The Difference Between Mass and Weight

The difference between mass and weight is that they are quantities which ultimately mean different things, are measured differently, relate to different physical quantities and relationships. They are related to one another, sure. However, they are not the same.

Our weight is the amount of force that the Earth exerts on an object, whereas the mass of an object is literally how much matter that object is made of.

The reason why we confuse these concepts, or why they are confuse-able when one begins to learn science, is when used in everyday language, they mean the same thing. Most of the time when we are talking about weight we actually mean what the scientist called mass. Indeed, on an average day virtually no ordinary person is going to be talking about weight as the scientist means it.

The Difference Between Mass and Weight

Mass is a measure of an actual quantity of material. Your mass does not vary regardless of where you happen to be in the universe. It is a measure literally of the total quantity of atoms within your body — or within any object — taking into account the various types of atoms even. It is how much stuff you are made of, measured in kilograms (kg), and other non-SI units like pounds (lbs).

Weight on the other hand is an exact measure of the force exerted onto an object by the Earth. Technically speaking, we call this force the force of gravity or gravitational force acting on a body at a given time, $F_g$.

$F_g$ is measured in the units of force called newton’s ($N$). We measure the gravitational force acting on a person with the same units as the weight of a person, because these are the same quantities. This means that weight (symbolized as $W$) is equal to force of gravity $(F_g$)

\[ F_g = mg = m a_g = W \]

In this case the mass of a person, $m$, is in kilograms. While the acceleration due to gravity, written as either $g$ or $a_g$, is equal to $9.81 m/s^2$ which is the acceleration that the Earth’s gravity causes on objects near its surface. This is how to calculate the true weight of a person, and this is the difference between mass and weight.

An 54.5-kg person (about 120 lbs) has a mass of 54.5 kg. However, their weight is the force of gravity acting upon them given by the above equations. This means that a 120 lbs (54.5 kg) person has a weight of about 534.6 N.

\[ F_g = W = mg = (54.5 kg)(9.81 m/s^2) \simeq 534.6 N \]

However on Saturn, because the surface gravity is greater than that experienced on Earth at $10.44 m/s^2$ a person would also have a greater weight even though their mass hasn’t changed at all. This is given by the following equation. Consider that the force of gravity on Saturn’s surface as $F_{gs}$.

\[ F_{gs} = m a_{s} = (54.5 kg)(10.44 m/s^2) = 568.98 N \]

You can see how a person’s weight on Saturn will be just over 34 N greater than on Earth.

Resources

1. The difference between mass and weight: Though related, they’re actually quite different. Jake Port. 3 April 2018. Cosmos Magazine. <https://cosmosmagazine.com/science/physics/explainer-whats-the-difference-between-mass-and-weight/>. Accessed 22 April 2022.