Mass v. Weight v. Volume v. Density (w/ Examples!)

Mass, weight, volume, and density are all properties of matter that we measure to define and understand our world.

Mass and volume are intrinsic properties of physical materials, whereas weight and density are calculations that vary depending on specific conditions.

What is Mass?

If you are getting technical and recalling your High School physics, then the mass is a physical property that tells you about inertia.

If that is not ringing any bells, don’t worry – most people think of mass as a synonym for weight – it isn’t.

The mass of a body depends on atoms – how many and how close they pack together. You measure it in grams (g) and kilograms (kg). Mass tells you how much there is off something on an atomic level.

How Does Mass Relate to Inertia?

Here is the bit that takes a simple physical property (how much you have of something) and turns it into a more complex thought – mass is a measure of how a body resists acceleration under the action of a force. In other words – inertia.

Inertia is why you fly forwards if you hit the brakes too fast on your car. The mass of your body keeps moving when the vehicle stops because of its inertia.

If you are a theoretical physicist, rocket scientist, or engineer, knowing or calculating an object’s mass is extremely useful. You cannot send a rocket to the Moon without a grasp of mass.

Mass in Everyday Life

In everyday life, mass is not particularly relevant.

When someone is talking about a massive body, they probably mean a heavy or large one. A mass of water probably means a high volume of water or an indefinite quantity.

Yet, everyone’s practical appreciation of what mass means works – would you rather push an elephant or a dog uphill?

Aside from co-operation (or lack of it), most people know they will use less effort moving the dog with its smaller mass.

Is Mass Constant Everywhere?

The critical aspect about mass is that it remains the same wherever it is – if you have a specific mass of sugar, you get the same number of atoms wherever in the universe you stash your sugar. But it won’t weigh the same.

What is Weight?

You measure weight and mass in the same unit – kilograms. You can also weigh an object in pounds and ounces for practical reasons, but scientific weights are grams and kilograms.

Weight and mass are not the same things, but you can forgive yourself for getting confused between the two terms on Earth.

How Does Weight Relate to Mass?

Weight is the measure of a mass under a force – usually gravity. You don’t go floating off into space because the Earth is a massive body, and it pulls smaller masses like you or an apple towards it – that translates into the weight of that smaller mass.

The Moon is a smaller mass than the Earth, and that is why an astronaut can bounce around like superman on the Moon’s surface. It is also why you see people flying around in the space station because they are weightless.

In other words, the person is still there with all their limbs and parts intact, but they have mass but no weight.

Is Weight the Same Everywhere on Earth?

In approximate terms, you can be comfortable knowing that your bag of apples weighs the same all over the Earth, and this weight is proportional to its mass because of gravity.

Scientifically speaking, weight is not a constant over the whole of the Earth because the gravitational field is not uniform – you weigh about 0.3% less on top of Everest. The difference is so slight that it does not affect your daily life.

What is Volume?

When you talk about the volume, you usually think of liquids, but every object has a volume – you, your cat, and a book all occupy three-dimensional space and have a volume.

Think back to High School maths and all those endless formulas for working out the volume.

A cube [a 3-D shape whose length(L), width(W), and height(H) are the same] or any other cuboid shape is the easiest:

L x W x H = volume

You measure volume in cubic centimeters or inches.

In other words – how many small cubes (1 x1 x1) can fit in the volume occupied by the object. Spheres, cylinders, pyramids, and complex shapes may have more complicated calculations, but the principle of working out the volume is the same.

How Do Volume and Mass Relate to Density?

Volume is a measurement of space occupied by an object or substance, but the amount or mass of material inside a volume depends on another measurement – density.

What is Density?

Density is a mathematical concept: mass divided by volume. Density is a measure of how much stuff you have in precise space. You measure it in grams (mass) per cubic centimeters (volume).

Matter is atoms – the ancient Greeks thought this was the smallest particle in the universe.

We now know that you can split the atom into smaller particles, but that takes you into the realm of quantum physics, which is not particularly helpful when thinking about density.

Matter (chairs, people, plants) contains atoms stuck together with space in between. More distance between the atoms means less of them fit inside a precise volume.

How Does Density Vary in Matter?

All matter exists in three primary phases – gas, liquid and solid. The phase depends on the atoms’ energy – hot atoms have more energy, and they can move further apart (lower density); cold atoms have less energy and must stay close together (higher density).

If you take the same mass of material and compare it in solid and gaseous forms – the gas will occupy more volume than the solid.

The gas is less dense than the solid because when you divide the mass by the volume, there are fewer atoms in each cubic centimeter.

What is the Density of a Solid?

The density of a solid depends on what type of material you have in a specific volume.

Gold has a 19.32g per cubic centimeter density, whereas iron is 7.87g per cubic centimeter. The density depends on how the atoms sit with each other and the mass of those atoms.

The mass of an atom relates to its atomic number (number of protons in the nucleus) plus the number of neutrons. The atomic number of gold is 79 compared with iron at 26. One gold atom has more mass than iron, and logically the density of gold is higher than the density of iron because density is mass divided by volume.

You have an intuitive grasp of what density means – oil floats on water, and you want a high content of orange juice in your drink for quality.

What is the Density of Water?

Water is the most crucial material on Earth; we depend on it for life and transport – buoyancy means an object will float on water. An item floats if its density is less than water’s density.

The density of liquid water is 1g/cm³, and wood floats because the wood is less dense than water. Some exceptionally dense woods sink like a stone, and some really light stones (pumice) float if you want to get technical.

Steel being more dense sinks, but you can make steel boats that float.

Why?

Because the density of a steel boat as a complete structure is different – you can make a structure less dense than water.

What is the Density of Air?

Air is a mixture of gases – mainly nitrogen. The precise mix of air, moisture, and dust particles will change the air’s measured density in any location.

The density of our atmospheric air depends on:

• Altitude – we describe the air as thinner at altitude, and people can suffer from altitude sickness because the air is less dense.
• Atmospheric pressure – the weight of air pressing down on the layers beneath and pushing the air atoms closer together.
• Temperature – energetic, warm atoms move further apart.
• Humidity – moisture droplets suspended in air increase density.

Measuring the density of air is not a simple process if you want to be super accurate.

Air is about one-thousandth water density at around 1kg/m³, but the precise density needs you to quote the conditions when you measure the air density.

Mass vs. Weight Definition – Does it Matter?

Mass is an intrinsic property of an object that does not vary with location, and weight is a calculation of mass and gravity.

How does gravity affect weight and mass?

Gravity is always present, so why is it essential in defining mass and weight?

Gravity does not change the mass of an object – but it does change the weight. If you have a constant gravity (here on planet Earth), you can act as if mass and weight are the same measurements.

Mass becomes essential when you want to do something like fly an aircraft or launch a satellite. The object’s mass allows you to calculate how much energy you need to push the item in the opposite direction to gravity.

Most aircraft technology focuses on getting the weight or the mass down – baggage restrictions and using aluminum instead of steel.

Even running shoe technology is interested in mass (and weight) to reduce weight using less massive (or dense) materials.

Mass vs. Density

Density is a ratio of mass to volume; in other words, density measures how much mass is present in a given volume. Density helps work out the mass of an object and vice versa.

Density matters in many industrial applications for processing and manufacturing.

Concentrating or increasing the density of orange juice allows a larger quantity of orange juice to fit in the same volume. Pressurizing a gas increases the density, and many industrial processes use bottled gas, as do scuba divers.

If you have the volume and mass of a metal cube that you think is gold – the density will give you an estimate of purity or carats in that gold sample.

Generally, you use your knowledge of density and its relationship to mass every day without thinking about it.

Mass vs. Volume

Both mass and volume are physical properties of a material. A kilogram of solid iron (mass) will always occupy approximately the same volume of space. The volume varies slightly depending on the temperature of the iron.

Volume is the measurement you use when working on how to pack a box, a truck, a plane, cargo hold, or fit furniture into a room.

Mass is the measurement you use to know if the truck bed or box is strong enough for everything packed into it. If you have cargo space on a boat or plane, you can fill it to complete the available volume, but the mass needs to be low enough to let the plane fly or float.

Both physical properties are crucial in working out how to transport objects.

How Does Mass Relate to Volume?

Mass and volume have a proportional relationship to each other because how much you have of something determines how much space it occupies.

Humans are not brilliant at visually telling the differences between the same volume and same mass objects.

If you have a tall thin glass and a short, squat glass, most humans assume the taller glass contains more liquid. It does not matter that the volume is the same; humans judge volume initially on height – taller means more.

Similarly, if you take the same mass of gold and iron and paint both blocks pink, visually, people will pick out the bigger block as being more massive.

Human judgment reaches for obvious conclusions on how things ought to behave.

Volume vs. Density

If you know the volume of something, do you automatically know the density?

The answer is no because density is a ratio of mass to volume, and you can change how much stuff packs into a given volume.

Take a glass jar and fill it with irregular rocks. When the glass jar is full, you have a specific density of rock and space. You can increase the density without increasing the volume by adding sand or water to fill the spaces between the rocks.

You may know the volume, but without knowing the mass, you can’t know the density.

Do Mass, Volume, Weight, and Density Matter?

As you go about your daily life, does measurement of mass, weight, volume, and density really impact your life?

Generally, you get along just fine without bothering about these measurements, except these measurements shape the world.

Practical examples of why these measurements matter include:

• Buying food – you pay by the weight or volume to indicate the amount of food you need, such as a gallon of water or a gallon of milk). The density or mass of the food indicates the quality or purity of the product.
• Drinking coffee – you order by volume.
• Running a bath – you trust that someone has worked out the load strength of a bath full of water, so you don’t go crashing through the floor.
• Flying on holiday – the calculation of luggage and passenger weight matters if you don’t want the plane to drop out of the sky from a lack of fuel.
• Moving home – the volume of your household contents must fit the removal truck.
• Sending a package – depending on what and where, volume and weight are critical factors in the delivery cost.
• Exercising – your footwear is precision-engineered to perform by paying attention to mass, volume, density, and weight.
• Staying healthy – if you go on a diet, you rely on the dietician to work out nutrient density while you focus on carefully weighing out everything you eat.

Most of the time, you don’t bother about these measurements, but they define everything you own and everything you do.