Pressure Calculator
Solve for pressure, force, or area using P = F / A. Switch between metric and imperial inputs, choose what you want to find, and get the result instantly in six pressure units: Pa, kPa, bar, atm, psi, and mmHg.
Formula
Worked example
A 500 N force spread over 0.25 m² gives P = 500 / 0.25 = 2000 Pa (2 kPa, 0.29 psi, 0.0197 atm). Reverse: to find the force a tyre at 220 kPa exerts on a 100 cm² (0.01 m²) contact patch, F = 220,000 x 0.01 = 2200 N.
Three ways to use this calculator
The "Solve for" dropdown at the top lets you use the same P = F / A relationship in all three directions. Choose Pressure to find how concentrated a force is on a surface. Choose Force to find the total push that a pressurised system (a hydraulic ram, a tyre, a compressed gas chamber) exerts on a given area. Choose Area to find the minimum contact area needed to keep pressure below a safe limit. In every mode the calculator shows the full unit conversion, so you can enter a force in pounds-force and get pressure in psi or pascals without any extra arithmetic.
Unit options: metric and imperial
Force can be entered in newtons (N), kilonewtons (kN), meganewtons (MN), pound-force (lbf), or kilogram-force (kgf). Area can be entered in square metres (m²), square centimetres (cm²), square millimetres (mm²), square feet (ft²), or square inches (in²). The pressure result is always displayed in six units simultaneously: Pa, kPa, bar, atm, psi, and mmHg. The SI base is always the pascal (Pa = N/m²); all other values are exact conversion factors from that base.
What pressure measures and why it matters
Pressure is the force applied perpendicular to a surface divided by the area over which it acts: P = F / A. Its SI unit is the pascal (Pa), equal to one newton per square metre. Because a pascal is small, everyday pressures are quoted in kilopascals (tyres, weather), bar (industrial equipment), psi (US engineering and plumbing), atm (diving, altitude), or mmHg (blood pressure, mercury barometers). A single atmosphere is 101,325 Pa, about 101 kPa, 1.013 bar, 14.7 psi, or 760 mmHg. Sharp knives, high heels, and snowshoe comparisons all illustrate the same physical law: concentrating force on a small area raises pressure sharply, while spreading force over a large area lowers it.
Practical examples across engineering and everyday life
Car and bicycle tyres are inflated to a gauge pressure (above ambient): typical car tyres run 200 to 250 kPa (29 to 36 psi), road-bike tyres 600 to 900 kPa (87 to 130 psi). Hydraulic systems exploit P = F / A to multiply force: a small pump pressure acting on a large piston generates a large force, which is how car lifts and hydraulic presses work. In structural engineering, the load a footing exerts on the soil is checked against the allowable bearing pressure, typically 100 to 300 kPa for common soils. Blood pressure is measured in mmHg (normal systolic is roughly 120 mmHg, or about 16 kPa). Deep-sea pressure increases by roughly 100 kPa per 10 m of water depth, reaching about 10,000 kPa (10 MPa, 100 atm) at 1000 m.
Real-world pressure benchmarks
| Situation | Pressure (kPa) | Pressure (psi) | Level |
|---|---|---|---|
| Human ear damage threshold | 35 | 5.1 | Moderate |
| Standard atmosphere at sea level | 101.3 | 14.7 | Reference |
| Car tyre (typical) | 220 | 31.9 | Moderate |
| Road bicycle tyre | 700 | 101.5 | High |
| Espresso machine brewing | 900 | 130.5 | High |
| Fire hose water pressure | 1700 | 246.6 | Very high |
| Deep ocean at 1000 m | 10100 | 1464.8 | Extreme |
| Industrial hydraulic press | 20000 | 2901 | Extreme |
Approximate values for comparison. 1 atm = 101,325 Pa = 14.696 psi = 1.01325 bar = 760 mmHg.
Frequently asked questions
What are the units of pressure?
The SI unit is the pascal (Pa), equal to one newton per square metre (1 N/m²). Common alternatives are the kilopascal (1 kPa = 1000 Pa), the bar (1 bar = 100,000 Pa), the atmosphere (1 atm = 101,325 Pa), pounds per square inch (1 psi = 6894.76 Pa), and millimetres of mercury (1 mmHg = 133.32 Pa). This calculator shows all six simultaneously.
How do I convert pascals to psi?
Divide the pressure in pascals by 6894.757. For example, 2000 Pa / 6894.757 = 0.29 psi. To go the other way, multiply psi by 6894.757. Standard atmospheric pressure is 101,325 Pa = 14.696 psi.
Why does a smaller area give a higher pressure?
Pressure is force divided by area, so for a fixed force, shrinking the area increases the result. A sharp knife blade, a stiletto heel, or a nail point all concentrate force on a tiny contact patch, producing very high pressure. Wide tyres and broad foundations spread the same force over more area to keep pressure low.
How do I solve for force from pressure and area?
Rearrange P = F / A to get F = P x A. Select "Force" in the "Solve for" dropdown, enter the pressure (in any unit) and the area (in any unit), and the calculator converts everything to SI, multiplies, and gives the total force in newtons. This is the principle behind hydraulic rams and pneumatic actuators.
What is gauge pressure versus absolute pressure?
Absolute pressure is measured from a true vacuum (zero). Gauge pressure is measured relative to local atmospheric pressure (about 101.3 kPa or 14.7 psi), so a car tyre at 220 kPa gauge has an absolute pressure of about 321 kPa. This calculator works with the numbers you enter and does not add or subtract atmospheric offset. Car tyre pressures, blood pressure, and most industrial gauges report gauge pressure.
How does pressure change with water depth?
Hydrostatic pressure increases by about 9810 Pa (9.81 kPa, approximately 1.42 psi) for every metre of water depth. At 10 m depth, the water adds roughly one additional atmosphere (101 kPa) of pressure. At 1000 m, the water pressure alone is about 9.8 MPa (1421 psi, 97 atm).