Pressure measures how concentrated a force is. The same body weight that barely dents a snowfield in snowshoes can dent a hardwood floor through a stiletto heel, because pressure depends on the area as much as on the force. This calculator solves P = F/A for pressure, force or area, and reports the answer in ten pressure units from pascals to inches of mercury.
How to use the pressure calculator
- Under Solve for, choose Pressure, Force or Area.
- Enter Force (F) in N, kN, lbf, kgf, dyn or ozf. Use the part of the force that acts perpendicular to the surface. For a resting mass, kgf is handy: 1 kgf is the weight of 1 kg under standard gravity.
- Enter Area (A) in m², cm², mm², km², in², ft² or yd², or Pressure (P) in Pa, kPa, MPa, bar, mbar, atm, psi, Torr, mmHg or inHg, depending on what you are solving for.
- Pick the output unit under Show the result in. The result lists other units, the pressure as a multiple of one standard atmosphere, and an equivalent load: the mass in kg and lb whose weight equals the force.
All three quantities must be greater than zero; the calculator rejects zero or negative values.
Pressure formula
Rearranged for the other two unknowns:
The SI unit, the pascal, is one newton per square meter, as defined in the BIPM’s SI Brochure. Watch area conversions: 1 cm² is 0.0001 m², not 0.01 m², because both sides of the square shrink by a factor of 100.
Worked example: standing on a floor
A person whose weight is 700 N (a mass of about 71.4 kg, or 157 lb) stands with 250 cm² of shoe sole touching the floor.
Convert the area: 250 cm² = 0.025 m².
Pressure: P = 700 N ÷ 0.025 m² = 28,000 Pa = 28 kPa.
In other units: about 4.06 psi, 0.28 bar, 210 mmHg, or 0.276 atm.
Same force, very different pressure
Keep the 700 N and change only the contact area:
| Contact | Area | Pressure |
|---|---|---|
| Stiletto heel tip, weight rocked onto it | 1 cm² | 7 MPa (about 1,015 psi) |
| Flat shoe soles | 250 cm² | 28 kPa (about 4.06 psi) |
| One snowshoe | 1,200 cm² | 5.83 kPa (about 0.85 psi) |
The heel concentrates the load 1,200 times more than the snowshoe. Knives, needles and nail tips exploit the same effect in the other direction: a modest 20 N on a 5 mm² blade edge produces 4 MPa. Wide tractor tires, foundation footings and snowshoes spread loads so soft ground can carry them.
Pressure units and conversion factors
| Unit | Value in pascals | Status |
|---|---|---|
| kPa | 1,000 | Exact (SI prefix) |
| bar | 100,000 | Exact by definition |
| atm (standard atmosphere) | 101,325 | Exact by definition |
| psi (lbf/in²) | 6,894.757293168 | Exact from the pound, inch and g₀ |
| Torr | 101,325 ÷ 760 ≈ 133.322368 | Exact by definition |
| mmHg (conventional) | 133.322387415 | Fixed by convention |
| inHg (conventional) | about 3,386.39 | Conventional |
The torr and the conventional millimeter of mercury differ by roughly one part in seven million, which only matters in metrology labs. NIST Special Publication 811 lists these factors for US use.
Gauge pressure and absolute pressure
Most everyday gauges read gauge pressure, the amount above the surrounding air. Absolute pressure adds the atmosphere back: a road-bike tire pumped to 90 psi on the gauge holds about 90 + 14.7 = 104.7 psi absolute at sea level. The F/A result is the pressure created by the force alone, so treat it like a gauge figure.
That is also why gauge pressure is the right input when solving for force. Enter a car tire’s 30 psi on a 160 cm² contact patch and the calculator gives about 3,309 N (744 lbf) per tire, enough to carry roughly 337 kg. Four tires support a car of about 1,350 kg, ignoring the small share carried by sidewall stiffness. If the tire lost air, the patch would grow until pressure times area again matched the load.
Related calculators
Convert any pressure reading with the pressure converter. To turn a mass into the force to enter here, use the weight calculator, and for pressure inside a sealed gas, the ideal gas law calculator.
Frequently asked questions
What is the formula for pressure?
Pressure is the perpendicular force divided by the area it acts on: P = F ÷ A. One newton spread over one square meter is one pascal (Pa), the SI unit. For example, 700 N on 250 cm² gives 28,000 Pa, or 28 kPa.
How many pascals are in one psi?
One pound per square inch equals about 6,894.757 Pa, or 6.895 kPa. The figure is exact in principle because it follows from the defined values of the pound, the inch and standard gravity. Going the other way, 1 kPa is about 0.145 psi.
Is the result gauge pressure or absolute pressure?
P = F ÷ A gives the pressure the force itself creates, which is what a gauge reads. To get absolute pressure, add the surrounding air pressure, about 101.325 kPa (14.696 psi) at sea level.
Why does a sharp knife cut better than a dull one?
The same hand force lands on a far smaller area. A 20 N push on an edge 0.1 mm wide and 50 mm long (5 mm²) produces 4 MPa, about 580 psi. Let the edge wear to twice that width and the pressure halves.
What if the force pushes at an angle to the surface?
Use only the component perpendicular to the surface. If the force makes an angle θ with the perpendicular, that component is F × cos θ. The sideways part creates shear stress, not pressure.