Article
Pressure from force and area
Pressure is force divided by contact area. The same force gives a higher pressure on a smaller surface.
The pressure p = F/S calculator does this. A fluid column is on p = ρgh.
The idea in brief
The same force on a sharp edge produces higher pressure than on a board. The force is unchanged. The contact area is not.
Pressure is force divided by area. Smaller area means higher pressure.
On this page: p is pressure. F is force, in newtons (N). S is contact area, in square meters. The result is in pascals (Pa). 1 kPa is 1000 Pa, and 1 MPa is 1,000,000 Pa. g is gravitational acceleration, about 9.81 m/s². The ρgh formula on the other card is density times g times the height of a liquid column.
When this helps
| Situation | What the card shows |
|---|---|
| You want the pressure of a crate on the floor, or of a press on a surface. | The card divides force by contact area and reports the result in pascals. |
| You compare the same force on a shoe sole and on a thin heel. | The force stays the same. A smaller area gives a higher pressure. |
| The problem gives mass, not force. | Compute force as mass times g first, then divide by area. |
The formula on this card
p = F / S. Force in newtons, area in square meters, result in pascals. 700 N on 0.02 m² is 35 000 Pa, or 35 kPa. On a 0.0001 m² heel the same 700 N is 7 MPa. Area zero does not divide; the card will not run it.
This is not tire-gauge pressure and not a water column. Fluid height is a separate card with density, g, and depth. Here you only type force and contact area.
Where it shows up
A crate on a floor, a press, a nail. If the problem gives mass instead of force, first F = mg, then divide by S. Units have to match: convert cm² to m² before you divide, or three orders of magnitude vanish quietly.
A worked example
700 N on 0.02 m²
700 / 0.02 = 35 000 Pa, or 35 kPa. On a 0.0001 m² heel the same 700 N is 7 MPa.
Typical numbers from the card
| Inputs | Result |
|---|---|
| The force is 700 N and the contact area is 0.02 m². | Pressure is 35000 Pa, or 35 kPa. |
| The same 700 N acts on 0.0001 m², as on a thin heel. | Pressure is then 7 MPa. |
Typical mistakes
| Mistake | What goes wrong | How to avoid it |
|---|---|---|
| You type 200 cm² as 200, without converting to square meters. | The result comes out four orders of magnitude too small. | 200 cm² is 0.02 m². Convert the area first, then divide. |
| You type mass in kilograms into the force field. | There is no multiplication by g, so the force is too small. | Compute force as F = mg first. |
| You treat this as the pressure of a liquid column. | That is a different formula. A liquid column is a separate card with density and height. | Count hydrostatic pressure on the separate card. |
| You enter an area of zero. | Division by zero has no meaning. The card will not compute it. | Keep the area greater than zero. |
Before you plug in the formula
- Force is in newtons, and area is in square meters.
- Square centimeters are already converted to square meters.
- If you know mass, compute force as F = mg first.
- This is not hydrostatic pressure and not a tire-gauge reading.
Frequently asked questions
What is 700 N on 0.02 m²?
35 kPa. 700 / 0.02 = 35 000 Pa.
Why does a heel raise p?
Because S is smaller. The same F on 0.0001 m² is 7 MPa.
Is this hydrostatic pressure?
No. That one uses ρgh, density times g times height. This card only uses force F and area S.
What if I know mass, not force?
First F = mg, then p = F/S. The pressure card does not multiply by g for you.
Can I type cm²?
Convert to m². 200 cm² is 0.02 m², not 200.
What if S = 0?
The division is undefined. The card will not compute it.