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Mass to Weight Conversion
Weight of an Object
The word “weight” refers to how heavy or light an object is. In physics, weight is defined as the non-contact force of Earth’s gravitational pull on an object. That is, weight is the force on an object due to gravity. A non-contact force is a force that acts on an object without having direct physical contact with it. An object’s weight depends on the gravitational acceleration force acting upon it, which varies by location. For example, the weight of an object on Earth’s surface is different from its weight on the surface of the moon. An object on the surface of the moon weights a sixth of what it weighs on Earth because the moon’s gravitational pull is only a sixth of Earth’s.
Weight is the force exerted by the gravitational acceleration, which makes it a vector quantity. A vector quantity possesses both mass and a direction. Consider the weight of an object that is placed on the surface of the earth. The object has a quantity of mass, and its direction is towards the Earth’s center. The weight of any object is quantified by multiplying its mass by the gravitational acceleration force, as shown in the equation.
{eq}W = m * g {/eq}
The standard metric unit (SI) for weight is Newtons (N), which is equivalent to {eq}frac{kg cdot m}{s^2} {/eq}.
How to Calculate Weight
The weight of an object can easily be calculated if the object’s mass and the gravitational acceleration force acting on it are known. To find the weight of an object in Newtons, all units must be converted to metric units. Mass must be in kilograms and the force of gravity must be in meters per second squared. The following examples show how to calculate the weight of an object on Earth and the moon.
Example 1: The Weight of An Object on Earth
If the mass of a boulder equals 600 kilograms and the gravitational acceleration force on earth is equal to 9.81 {eq}m/s^2 {/eq}, those numbers can be plugged into the equation below to find the object’s weight:
{eq}W = m * g {/eq}
{eq}W = 600 kg * 9.81 frac{kg}{s^2} = 5886 frac{kg cdot m}{s^2} = 5886 N {/eq}
The weight of the boulder on Earth is therefore 5886 Newtons.
Example 2: The Weight of An Object on the Moon
If the mass of a boulder is 600 kilograms, and the gravitational acceleration force on moon is equal to 1/6 of earth’s gravity,
{eq}g_{moon} = 1.625 m/s^2 {/eq}, the weight of the boulder can be found by plugging those numbers into the following equation:
{eq}W = m * g {/eq}
{eq}W = 600 kg * 1.625 frac{kg}{s^2} = 975 frac{kg cdot m}{s^2} = 975 N {/eq}
The weight of the boulder on the moon is therefore 975 Newtons.
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 of an Object
The mass of an object is a scalar quantity that measures the amount of matter. Unlike weight, the mass of an object remains constant no matter where it is. This is because mass is not affected by gravity. Mass is how much matter is present in an object. Mass has magnitude only and no direction, unlike weight, which makes it a scalar quantity. Mass is usually measured in metric units: grams (g) or kilograms (kg). Mass can also be measured in other units like pounds (lbs), tons (t), and stones (st).
The table below summarizes the differences between mass and weight.
| Parameter | Mass | Weight |
| Definition | Amount of matter in an object | The gravitational force exerted on an object |
| Type | Scalar quantity, only has a magnitude | Vector quantity, has a magnitude and a direction |
| Variations | Remains constant no matter the location | Alters from one location to another due to the fluctuations in the gravitational force |
| Zero | Can never be equal to zero | Can be equal to zero in space (no gravity acts on the object) |
| Units | Kilogram (kg), grams (g), pounds (lbs) | Newtons (N) |
How to Find the Mass of an Object
The mass of an object can be calculated if its volume and density are known. Mass is equal to the product of the object’s density and volume. The following example shows how to find the mass of an object.
Example: Finding the Mass of an Object
If an object’s density equals 600 kg/m^3 and its volume equals 50 {eq}m^3 {/eq}, the mass can be calculated by multiplying the density (600) by its volume (50):
{eq}m = d*V = 600 kg/m^3 * 50 m^3 = 30000 kg {/eq}
The mass of the object is therefore 30,000 kilograms.
How to Convert Mass to Weight
The weight formula can be used to convert mass to weight. If the mass of an object is known, it can be converted to weight by simply multiplying the mass by the gravitational force. The formula of conversion is:
{eq}W = m * g {/eq}
Example: Converting Mass to Weight
If an object has 500 kilograms of mass and the gravitational force of Earth is equal to 9.81 {eq}m/s^2 {/eq}, the weight can be calculated by multiplying the mass (500) by the gravitational force (9.81):
{eq}W = m * g = 500 kg * 9.81 m/s^2 = 4905 frac{kg cdot m}{s^2} = 4905 N {/eq}
The weight of an object on Earth with 500 kg of mass is therefore 4905 Newtons.
How to Calculate Mass From Weight
The same formula can be used to calculate mass from weight: {eq}W = m * g {/eq}. If the weight and gravitational force on an object are known, the mass can be calculated by dividing the weight by the gravitational force, as represented below:
{eq}m = W/g {/eq}
Example: Converting Weight to Mass
If an object on earth weighs 8700 Newtons and the gravitational force of Earth equals 9.81 {eq}m/s^2 {/eq}, the mass can be calculated by dividing the weight (8700) by the gravitational force (9.81):
{eq}m = frac{8700N}{9.81 m/s^2} = 886.85 kg {/eq}
The mass of an object on Earth that weighs 8700 Newtons is therefore 886.85 kilograms.
Lesson Summary
Weight is a vector quantity that has both magnitude and a direction. It is the non-contact force that gravity exerts on an object. The weight of an object is different at locations where the gravitational force is different. The weight of an object on the moon is a sixth of its weight on earth because the gravitational pull of the moon is a sixth of Earth’s. The weight formula is the product of the object’s mass and the gravitational force: {eq}W = m*g {/eq}. The standard unit for weight is Newtons (N), which is equal to {eq}frac{kg cdot m}{s^2} {/eq}.
Mass is a scalar quantity that represents the amount of matter in an object. Unlike weight, the value of mass remains constant no matter where it is positioned because mass is not a function of gravity. Mass is usually measured in kilograms (kg) or grams (g). Knowing an object’s dimensions and density is sufficient to compute its mass. Mass is the product of an object’s volume and density. The weight formula is used to convert between mass and weight. The mass is multiplied by the gravitational force to find the weight of an object. The weight is divided by the gravitational force to calculate the mass of an object.
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.
Lesson Summary
On Earth, we often use weight and mass interchangeably, but they’re definitely not the same thing. Mass is the amount of matter an object has and weight is the force on an object due to gravity. Your mass won’t change from Earth to the moon – you’ll still be made of the same amount of stuff. However, your weight will change because there is less gravity on the moon, so the force pulling you down is also less.
Though they’re not the same, mass and weight are proportional. This means that no matter where you are, a more massive object will weigh more than a less massive object. An elephant will weigh more than a mouse on both the Earth and the moon because it’s more massive than the small mouse, no matter where they are!
You can easily calculate an object’s weight from its mass, or the mass from its weight. In physics the standard unit of weight is Newton, and the standard unit of mass is the kilogram. On Earth, a 1 kg object weighs 9.8 N, so to find the weight of an object in N simply multiply the mass by 9.8 N. Or, to find the mass in kg, divide the weight by 9.8 N.
Working in pounds? Have no fear! On Earth, a 1 kg object weighs 2.2 lbs, which also means that 1 lb is the same as 4.45 N. So if you have an object’s weight in pounds, but want to know the mass, simply divide by 2.2 lbs. To find the weight from the mass, multiply the number of kilograms by 2.2 lbs, and you’ll end up with the object’s weight in pounds. Just be careful converting pounds to Newtons, because you may not like your sudden weight ‘gain’!
Learning Outcomes
When this lesson is complete, you should be able to:
- Describe the difference between weight and mass
- Explain how you can calculate for mass and weight and accomplish conversions between them using Newtons and kilograms
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.
Lesson Summary
On Earth, we often use weight and mass interchangeably, but they’re definitely not the same thing. Mass is the amount of matter an object has and weight is the force on an object due to gravity. Your mass won’t change from Earth to the moon – you’ll still be made of the same amount of stuff. However, your weight will change because there is less gravity on the moon, so the force pulling you down is also less.
Though they’re not the same, mass and weight are proportional. This means that no matter where you are, a more massive object will weigh more than a less massive object. An elephant will weigh more than a mouse on both the Earth and the moon because it’s more massive than the small mouse, no matter where they are!
You can easily calculate an object’s weight from its mass, or the mass from its weight. In physics the standard unit of weight is Newton, and the standard unit of mass is the kilogram. On Earth, a 1 kg object weighs 9.8 N, so to find the weight of an object in N simply multiply the mass by 9.8 N. Or, to find the mass in kg, divide the weight by 9.8 N.
Working in pounds? Have no fear! On Earth, a 1 kg object weighs 2.2 lbs, which also means that 1 lb is the same as 4.45 N. So if you have an object’s weight in pounds, but want to know the mass, simply divide by 2.2 lbs. To find the weight from the mass, multiply the number of kilograms by 2.2 lbs, and you’ll end up with the object’s weight in pounds. Just be careful converting pounds to Newtons, because you may not like your sudden weight ‘gain’!
Learning Outcomes
When this lesson is complete, you should be able to:
- Describe the difference between weight and mass
- Explain how you can calculate for mass and weight and accomplish conversions between them using Newtons and kilograms
- Activities
- FAQs
Overview
The practice problems below will give you an opportunity to convert between the units of mass and weight using multiple conversion factors. The conversion factors are given where necessary and an example is provided below to assist in answering the questions.
Example
The mass of an object was measured as 110 grams. What is the weight of the object in Newtons? (1000 g = 1 kg, 1 kg = 9.8 N)
1. First, convert the mass to kg
110/1000 = 0.110 kg
2. Next, convert kg to N.
0.110 * 9.8 = 1.078 N
The weight of the object is 1.078 N.
Practice
1. The weight of an elephant was measured as 8.5 N. What is the mass of the elephant in kg?
2. The mass of a grape was recorded as 125 mg. What is the weight of the grape in N? (Note: 1000 mg = 1 g, 1000 g = 1 kg)
3. The mass of an apple is 1.02 g and the weight of an orange is 0.05 N. Which is heavier?
Solutions
1. 8.5/9.8 = 0.87 kg
2. First, convert mg to g.
125/1000 = 0.125/1000 = 0.000125 kg
Then, convert from kg to N.
0.000125 * 9.8 = 0.001 N
3. Convert the weight of the apple so that you can compare the values.
1.02/1000 = 0.00102 kg
0.00102 * 9.8 = 0.01 N
The orange is heavier as its weight is 0.05 N and the apple is 0.01 N.
How do you convert weight to mass?
Weight is converted to mass by using the weight formula:
W = m * g
The formula can be adjusted to:
m = W/g
The weight to mass conversion is done by dividing the weight by the gravity.
Is your weight equal to your mass?
The words weight and mass are often used interchangeably, but that does not mean that they are the same property. A person’s mass is constant no matter where they are. Their weight, however, fluctuates from one place to another. That is because weight is a function of gravity; it changes with the change in gravity.
How do you convert mass to weight?
Converting mass to weight is done by using the weight formula, which is:
W = m*g
Mass is converted to weight by simply multiplying an object’s mass by the gravitational force.
What is the weight of a 40 kg mass?
The weight of a 40 kg mass can be computed by using the weight formula, which is:
W = m * g
The gravitational force on Earth is 9.81 m/s2. Assuming that an object’s mass is 40 kg is on earth, the weight is computed by:
W = 40 * 9.81 = 392.4 N
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