# Pounds is a unit of mass or weight

LURCH
LOL! just an example of how convoluted our language has become:

...In general conversation, a pound is considered to be the weight of an object in pounds mass...
Makes one ask, "In general conversation, how does one express the mass of something in pounds force?"

Dale
Mentor
To whom it may concern:

-Many Thanks
Dale

PS I won't hold my breath while waiting.

D H
Staff Emeritus
LOL! just an example of how convoluted our language has become:
In general conversation, a pound is considered to be the weight of an object in pounds mass.
In this case, it is scientists, not the general public, who are guilty of convoluting the language. Weigh and weight are very, very old words, predating Newton by many hundreds of years. The first definition of weight in my unabridged dictionary (Random House Unabridged Dictionary, 2006) is "1. the amount or quantity of heaviness or mass; the amount a thing weighs". The second definition is the scientific one: "2. Physics. the force that gravitation exerts upon a body, equal to the mass of the body times the local acceleration due to gravity". That Physics is italicized means that Random House at least considers the physical definition of weight as force due to gravity to be technical jargon. Collins Essential English Dictionary similarly qualifies weight as gravitational force as scientific jargon.

The American Heritage Science Dictionary, on the other hand, presents the jargon scientific definition as the primary definition of weight. It also has a very erroneous usage note regarding the translation of kilograms into pounds: "Although most hand-held calculators can translate pounds into kilograms, an absolute conversion factor between these two units is not technically sound. A pound is a unit of force, and a kilogram is a unit of mass." A pound is a unit of mass and a unit of weight, and when used as a unit of mass, a hand-held calculator can indeed convert kilograms into pounds and vice-versa with complete technical soundness.

In summary, one needs to be very careful in talking about weight.
• Legal weight is synonymous with mass. A balance scale measures legal weight.
• Actual weight is a force, tautologically defined as mass times the acceleration due to gravity. The actual weight of an object cannot be measured directly. It can only be computed via the tautological definition.
• Apparent weight is a force, defined as the total force acting on an object less the actual weight of the object. A spring scale measures apparent weight.

For an object at rest on the surface of the Earth, the apparent weight of an object differs from object's actual weight in direction and in magnitude. Actual weight is directed roughly downward (and is unmeasurable); apparent weight is directed exactly upward (and is measurable). The magnitude of the actual and apparent weight of an object at rest on the surface of the Earth differ in that apparent weight includes a centrifugal force term.

Gold Member
So, if I weigh 200lbs on Earth, I weigh weigh 200lbs on the Moon?
No weight depends on gravity (w = mg). If your mass was 200lb on earth it would be the same on the moon. Most people get confused because in every day conversation you would say "how much do you weigh" not "what is your mass". Spring scales measure the force applied and change it to a mass (depending on the force of gravity), so if you went to live on mars you would need some new scales.

I think a pound is both mass and force because (in the U.K) people would still put 1lb of butter etc in to a cake mixture, but people also say a rocket has so many 1000's of pounds of thrust.

Nim
To be picky, it is 9.80665 m/s2, not 9.81.
Sorry. I know I am dragging out an old thread, but I had to comment on this. Awhile back I was messing around with the equation to find out Earth's gravitational acceleration and couldn't figure out why I wasn't getting 9.81. I kept getting 9.80065745906891. But that was because I was using "Earth's Equatorial Radius". If you use "Earth's Quadratic Mean Radius" then you get 9.81708900527711. If you use "Earth's Polar Radius" then you get 9.86670995442209.

I actually came to this thread doing on a search on Google about pounds. I was wondering, if using the imperial system, how exactly would you do the equation weight = mass * 9.81? If pound = mass and you have 185 mass, then is your weight 1814.85 pound-force?

stewartcs
I actually came to this thread doing on a search on Google about pounds. I was wondering, if using the imperial system, how exactly would you do the equation weight = mass * 9.81? If pound = mass and you have 185 mass, then is your weight 1814.85 pound-force?
If using lbm, then it is:

$$lbf = \frac{lbm \cdot \frac{ft}{s^2}}{g_c}$$

where gc is the gravitational constant and has the value/units of 32.17 $$\frac{lbm \cdot ft}{lbf \cdot s^2}$$

Essentially, 1 lbm = 1 lbf if g (local acceleration) equals gc (i.e. you are at sea level and 45 degrees latitude on earth). Hence the confusion when using pounds to mean force and mass without a qualifier.

Otherwise, just use:

$$lbf = slugs \cdot \frac{ft}{s^2}$$

If you have the choice just use SI as it is less confusing.

Hope this helps.

CS

mgb_phys
Homework Helper
Sorry. I know I am dragging out an old thread, but I had to comment on this. Awhile back I was messing around with the equation to find out Earth's gravitational acceleration and couldn't figure out why I wasn't getting 9.81. I kept getting 9.80065745906891. But that was because I was using "Earth's Equatorial Radius". If you use "Earth's Quadratic Mean Radius" then you get 9.81708900527711. If you use "Earth's Polar Radius" then you get 9.86670995442209.
Then if you take into account the local geology and the rotation you get more variation -
The average is 9.80665 m/s2

"Because as of late 90's engineering professors were still teaching that a pound is a unit of force." You bet they were, and they continue to do so because it works!!

As an engineering dynamicist who works with this stuff on a daily basis, I see it occasionally in SI units but usually not. I can report to you that the pound-force is alive and well.

The Imperial system of units is just about as dead as the British Empire, but what is commonly used in the US today is called the US Customary system (USC). It comes in two versions: the Foot-Pound-Second (FPS) system and the Inch-Pound-Second system (IPS) where the only difference is in the choice of the lenght unit. Notice that the force unit is the pound which is a fundamental unit to both systems. Big systems like buildings and dams are usually described in FPS while machines are invariably described in IPS.

The mass unit that is used in dynamic calculations in the FPS system is the slug, which is not so rare as has been suggested, even if it is not often encountered in trade. For dynamic calculations in IPS, the mass unit is the lb-s^2/in. Now I am sure that some of you will be laughing all over, saying that this is ridiculous, but I assure you that I am dead serious and that I, and many others use this unit with great regularity to good results.

It is very important that we be able to write F = m*a without the need for any additional proportionality constants as has been suggested above (and many other places as well). The mass units described here enable that to be done without any difficulty whatsoever, so we may say that they work.

One final word: The pound-mass is a terrible idea that leads to massive confusion whenever attempts are made to apply it in advanced mechanics. I would not touch this concept with a 20 ft. pole!

mgb_phys
Homework Helper
I would not touch this concept with a 20 ft. pole!
That's 6.1m for our international readers!

Nim
Then if you take into account the local geology and the rotation you get more variation -
The average is 9.80665 m/s2
Ya I know, and distance from the surface adds variation too. But I thought it was the "Quadratic Mean Radius" that gives you the average. But it's the "Equatorial Radius"?

D H
Staff Emeritus
Then if you take into account the local geology and the rotation you get more variation -
The average is 9.80665 m/s2
That 9.80665 m/s2 is purely definitional and is an exact figure (something you only get with definitions). It is not an average value. It is what the value would be at Paris were Paris at sea level and if the Earth had a uniform mass distribution, truncated to five decimal places.

mgb_phys
Homework Helper
That 9.80665 m/s2 is purely definitional and is an exact figure
Sorry loose wording - it's an accepted aggregate value, not strictly an average.
It's actually aimed at 45deg N, not Paris (which is near 49N and has g=9.809)

Pounds slugs?What about dynes ,ergs and other units?Physicists around the world started to phase these units out on the early 1960s.

Dear all,

I know that this is a very old post.
I am also bit confused, since the imperial system of units are not consistent, or, are not used as it should be.

Here's the difference: -

In Metric system, or SI system, Mass (kg) is a fundamental unit and Force is a derived unit (N), that means, force is derived from mass, so when you multiply the fundamental unit, kg with acceleration, we get the derived unit, N (F = Ma).

In imperial system (or British or American) system, the Force (called as pounds or pound-force, lb or lbf) is the fundamental unit, and mass (lbm) is a derived unit, so when you divide force (lbf) with acceleration (in/sec^2) we get mass (lbm).

In actuality, one should never use lb as a unit of mass, it should be lbm (pound-mass).

Proof:

Metric system units

Mass: kg
Acceleration: m/s^2
Force: N or kg.m/s^2

Imperial system units (I am considering IPS system here)

Force: lb or lbf
Acceleration: in/s^2
Mass: lb.s^2/in

People have become so lazy that the standards are not followed properly.

Thanks,

Binoy John.

Last edited:
D H
Staff Emeritus
Dear all,

I know that this is a very old post.
I am also bit confused, since the imperial system of units are not consistent, or, are not used as it should be.
Your "proof" is incorrect. English units are not consistent. That's the way it is. Then again, SI units aren't consistent, either.

Prior to the development of the metric system, Newton's second law was of the form F=kma, where k is a constant of proportionality. It is important to remember that Newton said that force is proportional to the change in momentum. He did not say F=ma. The English system explicitly maintains this constant of proportionality. In SI units, the force unit was chosen to make this proportionality constant have a numeric value of 1. While it is a pain in the rear that the proportionality constant is not 1 in English units, it is not incorrect. It is just "inconsistent."

However, we still write Newton's law of gravitation as F=GMm/r2. The G in this expression is a constant of proportionality. A fully consistent set of units would have units of length, mass, and time such that G has a numeric value of 1.

Hi DH,

Is it really important to talk about F=ma, F=kma??
What is the unit of G? Let G be infinite to the power infinite, but still a constant. Will it make a difference to the unit of Force, mass or acceleration??
I believe that our topic was about the consistency in usage of units.

Thanks

Binoy

D H
Staff Emeritus