Pressure (P = F/A)

Pressure is force divided by the area it is spread over, $P = F/A$. The same force can be gentle or destructive depending entirely on how much surface it acts through, and that is the whole content of the idea. One pascal is one newton per square metre, which is a very small pressure — a sheet of paper lying on a table exerts about 1 Pa — so real numbers are almost always in kilopascals or higher. Standard atmospheric pressure is 101.325 kPa.

An 80 kg person weighs about 785 N. Standing in winter boots with maybe 350 cm² of sole in contact — 0.035 m² — the pressure under them is $785/0.035 \approx 22$ kPa, enough to break through crusted snow. Strap on snowshoes with 0.30 m² of bearing surface and the same 785 N becomes 2.6 kPa, and the snow holds. Run it the other way: lean on a thumbtack with 20 N through a point of about 0.01 mm², which is $1\times10^{-8}$ m², and the pressure at the tip is around 2 GPa — well past what wood fibre can resist.

The same relation is behind hydraulics. Pascal's principle says pressure applied to a confined fluid is transmitted undiminished throughout it, so a small force on a small piston becomes a large force on a large one: same $P$, bigger $A$, bigger $F$. A hydraulic jack with a 200:1 area ratio multiplies force 200-fold, at the price of moving 200 times as far. It also underlies the hydrostatic pressure page, where the force is simply the weight of the fluid standing above.

The area to use is the area actually in contact, and it is usually smaller than it looks. A tyre bears on its contact patch, not on the outline of the tread; a bolted flange bears on the annulus under the washer, not on the whole plate. Getting that wrong understates the real pressure, sometimes badly. The unit conversion is the other reliable trap: a square metre is 10 000 square centimetres and a million square millimetres, so an area entered in cm² against a force in newtons is out by four orders of magnitude. And $F$ must be the component perpendicular to the surface — a force at an angle contributes only its normal component to pressure, with the rest showing up as shear. Finally, be clear whether a quoted pressure is gauge or absolute. Gauge pressure is measured against the surrounding atmosphere, so a tyre reading "zero" is not empty; it holds about 101 kPa absolute. The suffixes psig and psia exist precisely because this goes wrong so often.