# Scale? -- mass or weight

## Main Question or Discussion Point

When I step on a scale I see that it says....70kg. We typically call this value weight? However, kg is used for "mass" and not "weight". So when we say 70kg do we mean that my mass is 70kg OR do we mean that my weight is 70 N?

So if it does mean mass, then my ACTUAL weight is 686N!!! lol
And if it means weight, then my mass is roughly 7kg.

See where I'm coming from?

And just to let you guys know, b4 u waste ur time, I def. know the difference between mass and weight. I'm just uncertain about what we are actually measuring.

I truly appreciate anyones help! thanks

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pao
you are measuring your mass!! Doc Al
Mentor
When I step on a scale I see that it says....70kg. We typically call this value weight? However, kg is used for "mass" and not "weight". So when we say 70kg do we mean that my mass is 70kg OR do we mean that my weight is 70 N?
Since on the Earth's surface weight and mass are proportional, for everyday usage it doesn't matter which units you use. You can say that you "weigh" 70kg or 686 N (not 70 N!). (But in physics, weight is a force, measured in N not kg.)

What a scale actually measures depends on the type of scale. A typical "bathroom" scale measures force--your "weight". Bring it to the moon and you'll weigh less according to the scale, but your mass is unchanged. But a balance scale compares masses; it will read the same on the moon.

arildno
Homework Helper
Gold Member
Dearly Missed
Well, what the scale actually actually measures is how much a spring within the apparatus has been compressed, or, if a torsional spring has been used, the displacement angle.

And then that is correlated to the effective weight the person standing upon it must have exerted upon the scale..

D H
Staff Emeritus
A spring scale (e.g., the typical bathroom scale) comes close to measuring your weight (within about 0.3% on the Earth). What a spring scale measures is the normal force needed to keep a person from sinking into the floor. This normal force is your apparent weight, not your "actual" weight. The difference: weight is tautologically the force due to gravity while apparent weight is the sum of all forces acting on a body except gravity.

Since on the Earth's surface weight and mass are proportional, for everyday usage it doesn't matter which units you use. You can say that you "weigh" 70kg or 686 N (not 70 N!). (But in physics, weight is a force, measured in N not kg.)

What a scale actually measures depends on the type of scale. A typical "bathroom" scale measures force--your "weight". Bring it to the moon and you'll weigh less according to the scale, but your mass is unchanged. But a balance scale compares masses; it will read the same on the moon.
um, if you're saying that it actually measures "weight" as we know it is in physics, then why not say 70N? B/C if it is truly measuring weight then the gravatational pull is already factored in....so saying 686 in that case would be incorrect.

So if I'm reading this right are you guys saying that my mass IS 7kg?

Doc Al
Mentor
um, if you're saying that it actually measures "weight" as we know it is in physics, then why not say 70N? B/C if it is truly measuring weight then the gravatational pull is already factored in....so saying 686 in that case would be incorrect.

So if I'm reading this right are you guys saying that my mass IS 7kg?
You're the one who said it reads 70 kg in your first post. In everyday usage 70 kg = 686 N (:yuck:). (I thought you said you understood the difference between mass and weight? )

You have to differentiate between the formal definition in physics and the everyday definition in commerce. The weight of a head of lettuce will be in kg as will the weight of a baby at the pediatrician. In America, both will be in pounds. That's just the system that exists.

You're the one who said it reads 70 kg in your first post. In everyday usage 70 kg = 686 N (:yuck:). (I thought you said you understood the difference between mass and weight? )
you said that you can say that you weigh 70kg or 686N....which doesn't make any sense. What can be said is that one is Mass and the other is weight, respectively. Everyone is saying that the scale measures weight, so therefore it would be more correct to say 70N. I don't get it.

I'm not trying to be stupid but i'm trying to understand this 100%

You have to differentiate between the formal definition in physics and the everyday definition in commerce. The weight of a head of lettuce will be in kg as will the weight of a baby at the pediatrician. In America, both will be in pounds. That's just the system that exists.
...and what is the formal definition in commerce?

Doc Al
Mentor
you said that you can say that you weigh 70kg or 686N....which doesn't make any sense. What can be said is that one is Mass and the other is weight, respectively. Everyone is saying that the scale measures weight, so therefore it would be more correct to say 70N. I don't get it.
As I said in my initial post, what it really measures is force. (Jump up and down and your scale "weight" will change.) What units you use to express that force is arbitrary. When they say your "weight" is 70 kg, that's the same as saying your weight is the same as that of a 70 kg mass--the weight of which is 686 N.

...and what is the formal definition in commerce?
That will be determined in each case by the agency having legal jurisdiction. In interstate commerce, it may be the ICC. In the grocery store, it may be the state bureau of weights and measures. In most cases, these will be traceable back to a standards body such as NIST.

There is, I think, no understanding available in such matters. Like the difference between aircraft heading and engineering standard angles, it's just a matter of usage.

As I said in my initial post, what it really measures is force. (Jump up and down and your scale "weight" will change.) What units you use to express that force is arbitrary. When they say your "weight" is 70 kg, that's the same as saying your weight is the same as that of a 70 kg mass--the weight of which is 686 N.
i'm gonna try one more time to understand this.

I now understand that it is measuring your force. I see that it's dependant on the gravataional pull. The scale is reading your mass affected by gravity. So therefore, gravity is by default factored in? So that's my problem. I don't see why you would multiply it by 9.8 when gravity was already factored in to give you the reading of 70kg. That's why I was saying that it would make more sense if we would say 70N.

And I do understand the difference. Mass is absolute....doesn't change. Weight is dependant on gravity...so it can change.

Doc Al
Mentor
I now understand that it is measuring your force. I see that it's dependant on the gravataional pull. The scale is reading your mass affected by gravity. So therefore, gravity is by default factored in? So that's my problem. I don't see why you would multiply it by 9.8 when gravity was already factored in to give you the reading of 70kg.
Think of multiplying by 9.8 as doing a units conversion. A mass of 1 kg weighs 9.8 N. So, can refer to that same mass using either units.
That's why I was saying that it would make more sense if we would say 70N.
But that's the weight of a 7.1 kg mass. You can't just take the number 70 and change the units from 70 kg to 70 N, since kg and N are already defined to be related by w = mg. (Note that we are talking about "everyday" usage, not technical usage in physics.)

• Bathroom scales assume you are under the influence of Earth's gravity at 9.8m/s/s, and calculate your assumed mass off of that assumption. A quick way to fool your scale is to get on an elevator that accelerates upwards and downwards, making it look like you weigh more then less of what you actually do.
Should your scale read 70kg, it believes you have a mass of 70kg, as you are probably exerting a force of 686N on the scale. If the world were less complicated, your scale would read out in Newtons, or we would say you mass yourself on a scale, instead of weighing yourself. Do keep in mind, though, that pounds are a unit of force, so you can weigh yourself in pounds or newtons, and mass yourself in kilograms (or slugs).

• D H
Staff Emeritus
There is, I think, no understanding available in such matters. Like the difference between aircraft heading and engineering standard angles, it's just a matter of usage.
The people at NIST know the difference between mass and force. The English system units of mass and force are pounds-mass and pounds-force, respectively. Note the qualifiers. We say pounds in the vernacular. So what? Scientists and engineers who are forced to use English units do use the precise terms (or their abreviations, lbm and lbf).

Derived units can be used in lieu of the standard ones to enable the use Newton's second law in the form applied by our metric system-using cohorts (i.e., F=ma). With lbm and lbf, one has to use the more generic form F=kma.

Think of multiplying by 9.8 as doing a units conversion. A mass of 1 kg weighs 9.8 N. So, can refer to that same mass using either units.
that's sort of what I've been trying to get at this whole time. You're saying that 1kg = 9.8N.

How did we get the 1kg measurement? Obviously it had to come from weighing it on a scale to get the mass...NOT the weight. B/C if the scale gave us our weight then there would be no need to multiply it by 9.8

I emailed the admin at "http://www.mathsisfun.com" [Broken] b/c he had an article on weight vs. mass which can be found at http://www.mathsisfun.com/measure/weight-mass.html

He said and I quote "The scale estimates your mass based on the force your body exerts on it.

If the scale measures kg, you can work out how much force your body is
exerting on it by multiplying by 9.8 (to convert kg into Newtons)."

According to him the scale measures mass and not weight. This is more consistent than saying that the scale measures weight. B/c if you said that the scale measures weight than you would be multiplying by 9.8 two times (one from the scale figuring out your weight and the other from multiplying it by 9.8).

So I think by weight, you REALLy mean mass.

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D H
Staff Emeritus
Dr. Al is most certainly not saying 1kg = 9.8N. Your bathroom scale measures force, not mass. Pick the scale up and give it a good squeeze with your hands. It will register some value.

If you want to be real picky, it isn't even measuring force. As Arildno said earlier, it is actually measuring the displacement of a spring. The spring has a known spring constant, so the displacement of the spring varies linearly with the force that caused the displacement. The normal force that keeps a person standing on the scale from sinking into the scale is proportional to the person's mass; the constant of proportionality is the Earth's gravitational acceleration. Your scale automatically converts the spring displacement (units=length) to mass via the known spring constant and the known gravitational acceleration.

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• Doc Al
Mentor
that's sort of what I've been trying to get at this whole time. You're saying that 1kg = 9.8N.

How did we get the 1kg measurement? Obviously it had to come from weighing it on a scale to get the mass...NOT the weight. B/C if the scale gave us our weight then there would be no need to multiply it by 9.8

I emailed the admin at "http://www.mathsisfun.com" [Broken] b/c he had an article on weight vs. mass which can be found at http://www.mathsisfun.com/measure/weight-mass.html

He said and I quote "The scale estimates your mass based on the force your body exerts on it.

If the scale measures kg, you can work out how much force your body is
exerting on it by multiplying by 9.8 (to convert kg into Newtons)."

According to him the scale measures mass and not weight. This is more consistent than saying that the scale measures weight. B/c if you said that the scale measures weight than you would be multiplying by 9.8 two times (one from the scale figuring out your weight and the other from multiplying it by 9.8).

So I think by weight, you REALLy mean mass.
We're making a mountain out of some trivial semantics. When I say weight, I mean weight: the force of gravity.

He's just saying it "measures" mass because the units it's marked in are mass units! Cross them out and write the units in Newtons. Now it measures weight!

Again, what the scale actually does is measure the force you exert on it. We use it to measure our mass or weight--since they are proportional, you can choose which units you'd like your answer in. The same scale can be marked to show both units at the same time, if you like. (I've seen scales that give readings in both pounds and kilograms.)

As far as weight goes, it's most accurate to say the scale measures "apparent" weight (as D H mentioned). If you jump up and down on the scale, your apparent weight changes. Obviously, the scale is not directly measuring your mass since your mass doesn't change. (Of course we can use it to measure our mass, again, because weight and mass are proportional.)

I would say that it's more accurate to say the scale measures weight, not mass--since I can take it to the moon and it will show your weight (in whatever units the scale is marked with) on the moon. If it uses kg, then your weight will no longer show as 70 kg, but only about 11.6 kg. Do you really think your mass has changed?

You might want to read this: http://en.wikipedia.org/wiki/Weighing_scale" [Broken]

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I emailed a professor of Physics @ a University in Ohio and he had this to say:

That makes complete sense to me! However, everything else I've read on here just sounds completely contradictory. I'm just gonna stick w/ what the professor says b/c it makes more sense to me.

Doc Al
Mentor
I emailed a professor of Physics @ a University in Ohio and he had this to say:

That makes complete sense to me!
To me too! That's completely consistent with everything that I've been saying. Where have you been?

All you really asked him is: If the number is in kilograms, is it my mass or my weight? What else can he say but that it's your mass! :rofl: (He probably thought you were nuts!) Of course that number represents your mass--and you can convert it to your weight.

(Of course you didn't ask him the real question of how does the scale actually work? Does it really measure mass or does it measure force? No big deal.)

However, everything else I've read on here just sounds completely contradictory. I'm just gonna stick w/ what the professor says b/c it makes more sense to me.
Good for you. You were spending way too much mental energy on this one. (But be careful of those trick questions on the physics test! You really should learn the difference between how a weighing scale works and how a mass balance works.)

• Should your scale read 70kg, it believes you have a mass of 70kg, as you are probably exerting a force of 686N on the scale. If the world were less complicated, your scale would read out in Newtons, or we would say you mass yourself on a scale, instead of weighing yourself. Do keep in mind, though, that pounds are a unit of force, so you can weigh yourself in pounds or newtons, and mass yourself in kilograms (or slugs).
Listen to Doc Al and Jakell.
When your scale reads 70 kg what it is really doing is weighing 686N and just dividing by 9.8m/s2 and giving you a reading in kg. It assumes your mass from your weight becuase the kg it is a usefull unit.

In your post you mentiong 70 kg. Now on earth that will give you a force of 686 N but you can only go from kg to Newtons by multiplying by 9.8 and you can only go from Newtons to kg by dividing by 9.8. You took kg and divided (that is an illegal step).

Bathroom scales assume you are under the influence of Earth's gravity at 9.8m/s/s, and calculate your assumed mass off of that assumption. A quick way to fool your scale is to get on an elevator that accelerates upwards and downwards, making it look like you weigh more then less of what you actually do.
Should your scale read 70kg, it believes you have a mass of 70kg, as you are probably exerting a force of 686N on the scale. If the world were less complicated, your scale would read out in Newtons, or we would say you mass yourself on a scale, instead of weighing yourself. Do keep in mind, though, that pounds are a unit of force, so you can weigh yourself in pounds or newtons, and mass yourself in kilograms (or slugs).
yeh but earths gravity isnt always 9.8 is it?????? as doc al was saying its just how much you are depressing the spring, so its the force exterted by your weight on the scale caused by gravity,,, i dont think the scale assumes anything

D H
Staff Emeritus
The manufacturers of the bathroom scale made many assumptions. Some are printed as user instructions. "To obtain an accurate reading, stand still with all of your mass supported by the scale and centered over the scale." There are several unprinted assumption as well. Two of these are F=-kx (Hooke's law) and g=980665 m/s2 (Earth standard gravity).

What the scale truly measures is the deflection of the spring. That deflection is proportional to the force applied to the scale if the spring in the scale is truly "Hookean". There is no such thing as a purely linear spring. The scale will do a fair job of measuring your weight if you have something close to the average weight. It will not do such a good job measuring the weight of an ant or an elephant.

The second assumption is the acceleration due to gravity. A spring scale measures weight, not mass. There is a linear relation between weight and mass, but that relation varies with location. Suppose you take the scale and a big rock with you on a circumpolar trip around the world. The scale will show that the rock has a different mass in Helsinki than it does in Djakarta. The mass of the rock hasn't changed but its weight has. The scale measures weight, not mass. The manufacturers assumed some value for g to give the appearance that the scale measures mass.

Bathroom scale questions

I've been struggling with the whole "weight" issue...I'm a former engineer, and current teacher. I always strive to make sure I'm accurate with my lessons. I understand the physics definition of weight, which has the units of force (either in N or lbf). I understand my weight will be different depending upon gravity (or change in acceleration for that matter). I've spent two hours searching the internet to really understand what a scale DISPLAYS...which led me down a huge path, and ultimately to this site. Fantastic, frustrating, interesting discussion.

I think the root of my confusion (and other people as well) is with pounds force and pounds mass, and how it relates to my bathroom scale. Is my understanding correct that:

A scale MEASURES pounds FORCE, or N. The typical scale is, however, calibrated to factor in gravity. Thus,

A scale DISPLAYS either pounds or kg. In this case, aren't the units pounds MASS (otherwise, you couldn't simply convert kg to lbm by dividing by 0.453, because your units wouldn't work out)?

Although I'm sensing those that found nirvana and truly understand the differences between weight and mass are getting frustrated with the constant questions, I'd really appreciate your feedback...