# Calculating Mass From Force and Weight

By Kathleen Cantor, 07 Oct 2020

We've all heard the term “mass” in school before. But what actually is mass? And how can we calculate it if we know the force and weight of an object? Well, I’m glad you asked.

To calculate mass, you need to know the force of gravity that's acting on the object, and its weight. And then, you can calculate the mass by following this equation:

W = m x g

We will go into more detail later. First, let me explain the basics, so you have a clear understanding of how mass works.

## Weight

Weight is a measure of an object’s force pressing on a surface because of gravity. The SI (Système International) of weight is Newton. SI is the international standard of measurement used by every country in the world except in the USA.

Since weight is a force, it's measured in Newtons. The weight is represented by the ‘W’ letter in the equation. It’s a common misconception that weight is often mistaken with mass, we’ll get into that later.

## Mass

Mass is a measure of how much stuff or matter exists in an object. Matter, or stuff, is measured in atoms or molecules. Counting all the atoms that make up your entire body one at a time would be practically impossible, but sometimes you need that data quickly.

Instead of using ‘millions and billions of atoms’ for scale, we simply use kilograms or grams as a measure. The mass is represented by the 'm' letter in the equation.

## Force

The force that is mentioned in the equation above refers to gravity. The earth is massive, and it has a lot of mass. Mass creates gravity. Gravity pulls on every object around it, including us! Gravity is constantly pulling us down, towards the core of the earth, so that we don’t fly into outer space.

The force of gravity is measured in meters per second squared (m/s2). The gravity of the earth is represented by the ‘g’ letter in the equation. The earth’s gravity is 9.8 m/s2. It’s a constant.

## Calculating Mass from Force and Weight

So, let me repeat the equation clearly:

W = m x g

- W = Weight (Newton or kg)
- m = Mass (kg)
- g = Gravity (9.8 m/s2)

From the equation, we can conclude that weight is a direct result of mass times gravity.

### Example 1: Apple

Isaac Newton is peacefully enjoying himself under the apple tree. He was about to drift asleep when suddenly *bonk* an apple fell into his head and woke him up from his half-sleep. Upon waking up, Mr. Newton immediately weighs the apple, and it weighs 250 grams.

Help Mr. Newton find his apple’s mass.

From that problem, we can conclude that:

- W = 250 grams = 0.25 kilograms = 2.4517 Newton
- g = 9.8 m/s2

So, we substitute that data into the equation, and we’ll get:

- W = m x g
- 2.4517 = m x 9.8
- m = 2.4517 / 9.8
- m = 0.25017 kg = 250.17 grams

*Voilà!* The mass of the apple is 250.17 grams.

### Example 2: Apple, but on The Moon

Neil Armstrong just landed on the moon with his spacecraft. To celebrate it, Neil would like to eat an apple. Before eating it, Neil has to weigh the apple to measure his daily intake. The weight scale says that the apple weighs 41.3 grams. The gravity on the moon is 1.62 m/s2.

From that problem, we can conclude that:

- W = 0.0413 kilograms = 41.3 grams = 0.4052 Newton
- g = 1.62 m/s2

So, we substitute that data into the equation, and we’ll get:

- W = m x g
- 0.4052 = m x 1.62
- m = 0.4052 / 1.62
- m = 0.25017 kilogram = 250.17 grams

From that equation, the mass of the apple is 250.17 grams. That’s the same mass as Mr. Newton’s apples back on earth! What a coincidence.

## Misconception about Mass and Weight

Mass is the amount of stuff in an object. Weight is the force exerted from an object to the surface of the earth. Essentially, the mass is the volume while weight is the force. That’s why the SI of mass in kilograms and the SI of weight is Newton.

From the example above, about the apple belong to Isaac Newton and Neil Armstrong, you can deduct that mass is unchanged regardless of the location. Unless something blew up the apple and shattered it to pieces.

Meanwhile, weight is subject to gravity. Weight will change when the gravity changes. The gravity can change when the object is placed on other space bodies, like the moon or mars. You can also create an artificial gravity or increase the amount of gravity. One way to do it is to ascend tremendously quickly to the sky, like the astronauts inside a launching rocket or executing certain maneuvers on a fighter jet.

Fighter jet pilots and astronauts can experience about 6 to 8 g of force. That's 6 to 8 times of the earth's gravity. More than that, the pilot will most probably pass out. That’s because the bodyweight is also multiplied by that number. The body is buckling under pressure before eventually pass out under its own weight.

## Conclusion

- Mass is the amount of matter that makes up an object.
- An object’s mass will always stay the same regardless of the gravity or location unless the object is undergoing an internal chemical reaction.
- Weight is a measure of an object’s force pressing on a surface because of gravity.
- Force of gravity is a measure of pull exerted by a massive object like planets towards our body.
- Gravity is measured in meter per second squared (m/s2).

See the 1 Comment below.

14 Dec 2022 at 7:46 am [Comment permalink]

Some strange math shown above.

How is 250 grams = 2.4517 Newtons for starters? They are different units that represent different metrics. Mass is not Force. Depending on the motion and acceleration of the mass, the force could be various amounts.

The equation is F= m × a where a can be 9.8 m/s^2

How did you get 2.4517 ?

If the mass is measured to be 250 g, why is it then calculated to be 250.17 g ?

The example with Newton isn't doing justice to the problem and will confuse many.