Pressure formula

I have recently been studying pressure and the basic pressure formula:

$$\ P= F\ /A$$

and I was wondering why it does not include direction of the force in the formula and I played around with it for a bit and I got the formula:

$$\ P= F\sin( \theta)\ /A$$

(not including calculus or varying pressure or area for now). Is this formula correct?

And if so how could I change it to account for a change in area or force?

For example here 30 degrees is theta and the hypotenuse is 10N

• I think pressure is equal to perpendicular component of the force divided by the area.
– user240696
Commented Feb 8, 2020 at 10:35
• yes sin(theta) would give you the perpendicular value of the force if you take the value of the force as the hypotenuse. Commented Feb 8, 2020 at 10:43
• Please specify with which (vertical or horizontal) the force makes an angle of $\theta$ in your question.
– user240696
Commented Feb 8, 2020 at 10:44
• I edited the question to include an example Commented Feb 8, 2020 at 10:57
• Yes your equation is correct.
– user240696
Commented Feb 8, 2020 at 10:58

From the wikipedia page: Pressure is the amount of force applied at right angles to the surface of an object per unit area.

So your formula including sin(θ) is correct.

• What about this And if so how could I change it to account for a change in area or force? ?
– user240696
Commented Feb 8, 2020 at 11:27
• Pressure is an instantaneous magnitude, i.e. if the force or the area change, the pressure at each instant is the value of F/A at that precise instant. If these are functions of time, then P(t) = F(t)/A(t).
– Leo
Commented Feb 8, 2020 at 11:30
• Well that's really what I wrote in my comment but OP didn't reply therefore I deleted it and asked him this
– user240696
Commented Feb 8, 2020 at 11:32
• Sorry I had logged off my computer by that time and i didn't see your comment. Commented Feb 9, 2020 at 11:23