of mass to volume. Any solid object that’s less dense than water floats. Density is an important property of a fluid because mass is continuously distributed throughout a fluid; the static forces and motions within the fluid depend on the concentration of mass (density) rather than the fluid’s overall mass.

• Density is mass (m) divided by volume (V), so here’s the formula for density:
• In the MKS (Meter-Kilogram-Second) system, the units are kilograms per cubic meter, or kg/m3.

Say you have a whopper diamond with a volume of 0.0500 cubic meters (that’s a cube that’s about 1 foot on each side, so it’s truly a whopper). You measure its mass as 176.0 kilograms. So what’s its density?

Plugging in the numbers and doing the calculations gives you your answer: So the density of diamond is 3,520 kg/m3. That’s pretty dense.

You can see a sample of the densities of common materials in the table. Note that ice is less dense than water, so ice floats. Generally, solids and gases expand with temperature and therefore become less dense.

This table includes the density of water at 4°C as a reference point because the density of water varies with temperature.

The densities of the gases generally have a stronger dependence on temperature than the solids do, though.

Densities of Common Materials

Substance
Density (kg/m3)
Gold (near room temperature) 19,300
Mercury (near room temperature) 13,600
Silver (near room temperature) 10,500
Copper (near room temperature) 8,890
Diamond (near room temperature) 3,520
Aluminum (near room temperature) 2,700
Blood (near body temperature) 1,060
Water (4 degrees Celsius) 1,000
Ice (0 degrees Celsius) 917
Oxygen (at 0 degrees Celsius, 101.325 kPa) 1.43
Helium (at 0 degrees Celsius, 101.325 kPa) 0.179

## How to Calculate the Density of Solids or Liquids – Video & Lesson Transcript

Density is a measure of how compact the mass in a substance or object is. The density of an object or substance can be calculated from this equation: density in kilograms per meter cubed is equal to mass in kilograms, divided by volume in meters cubed (p = m / v). So density could be described as the number of kilograms that 1 meter cubed of substance weighs.

When two materials are mixed together, the density is what determines which one will rise and which one will sink. This tells you whether objects sink or float and explains why cold fronts sink below warm fronts in weather patterns. Understanding density is an important step in understanding the world around us.

### Calculating Density of Solids or Liquids

When you're asked to calculate density, you need to use a combination of the density equation we've already introduced and an understanding of volume. For example, you might not be given the actual volume of the material or object to put into the density equation. Instead, you may be given the measurements of the object and be expected to figure out the volume yourself.

The volume of a cube or cuboid is length times width times height (L * W * H). So if you needed to calculate the density of a cube, you would first measure the length of one of the sides. Let's say that the length of our cube turned out to be 3 meters.

You would first need to calculate the volume by multiplying 3 by 3 by 3 (V = 3 * 3 * 3). You would also need to put the cube on a scale to measure its mass. Last of all, you would divide your volume by your mass to get the density of the cube (p = m / v).

But what if the material isn't a solid? What if it's a liquid?

## This Example Shows How to Calculate Density

Density is the measurement of the amount of mass per unit of volume. In order to calculate density, you need to know the mass and volume of the item. The mass is usually the easy part while volume can be tricky. Simple shaped objects are usually given in homework problems such as using a cube, brick or sphere.

The formula for density is:

This example problem shows the steps needed to calculate the density of an object and a liquid when given the mass and volume.

• Density is how much matter is contained within a volume. A dense object weighs more than a less dense object that is the same size. An object less dense than water will float on it; one with greater density will sink.
• The density equation is density equals mass per unit volume or D = M / V.
• The key to solving for density is to report the proper mass and volume units. If you are asked to give density in different units from the mass and volume, you will need to convert them.

Question 1: What is the density of a cube of sugar weighing 11.2 grams measuring 2 cm on a side?

Step 1: Find the mass and volume of the sugar cube.

Mass = 11.2 gramsVolume = cube with 2 cm sides.

Volume of a cube = (length of side)3Volume = (2 cm)3Volume = 8 cm3

Step 2: Plug your variables into the density formula.

density = mass/volumedensity = 11.2 grams/8 cm3density = 1.4 grams/cm3

Answer 1: The sugar cube has a density of 1.4 grams/cm3.

Question 2: A solution of water and salt contains 25 grams of salt in 250 mL of water. What is the density of the salt water? (Use density of water = 1 g/mL)

Step 1: Find the mass and volume of the salt water.

This time, there are two masses. The mass of the salt and the mass of the water are both needed to find the mass of the salt water. The mass of the salt is given, but the only the volume of water is given. We've also been given the density of water, so we can calculate the mass of the water.

densitywater = masswater/volumewater

masswater = densitywater·volumewatermasswater = 1 g/mL · 250 mLmasswater = 250 grams

Now we have enough to find the mass of the salt water.

masstotal = masssalt + masswatermasstotal = 25 g + 250 gmasstotal = 275 g

Volume of the salt water is 250 mL.

Step 2: Plug your values into the density formula.

• density = mass/volumedensity = 275 g/250 mL
• density = 1.1 g/mL

Answer 2: The salt water has a density of 1.1 grams/mL.

If you're given a regular solid object, you can measure its dimensions and calculate its volume. Unfortunately, the volume of few objects in the real world can be measured this easily! Sometimes you need to calculate volume by displacement.

How do you measure displacement? Say you have a metal toy soldier. You can tell it is heavy enough to sink in water, but you can't use a ruler to measure its dimensions. To measure the toy's volume, fill a graduated cylinder about half way with water.

Record the volume. Add the toy. Make sure to displace any air bubbles that may stick to it. Record the new volume measurement. The volume of the toy soldier is the final volume minus the initial volume.

You can measure the mass of the (dry) toy and then calculate density.

In some cases, the mass will be given to you. If not, you'll need to obtain it yourself by weighing the object. When obtaining mass, be aware of how accurate and precise the measurement will be. The same goes for measuring volume.

Obviously, you'll get a more precise measurement using a graduated cylinder than using a beaker, however, you may not need such a close measurement. The significant figures reported in the density calculation are those of your least precise measurement.

So, if your mass is 22 kg, reporting a volume measurement to the nearest microliter is unnecessary.

Another important concept to keep in mind is whether your answer makes sense. If an object seems heavy for its size, it should have a high density value. How high? Keep in mind the density of water is about 1 g/cm³. Objects less dense than this float in water, while those that are more dense sink in water. If an object sinks in water, your density value better be greater than 1!

Need more examples of help with related problems?

## How to Calculate the Density of a Solution

••• luchschen/iStock/GettyImages

Updated March 13, 2018

By Robert Preston

The density of a solution is a relative measurement of the mass of an object compared against the space that it occupies. Finding a solution's density is a simple task. Once measurements have been taken to determine the volume and mass of the solution, it is easy to calculate the density of the solution.

Measure the mass of a beaker in grams.

Fill the beaker with the solution being measured.

Read the volume of the solution in the beaker and record.

Measure the mass of the filled beaker in grams.

Subtract the mass of the empty beaker from the mass of the filled beaker to determine the mass of the solution.

Divide the mass of the solution by the volume of the solution.

## Density Calculator

home / other / density calculator

Please provide any two values to the fields below to calculate the third value in the density equation of .

The density of a material, typically denoted using the Greek symbol ρ, is defined as its mass per unit volume.

 ρ = where: ρ is the density m is the massV is the volume

The calculation of density is quite straightforward. However, it is important to pay special attention to the units used for density calculations. There are many different ways to express density, and not using or converting into the proper units will result in an incorrect value.

It is useful to carefully write out whatever values are being worked with, including units, and perform dimensional analysis to ensure that the final result has units of . Note that density is also affected by pressure and temperature. In the case of solids and liquids, change in density is typically low.

However, when regarding gases, density is largely affected by temperature and pressure. An increase in pressure decreases volume, and always increases density. Increases in temperature tend to decrease density since volume will generally increase.

There are exceptions however, such as water's density increasing between 0°C and 4°C.

Below is a table of units in which density is commonly expressed, as well as the densities of some common materials.

## How can I calculate density of a solid?

• Density is a comparison of the mass of an object and the volume of that object.
• #D = (mass)/(volume) or D = m/V#
• This equation can be rearranged algebraically to solve foray of the values.
• #D = m/V or DV = m or V =m/D#
• Let us look at two sample problems.

A rectangular prism has a mass of 42.0 grams and has dimensions of 2 cm in width, 6 cm long and 0.5 cm in height.

What is the density of this object?

Volume of a rectangular prism is #l x h x w#
# 6.0 cm x 0.5 cm x 2.0 cm = 6.0 cm^3#

1. Now the density is #(mass)/(volume)#
2. #D = (42 g)/(6.0 cm^3)#
3. #D = 7.0 g/(cm^3)#

A rectangular prism has a mass of 42.0 grams and has dimensions of 2 cm in width, 6 cm long and 0.5 cm in height. What is the density of this object?

Volume of a rectangular prism is #l x h x w#
# 6.0 cm x 0.5 cm x 2.0 cm = 6.0 cm^3#

• Now the density is #(mass)/(volume)#
• #D = (42 g)/(6.0 cm^3)#
• #D = 7.0 g/(cm^3)#

A cylinder has a mass of 33.0 grams and has a diameter of 4 cm and measure 3.0 cm in height. What is the density of the cylinder?

Volume of a cylinder is # (3.14) r^2h#
# (3.14) (2cm)^2(3.0cm) = 37.68 cm^3#

Now the density is #(mass)/(volume)#

#D = (33.0 g)/(37.68 cm^3)#

1. #D = 0.876 g/(cm^3)#
2. I hope this was helpful.
SMARTERTEACHER

## How to Calculate the Density of a Solid

Mass:   Learn how to measure the mass of an object using a triple beam balance

Mass vs. Weight:    Mass and weight are often confused by many students. Learn the difference and try some challenging problems.

Volume:   Measure volume using a graduated cylinder.

Density of a Solid:   Learn to calculate the density of an unknown solid from knowing its mass and volume.

Density of a Liquid:   Learn to calculate the density of an unknown liquid from knowing its mass and volume using a graduated cylinder and triple beam balance. Learn what a hydrometer is, and what it can do.

Density Challenge:   Great page for gifted and talented students! Some excellent challenging problems.

Assessment:   Twenty questions on mass, volume and density (two levels of difficulty). Your test is marked online.

• Science Project Ideas:   Ideas for science projects using mass, volume and density concepts learned from this module.
• Mass Volume Density Lab Exercise: Problem: What is the relationship between water pressure and depth of water?
• An Integrated Math Science and Art  (STEAM) Activity- Mass, Volume Density Activity using the Gates Project from Central Park NYC.

## Density Formula

By Becky Kleanthous|
Last update: 22 August 2019

If you've ever been fooled by the old question, 'Which weighs more: a pound of feathers or a pound of lead?' then you wouldn't be alone.

Although the feathers and the lead both weigh exactly the same (um, a pound), their density is wildly different, and we can sometimes mentally conflate weight and density – even though they're different concepts. So – hey – don't feel dense.

Read on to find out exactly what density is, how it works, and how to calculate density.

### What is density?

Density is the mass per volume – not just the straight-up mass. So if the question was, 'Which weighs more: a 500ml jug full of feathers or a 500ml jug full of lead?' then the answer would be the lead. For an equal amount of space it takes up (volume), lead weighs much more than the feathers (mass).

Density can also be thought of as how compacted or compressed a substance is. A pound of feathers is filled with airy space, so it's not very dense at all, while a pound of lead feels much more solid, so it's more dense. This is why you should never comment on your Auntie Mabel's sponge cake by describing it as dense: she was probably going for something a little more airy.

Density is also what makes things float or sink. When you mix two or more substances, the most dense substance sinks to the bottom, whilst the least dense substance is more buoyant and floats to the top. Try mixing oil and water and see how they separate into layers, with the less dense oil on top.

### How do you calculate density?

Always keep an eye on your units: it's standard to use g or kg per cm³ or m³, so use our unit converters if your measurements are in different units.

To calculate density, you divide the mass by the volume:

Density = Mass ÷ Volume