# Convert from lb/ft^2 to kg/ms^2 [closed]

I got this question today, and the teacher explained it really badly help!

How do you convert from lb/ft^2 to kg/ms^2:

I don’t think it’s possible as lb can’t become kg?

• Is the exotic unit lb also a unit of force, perhaps? In that case, it is of dimension mass times acceleration, or mass times length divided by time². And if you divede that by ft², which is of dimension length², you arrive at mass divided by length and time², which is exactly teh dimension of kg/ms². Mar 24 at 16:26
• You are pedantically correct. A kilogram is a measure of mass while a pound is a measure of force. But, since we all live close to the surface of the earth, it is common to say a kilogram is $2.2$ pounds. Mar 24 at 16:34
• @HagenvonEitzen The pound and the pound-force are different units. $1 \mathrm{lb-force}$ is the force experienced by $1 \mathrm{lb}$ of mass when accelerated by approximately $9.80665 \mathrm{m}/\mathrm{s^2}.$ So the conversion is a bit trivial, but it is there, nonetheless. The pound has always historically been a unit of mass. Mar 24 at 16:51
• See my comments under my own post. Mar 25 at 12:03

$$1\;\mathrm{lb}$$ is defined as exactly $$0.45359237\;\mathrm{kg}.$$

So you absolutely can convert between the two.

• You are correct when it comes to conversion between the two but the same Wiki article that says that thinks a pound is a unit of mass. That is nonsense. A kilogram is a measure of mass and a pound is a measure of force. Mar 24 at 16:37
• @JohnDouma No. The pound-force is a unit of force. In colloquial discourse, we tend to omit the "-force" part, but a pound-force and a pound are different units. Also, I did not get my information from the Wiki. I get my information from the SI directly. Mar 24 at 16:48
• A pound is not the SI unit of force: the newton is. I have never heard of a pound-force. A pound is the unit of force in the English system where the slug is the unit of mass. This is basic physics. Mar 24 at 19:48
• en.wikipedia.org/wiki/Pound_(force) "The pound of force or pound-force (symbol: lbf,[1] sometimes lbf,[2]) is a unit of force used in some systems of measurement, including English Engineering units[a] and the foot–pound–second system.[3] Pound-force should not be confused with pound-mass (lb), often simply called pound, which is a unit of mass, nor should these be confused with foot-pound (ft-lbf), a unit of energy, or pound-foot (lbf⋅ft), a unit of torque." Yes, you are right, this Is basic physics. So why are you getting it so wrong? Mar 25 at 11:57
• @JohnDouma Also, for your information, the slug and the averdupois pound belong to different measurement systems. One belongs to averdupois system. The other one does not. I never said anything about the English system. Mar 25 at 11:58

You can use dimensional analysis to convert between the two. If you're not familiar, dimensional analysis is a way you can convert between different units of measurement.

Also, you used $${ms}^2$$, which I'm going to assume means "meters." If this is the case, we usually use "m" to represent meters (not "ms").

You want to convert $$\frac{lb}{{ft}^2}$$ to $$\frac{kg}{{m}^2}$$

We know 1 lb ≈ .4535 kg. So $$\frac {lb}{{ft}^2} \times \frac {.4535kg}{lb} = \frac {.4535kg}{{ft}^2}$$

Applying the same reasoning to the $${ft}^2$$, we know that 1 square foot corresponds to .0929 square meters.

Therefore, $$\frac {.4535kg}{{ft}^2} \times \frac {{ft}^2}{.0929m^2} = \frac {.4535kg}{.929m^2}$$

Dividing .4535 by .0929, we obtain 4.87082885, which gives $$4.87082885 \frac {kg}{m^2}$$, which is our answer.

The reason dimensional analysis does not alter the value of the expression is because we are really multiplying by 1; in this example, .4535 kg divided by lb is 1, because those two values are the same. And we know that for all real numbers $$a$$ and $$b$$, where $$b≠0$$,

$$\frac {a}{b} \times 1 = \frac {a}{b}$$

So multiplying $$\frac {lb}{{ft}^2}$$ by $$\frac {.4535kg}{lb}$$ did not alter any values.

If you have further questions regarding dimensional analysis and complex unit conversion, you can watch Khan Academy's video: https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:working-units/x2f8bb11595b61c86:rate-conversion/v/dimensional-analysis-units-algebraically

Khan Academy's Algebra I section has an entire unit on unit conversion as well: https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:working-units