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Old Jul 18th 2013, 06:36 PM   #1
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Calculating mass from weight in lbs.

So, this has been bugging me for a while. I weigh about 150 lbs, and I want to calculate my mass in kg. A lot of forums are saying to simply divide my weight in lbs by 2.2, as there are ~2.2 kg/pound. However, my reasoning tells me that this would be my weight in kilograms, not my mass. Here's my thought process:

Force (F) = Mass (m) x Acceleration (a)
Weight = Fg = mg
150 lbs = F(g) = F(9.81)
(150/2.2) = 68.18 = weight in kg = Fg = mg
68.18=m(9.81)
68.18/9.81 = m

m = ~6.95 kg

Thoughts? I'm just looking for a little clarification, really. Thanks in advance!
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Old Jul 19th 2013, 08:00 AM   #2
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Originally Posted by Cosmophile View Post
So, this has been bugging me for a while. I weigh about 150 lbs, and I want to calculate my mass in kg. A lot of forums are saying to simply divide my weight in lbs by 2.2, as there are ~2.2 kg/pound. However, my reasoning tells me that this would be my weight in kilograms, not my mass. Here's my thought process:

Force (F) = Mass (m) x Acceleration (a)
Weight = Fg = mg
150 lbs = F(g) = F(9.81)
(150/2.2) = 68.18 = weight in kg = Fg = mg
68.18=m(9.81)
68.18/9.81 = m

m = ~6.95 kg

Thoughts? I'm just looking for a little clarification, really. Thanks in advance!
Beware the (mostly I think) European idea of weight in kg, but weight in kg is not equal to mg. There is a unit for kg-weight, but bear in mind that kg is a unit of mass. The conversion between lbs and kg is indeed 2.2

-Dan
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Old Jul 19th 2013, 12:18 PM   #3
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So the division by g isn't required, then?
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Old Jul 19th 2013, 12:23 PM   #4
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Originally Posted by Cosmophile View Post
So the division by g isn't required, then?
Nope. You are comparing a weight to a weight, so no g necessary. Now if you want to compare mass to mass you want to convert your weight in pounds to mass in stones. Don't bother with the kg-weight thing.

I just stick with the metric units. It's soooo much less confusing.

-Dan
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Old Jul 19th 2013, 12:33 PM   #5
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I'm writing an article about the Schwarzschild Radius (I know physics beyond this question, believe it or not), and I'm trying to put into words how to best find one's mass if they know their weight. If I divide by 2.2, my logic tells me that this wouldn't be actual *mass*, because I haven't taken into account the force of gravity.

I work better with math, so if you could perhaps show me where I'm wrong mathematically, I'd appreciate it!
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Old Jul 19th 2013, 12:36 PM   #6
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Originally Posted by Cosmophile View Post
I'm writing an article about the Schwarzschild Radius (I know physics beyond this question, believe it or not), and I'm trying to put into words how to best find one's mass if they know their weight. If I divide by 2.2, my logic tells me that this wouldn't be actual *mass*, because I haven't taken into account the force of gravity.

I work better with math, so if you could perhaps show me where I'm wrong mathematically, I'd appreciate it!
Is there any reason that you would need to use weight in lbs in the article? I'd use the weight in N. (That's also a 2.2 conversion and converts weight to weight directly.)

-Dan
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Old Jul 19th 2013, 12:43 PM   #7
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I write for a Facebook page (From Quarks to Quasars) and we try to keep our articles full of actual science while making it easy for our readers to see the connection to their lives. A lot of people are used to dealing with weight in lbs, so I figured it would be nice to include a quick section on how to find one's mass from their weight so that one could accurately calculate their Schwarzschild Radius.
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Old Jul 19th 2013, 01:37 PM   #8
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Maybe this will help. When you say you "weigh" 150 pounds what you mean is that when standing on the surface of the earth the force of gravity acting on your body is 150 pound-force. From F=mg this tells you that your mass is:

m = F/g = 150 lbf/(32.2 ft/s^2) = 4.66 lbf-s^2/ft

(Note that we use the term lbf or "pound-force" to clarify that pound here is a unit of force, not mass.)

This is not a terribly handy conversion. So, we can multiply this by a special version of 1: since 1 lbf = the weight of 1 lb-mass accelerated at g, we have 1 lbf = 32.2 lbm ft/s^2. Or in other words 1 = 32.2 lbm-ft/lbf-s^2. So from the previous formula we have

m = 4.66 lbf s^2/ft x (32.2 lbm-ft/lbf-s^2) = 150 lbm

So your mass is 150 lb-mass. Note that in imperial units one's mass (in pound-mass) is the same number as on'e weight (in pound-force)on earth. By the way the multiplier of 32.2 lbm-ft/lbf-s^2 comes in very handy quite often si yuor using imperial units.

Now to convert to SI. There are about 2.2 lbm per Kg, so your mass in SI units is 150 lbm/2.2 lbm/Kg = 68.2 Kg. And your weight in SI is W=mg = 68.2 Kg x 9.8 m/s^2 = 668 N. Hence 150 lbf = 668 N.

It is a common misnomer to use the term Kg to describe weight, because strictly speaking Kg is a unit of mass. Your mass is 68.2 Kg no matter where you are. If you traveled to the moon where the force of gravity is one sixth that of earth your mass remains the same (150 lbm or 68.2Kg) but your weight would be 150lbf/6 = 25 lbf or 668N/6 = 111 N. So, when people talk about one's weight in Kg they are implying that they are standing on the earth's surface, and their "weight" of xx Kg is the force of xx Kg being accelerated at g=9.8 m/s^2.

Hope this helps.

Last edited by ChipB; Jul 19th 2013 at 01:40 PM.
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Old Jul 19th 2013, 01:40 PM   #9
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Ah! I understand now! Thank you so much! The math was all I needed to see. Wow, now I feel a bit silly...
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Old Jul 19th 2013, 02:09 PM   #10
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Originally Posted by ChipB View Post
Maybe this will help. When you say you "weigh" 150 pounds what you mean is that when standing on the surface of the earth the force of gravity acting on your body is 150 pound-force. From F=mg this tells you that your mass is:

m = F/g = 150 lbf/(32.2 ft/s^2) = 4.66 lbf-s^2/ft

(Note that we use the term lbf or "pound-force" to clarify that pound here is a unit of force, not mass.)

This is not a terribly handy conversion. So, we can multiply this by a special version of 1: since 1 lbf = the weight of 1 lb-mass accelerated at g, we have 1 lbf = 32.2 lbm ft/s^2. Or in other words 1 = 32.2 lbm-ft/lbf-s^2. So from the previous formula we have

m = 4.66 lbf s^2/ft x (32.2 lbm-ft/lbf-s^2) = 150 lbm

So your mass is 150 lb-mass. Note that in imperial units one's mass (in pound-mass) is the same number as on'e weight (in pound-force)on earth. By the way the multiplier of 32.2 lbm-ft/lbf-s^2 comes in very handy quite often si yuor using imperial units.

Now to convert to SI. There are about 2.2 lbm per Kg, so your mass in SI units is 150 lbm/2.2 lbm/Kg = 68.2 Kg. And your weight in SI is W=mg = 68.2 Kg x 9.8 m/s^2 = 668 N. Hence 150 lbf = 668 N.

It is a common misnomer to use the term Kg to describe weight, because strictly speaking Kg is a unit of mass. Your mass is 68.2 Kg no matter where you are. If you traveled to the moon where the force of gravity is one sixth that of earth your mass remains the same (150 lbm or 68.2Kg) but your weight would be 150lbf/6 = 25 lbf or 668N/6 = 111 N. So, when people talk about one's weight in Kg they are implying that they are standing on the earth's surface, and their "weight" of xx Kg is the force of xx Kg being accelerated at g=9.8 m/s^2.

Hope this helps.
Very clear. Thank you.

-Dan
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