# What do scales measure?

What do scales measure? The obvious answer is kilograms (or grams). That is what the reading on the scale indicates. However this is not what the scale is measuring. It actually measures force, and it is all to do with the way in which the scale is constructed.

## A mechanical scale

Inside a mechanical scale is a spring. And springs are used to measure force. The way they measure force is through the fact that if you shorten the length of a spring, a force is required. The greater the amount you shorten the spring, the more the force that is required. So by measuring the change in length of the spring, you have an indication of the force applied.

In the scale, this change in spring length is used to move a dial which indicates the force from your weight acting on the spring. We measure force in the unit known as a newton. So your scale should display your weight in newtons. However it will normally indicate your weight in kilograms. But kilograms is actually a measure of your mass and this is where the confusion starts.

## Mass and weight

Mass and weight are not the same thing. You may think of mass as the amount of matter in an object. And objects with matter attract each other simply because they have mass. This is the result of the gravitational force of attraction between the masses of the objects. Our weight is simply the force on us due to the pull of the Earth on our mass. This pull force is directly related to our mass. So the larger our mass the larger the pull force from Earth. Since there is a direct relationship between mass and weight it is possible to convert the scale reading directly from newtons to kilograms and thereby indirectly measure our mass.

## What do scales measure?

So how do you know that your scale is actually reading force and not mass? Well there is an easy way to confirm this. Stand on your scale close to a fixed object and then carefully push yourself down on the scale using the fixed object as a support. You will suddenly see the scale reading increasing, indicating that your mass has increased. However this is not the case since you haven’t suddenly put on mass. What you have done is added an extra force to the scale, and it is this force, combined with the force of your weight, that the scale has measured.

This simple experiment is an easy demonstration that a spring scale actually measures force and not mass.

## Before you go!

Can you explain what gravity is? You’ll be surprised how easy it is to explain if you take a look at my video on Newton’s Law of Universal Gravitation.

Mac

Thank you for the explanation.

As per your discussion, the weighing machine actually measures the weight and it is calibrated to give mass, ie, the value (weight) is divided by g=9.8 m/s2 to give the mass value. Since the weighing machine is calibrated for the condition in the Earth, If the same weighing machine is taken to the Moon, whether it will show the same mass?

Hi Gayu. The scales measure force and then convert that to mass as a result of the label on the scales being printed with a calibration relating the force to mass on Earth. On the Moon the force measured would be less and therefore the mass reading would be less. The mass reading would therefore be incorrect. Note that the scales would be measuring the force correctly. The force is not normally displayed on a scale label and instead the conversion of the force to mass is shown. This is why there is the discrepancy. We are not using the scales to measure the mass directly.

So, if I stand on a normally used scale that shows reading is 70 kg… Is it the reading of my mass?

Hi Zul. It is not directly measuring your mass. It measures the force created by your mass being attracted to Earth. This is called your weight. Since there is a direct relationship between mass and weight, the manufacturer of the scales can put a scale on it which gives a reading of your mass calculated from your weight. So when it says 70kg mass it is correct. Your mass is 70kg. But it has calculated this from measuring your weight.

Hi Sir,

If my mass is 70kg. then what is my weight?

Is the force 70 x 9.8 N ?

Hi Sasi. Yes that is correct. The force is your weight.

Hi Professor,

I’m doing this experiment to test how the mass of an object affects the weight of an object due to gravity. I don’t know how to make a good experiment out of this. I first started by measuring the distance and having different masses in similar containers. Although distance doesn’t seem that important in this case. Are you able to help me?

Thanks

Hi Felicity. Scales measure the weight of material placed on the scale due to gravity producing a force on the mass of the material. Coins of the same monetary value are very carefully made to have the same amount of mass in them. So you can use these facts to help you do the experiment. Take two coins of the same monetary value and weigh them together on scales. Now take one of the coins off the scales and measure the weight of one of them. You will have reduced the total mass of material on the scales by 50% when you removed one of the coins. You should find that when you removed 50% of the mass that the weight reduced by 50%. Therefore the mass has a direct influence on the weight. It doesn’t matter that the coins are separate objects as we are investigating total mass of material. What do you think would happen if you measured three coins? See my video on Hooke’s law to see this in action.

Thanks Professor

I’ll check out other information

Best way to understand ! Thanks a million Professor for your examples and quick responses to queries.

Hi professor, don’t you think that the scale has been calibrated to measure mass instead of force.

From your example one could infer that the scale calculates a person’s mass from the weight given to it.

Hi Horia. Yes the scale has been calibrated to display mass from an applied force on the scale. The internal mechanism inside the scale measures force. The printed label on the scale display has been calibrated to convert this into a reading of mass.

I have a mass, so do i produce gravity?

Also, if i get rid of my mass, will i float?

Hi Chris. Yes you produce an attractive gravitational force between you and other objects since you have mass. If you have no mass you would have no force between you and Earth so in theory you would float if you were above the ground.

Thank you very much Professor. it was my very big confusion between weight and mass which is showing in scale.

Dear Professor,

Have a doubt on this subject, when I standing on a weight machine, it shows 80Kg.

Now my daughter tried to pull me up, for her she can’t pull me up, but she is giving an upward with some force, I am still on the weight machine, does the weight machine will show lesser than 80Kg? or still, it will show 80Kg?

Hi Manjunathan. Assuming your daughter is not on the scales when she applies an upward force to you, she reduces the downward force on the scale, and therefore the scale reading will reduce (to less than 80kg). Since the scale is showing mass it will say that your mass is reducing. Your mass is not reducing but the force on the scale is reducing, and since it measures force you will see the scale reading reduce.

Thanks, Professor. I really appreciate your quick reply and making a correction in my understanding.

If say my daughter is 20KG and standing on another separate scale, and when she tried to pull me up, where my scale reading is reduced by say 9.8N(1KG), in my scale it would be 79KG and in her scale, it would be 21 KG ? Basically overall MASS remains same?

Thanks once Again.

Manjunathan

Hi Manjunathan, Yes her scale reading would increase by the amount your scale reading decreased.

But when I am weighing myself on a scale what am I measuring

Hi Leila. The scale is measuring the force between you and Earth. This is your weight. The reading on the scale may have been calibrated so that it converts this force into mass. Use the reading and units on the scale to determine what you have measured.

That was a very useful Information. Thank u very much.

Thanks for your feedback Sarath.

Pounds are actually a measure of force — slugs being the related unit for mass. We can convert a scale “weight” of kg (mass) to pounds (force) by multiplying by ~2.2. So a kg scale is calibrated to give out its readings in mass but a pound scale gives out its readings in force? Don’t we have an apples and oranges situation here units-wise?

Hi Anderson, You can calibrate the reading of the scale in any appropriate unit. However the mechanism inside the scale is measuring force and that was the point that I was explaining.

Then should I confidently say that my mass is 90 Kg weighed on weighing machine? & Weighing machine measures mass only not a weight?

Hi Sagar, yes if the weighing machine says your mass is 90 kg then that is your mass (assuming the weighing machine has been calibrated correctly). The confusion is that the weighing machine actually measures your weight, that is a force between you and Earth. We can calibrate the scale to show your mass since there is a direct relationship between your mass and your weight on Earth. See my video on gravitation here.

So if I weigh 98 kg on Earth is my mass 98 kg or 98/9.8 = 10 kg?

Hi Doug. Your weight is not measured in kg, that is your mass. On Earth if you have a mass of 98kg your weight is 98 x 9.81 Newtons. When you weigh yourself on scales the display is actually showing your mass in kg even though it is measuring your weight.

If the scale reads in kg, how do you convert it to Newtons if the kg reading is not mass.

Hi Fred, you convert mass to force by multiplying by the acceleration of the object. On Earth you multiply by 9.81 m per second per second. The 9.81 represents the acceleration that the object has during free fall and results from the attractive force between the mass of the object and the mass of Earth. This attractive force is the weight of the object on Earth. See my video on Newton’s law of gravitation.

So do we get a value that is divided by acceleration due to gravity or we get a value on the scale that includes the value of g

Hi Meriam, The scale is calibrated, which means that a force is applied to it and then the scale is created to provide this reading in kg to give a mass reading. You would need to divide the force by g to get the mass.

Very well explained. Thanks. Now I can use this explanation to help my students understand this concept

Thanks for your feedback Raadhika.

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