# Mass and Weight: Differences and Calculations

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• 0:03 Weight Is a Force
• 1:11 Mass Is the Amount of Matter
• 2:21 Calculating Mass and Weight
• 4:06 Lesson Summary
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Lesson Transcript
Instructor: Sarah Friedl

Sarah has two Master's, one in Zoology and one in GIS, a Bachelor's in Biology, and has taught college level Physical Science and Biology.

We often talk about mass and weight as if they are the same. While they are proportional to each other, they are not in fact the same. In this video lesson you will learn to distinguish between the two, as well as convert one to the other.

## Weight Is a Force

Though you may not like what it says, when you stand on a scale, the reading you see is your weight. Weight is the force on an object due to gravity, so this is how much the Earth is pulling you toward it. The more you weigh, the greater the force, so the scale reads a higher number. Want to lose weight? Try thinking of it as lessening your force on the earth due to gravity!

Another option is to go to a higher elevation on Earth. While you probably wouldn't notice the difference, the force due to gravity decreases slightly as you go higher in elevation. Basically, the earth is pulling you down with slightly less force than at sea level, so your weight is reduced!

This is also why objects in space are 'weightless' - weight is relative to the amount of gravity. In space, where gravity is minimal, weight becomes almost insignificant. You might weigh 150 pounds on Earth where there is a lot of gravitational force pulling you down, but travel to the moon and your weight will drop significantly - to about 25 pounds! This is because gravity on the moon is about 1/6 of the gravity on Earth, so the force pulling you down is less.

## Mass Is the Amount of Matter

When you travel to the moon you weigh less, but do you actually become smaller? Is there less of your body than on Earth? Not at all! Your body has the same amount of 'stuff' on the moon as it does on Earth. This measurement is your mass, the amount of matter in an object.

On Earth, we often use mass and weight interchangeably because they're directly proportional to each other, but they aren't the same thing at all. An elephant has more mass than a mouse because the elephant has more matter than the mouse. It also weighs more than the mouse because the force due to gravity is greater.

What we mean when we say they are proportional is that even though the weight of an object might change with its location, that change is the same for every object. So the elephant weighs more than the mouse on both Earth and the moon by the same amount. Twice the mass means twice the weight, no matter where you are! So if you take that elephant into space and you try and push it, you'll find it's just as difficult as on Earth. This is because it still has the same amount of mass - the same amount of 'stuff' that you're trying to move no matter what it weighs.

## Calculating Mass and Weight

Luckily, if we know how much something weighs, we can easily calculate its mass. Likewise, we can also calculate the weight of something if we know how much mass it has. People usually refer to weight in pounds in everyday life, but in physics the standard unit of this force is the Newton. The symbol we use for Newton is N. Mass also has a standard unit, the kilogram, or kg.

The conversion factor between these two is 1 kg to 9.8 N. An object that has a mass of 1 kg weighs about 9.8 N. So if you already know the mass of an object and you want to know its weight in Newtons, you simply multiply the number of kilograms by 9.8 N. Conversely, if you know an object's weight in Newtons, you can divide by 9.8 N, and you'll get that object's mass.

Using Newtons is standard in physics, but what exactly is a Newton? Well, it's about 0.225 pounds. To look at it the other way, one pound (symbol lb) is the same as 4.45 N. So if you weigh 150 lbs on Earth, you weigh 4.45 times as much in Newtons - 667.5 N, in fact! Next time you think you need to lose weight, just think about how much more your scale would read if it was in Newtons instead of pounds!

You can also convert pounds and kilograms directly, because 1 kg weighs 2.2 lbs on Earth. So in order to get an object's weight in pounds, simply multiply the mass by 2.2 lbs. If you want to know an object's mass, divide by 2.2 lbs, and you'll get the object's mass in kilograms.

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