On various websites I see torque expressed as $\rm kg\: m$, but I was always thought that torque is $\rm N\:m$ or $\rm kg\: m^2/s^2$. These are clearly not the same, so why are they called the same, and when do I use one or the other?

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    $\begingroup$ Don’t trust websites for introductory physics help. There’s a lot of crap and noise out there. The one you were always taught is perfectly right! $\endgroup$ – knzhou Jan 10 at 23:21
  • $\begingroup$ @knzhou I see this unit of torque kg/m , in the details of electric motors. They always give the torque of an electric motor in kg/m. Do they just call it "torque" but mean something else? $\endgroup$ – sparpo Jan 10 at 23:30
  • $\begingroup$ @knzhou Actually "kg/m" was probably just a mistake on this website, they probably meant kg*m. $\endgroup$ – sparpo Jan 10 at 23:37
  • $\begingroup$ It has any number of units, since there are any number of unit systems. In cgs it has unit $dyne \cdot cm$. If you stick to a single unit system you cannot go wrong. My advise is mksi, so $Nm$. $\endgroup$ – my2cts Jan 10 at 23:40
  • $\begingroup$ @sparpo, kg is a unit of mass, and N is a unit of force. kg-m is NOT a unit of torque. This usage no doubt comes from the usage of ft-lb in the English system, but what most people don't realize is that there are pounds-force and pounds-mass, and the two units differ by a factor of 32.2. $\endgroup$ – David White Jan 10 at 23:54

Those other sources were probably referring to kilogram-force instead of Newtons. Given the constant conversion between mass and weight on Earth (i.e., $g = 9.8\,\textrm{m/s}^2$), mass and weight units are often used interchangeably in non-scientific contexts. So, torque can be expressed in kgf-m, where 1 kgf is the weight of 1 kg on Earth's surface. Notice that this is a multiplication, not a division. Units of kgf/m would be completely incorrect.

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    $\begingroup$ Yes, and in particular it is strictly speaking wrong - though commonly done, and moreover this shows exactly why you shouldn't do it - to write the unit kgf as "kg". $\endgroup$ – The_Sympathizer Jan 11 at 3:41
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    $\begingroup$ @The_Sympathizer Nah, it's fine in the right context. As long as your audience understands, anything works. Though I do get more annoyed at particle physicists who set $c=1$. The equation $E^2 = m^2 + p^2$ makes me twitch due to the loss of units. $\endgroup$ – Mark H Jan 11 at 4:08
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    $\begingroup$ The problem is there are then two units with the same symbol and yet quite different meanings, and they are likely to be in rather close proximity with each other if not coming together. That's a recipe for confusion. Moreover when I say "wrong" I mean with regard to the standards that define the meaning of the symbol $\mathrm{kg}$. That's why I said "strictly speaking", i.e. according to rigorous application of the standards. $\endgroup$ – The_Sympathizer Jan 11 at 5:29
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    $\begingroup$ And yes, you don't have to follow standards, but if your usages are not strongly set apart enough, you are creating a recipe for confusion with more standard usages. Especially if your non-standard usages blur together lines that should otherwise be there - e.g. force is not mass. $\endgroup$ – The_Sympathizer Jan 11 at 5:31
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    $\begingroup$ And with something like torque where mass enters in in a significant way, there is strong potential for contact between the two and that (depending on what kind of measurements you're given) may lead to improper unit arithmetic which is a mistake and definitely wrong by the rules of mathematics. $\endgroup$ – The_Sympathizer Jan 11 at 5:33

The non SI unit is often written as 1 kg-m and is equal to 9.8 N m.

In such a case the 1 kg refers to the unit 1 kg force which is the weight of one kilogram.

Another unit is the Imperial (and US) unit the pound-foot which is equal to approximately 1.36 N m.
Here the unit of force is the pound force.


Well I think both of the Units are right. But its not kgm it should be kgf-m. Torque means - - - > F×R. .. Hence it has units of Force times distance.

N-m is one of the units where N is unit of Force and m is distance.. While in Kgf-m Kgf is unit of force and m is distance as Usual.


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