Pressure Calculator (P = F/A, Force per Area)
Calculate pressure from force and area with P = F/A.
Enter any force and contact area to get pressure in pascals, kPa, bar, psi, atm, and mmHg at once.
The most basic definition of pressure
Pressure is just force spread over an area. Push with the same force on a small area and the pressure is high; spread it over a large area and the pressure drops. That single idea explains why a sharp knife cuts (tiny contact area, huge pressure), why snowshoes keep you on top of snow (large area, low pressure), and why a woman in stiletto heels can dent a wooden floor that an elephant would not.
The formula
P = F / A
Where:
- P = pressure
- F = force, in newtons (N)
- A = area over which the force acts, in square meters (m²)
In SI units, one newton spread over one square meter is one pascal (Pa). The pascal is a small unit, so real-world pressures usually run into thousands (kPa) or hundreds of thousands (bar, atm) of pascals.
Rearrangements
This calculator solves for whichever value you leave blank:
- Force from pressure and area: F = P × A
- Area from force and pressure: A = F / P
Leave one of the three fields empty and enter the other two.
Pressure units and how they relate
Pressure is one of the most unit-cluttered quantities in all of physics, because different fields settled on different standards. The conversions:
| Unit | Equals |
|---|---|
| 1 pascal (Pa) | 1 N/m² (the SI base) |
| 1 kilopascal (kPa) | 1,000 Pa |
| 1 bar | 100,000 Pa = 100 kPa |
| 1 standard atmosphere (atm) | 101,325 Pa |
| 1 psi (pound per square inch) | 6,894.76 Pa |
| 1 mmHg (torr) | 133.322 Pa |
Tire pressure is usually quoted in psi or bar, weather pressure in hPa (hectopascals, same as millibars), blood pressure in mmHg, and engineering loads in kPa or MPa. This calculator shows all of them at once so you do not have to convert by hand.
Worked example, the stiletto versus the elephant
A 60 kg woman puts her full weight on one stiletto heel of area 1 cm² (0.0001 m²). Her weight is F = mg = 60 × 9.81 = 588.6 N.
P = 588.6 / 0.0001 = 5,886,000 Pa = 5.89 MPa = about 854 psi
A 5,000 kg elephant stands on four feet, each about 0.05 m² (500 cm²). Weight = 49,050 N, spread over 0.2 m² total.
P = 49,050 / 0.2 = 245,250 Pa = about 36 psi
The heel exerts roughly 24 times the pressure of the elephant’s foot, despite the elephant weighing 80 times more. That is why heels damage soft floors and elephants do not sink into firm ground. Contact area, not weight, sets the pressure.
Pressure versus stress
If you have seen the formula sigma = F/A for mechanical stress, that is the same arithmetic applied inside a solid material rather than at a contact surface or in a fluid. Engineers reserve “stress” for internal forces in structures and “pressure” for fluids and surface contact, but the units (pascals) and the math are identical. Hydrostatic pressure in a fluid (P = rho g h, pressure from a column of liquid) is a separate formula because there the force comes from the weight of the fluid above, not an applied push.
Where this shows up
Hydraulics multiply force by exploiting P = F/A across two pistons of different area (a small force on a small piston makes a large force on a large piston at the same pressure). Vacuum systems, pneumatics, foundation engineering (bearing pressure of footings on soil), and even cooking (pressure cookers raise the boiling point by raising pressure) all trace back to this one relationship.