# Unit of Pressure - $\frac{N}{m^2}$ or $\frac{kg}{cm^2}$

I am came across Pressure being given with unit $$\frac{kg}{m^2}$$ at a lot of technical papers I am reading.

However, as far as I understand, Pressure is defined as $$\frac{N}{m^2}$$ which is not same as $$\frac{kg}{m^2}$$.

Can you please clarify if I am going wrong somewhere?

• In what context did you read this? – Bob D Sep 26 at 12:33
• $kg/cm^2$ is NOT a pressure. It's mass per area. – Hilmar Sep 26 at 17:37

Technically, pressure is better defined as force per unit area, without any specific units in mind.

But your confusion is justified. Pressure should be measured in units of force per area, in metric, we typically use Pascals ($$Pa$$) which are given by $$\frac N{m^2}$$.

$$\frac {kg}{m^2}$$ is not a measure of pressure, so your reasoning seems solid to me. Besides in some specific cases where pressure would scale linearly with mass, I don't think it makes a lot of sense to refer to pressure in $$\frac {kg}{m^2}$$. You are right to question it, calling that pressure is confusing at best.

Odds are they were actually talking about kilogram-force per metre squared. That would be a measure of pressure, but typically you would write $$kg_f$$ or $$kgf$$ to distinguish it from the unit of mass, $$kg$$. Pressure as $$\frac {kg_f}{m^2}$$ would make sense.

• English units are already ambiguous due to the difference between pounds-force and pounds-mass, with both being designated by "lb". We don't need the same ambiguity in the SI world. – David White Sep 26 at 16:36
• I have worked for Japanese and Italian engineering companies. Both used kg/m^2 for pressure and stress. Does anyone in the real world really follow SI? – JohnHoltz Sep 26 at 22:23
• @JohnHoltz ... It's not just a matter of SI in this case. Pressure is force over area, not mass over area. Kilograms are a measure of mass, not force. Typically, it's more clear if you say "kgf" when you mean kilogram-force instead of just a kilogram. And yes... people in the real world follow SI. At very least, they often try to make sure the units represent the quantity they are trying to show. – JMac Sep 26 at 22:54

Mathematically pressure is defined as force per unit area: $$p = \frac{F}{A}$$, if the only force which is acting on area is weight then we can extend expression according to second Newton law as: $$p = g\frac{m}{A}$$, so because $$g$$ is constant we can consider a pressure as a mass per unit area as well.

Check your sources for the exact terms they are using for kg. It is possible they are referring to kilogram-force as opposed to kilogram-mass. According to Wikipedia kilogram-force is a gravitational metric unit of force. It is equal to the magnitude of the force exerted on one kilogram of mass in a 9.80665 $$\frac{m}{s^2}$$ gravitational field.

Hope this helps.

• Which means that a kg-force is 9.8 Newtons. – David White Sep 26 at 16:37
• @David White Yup. That’s what it means to me – Bob D Sep 26 at 16:45