Pressure Calculator

Pressure is one of the most widely used quantities in physics and engineering. Whether you are working out the stress on a structural beam, the pressure under a hydraulic piston, or the load a foundation must support, the calculation always comes back to the same relationship: pressure equals force divided by area. A larger area distributes a given force over more surface, reducing pressure. A smaller area concentrates it. That is why a sharp knife cuts easily (tiny contact area, high pressure) while snowshoes prevent sinking (large area, low pressure on snow). The same force applied to different areas produces dramatically different pressures. This calculator solves for any one of the three variables when the other two are known. Results are shown in pascals (the SI unit) alongside kilopascals, psi (common in the US), and atmospheres, so you can cross-reference with any data source or standard.

• Hydraulic system design: Calculate the force a hydraulic cylinder can exert given its operating pressure and piston area, or find the required area to achieve a target force at a known system pressure.
• Foundation and soil engineering: Determine the contact pressure (stress) at the base of a footing by dividing the column load by the footing area. Compare with the allowable bearing capacity of the soil.
• Tyre pressure and contact patch: Estimate the contact patch area of a tyre by dividing the vehicle weight on that wheel by the tyre pressure. Tyres with lower pressure have larger contact patches.
• Physics experiments: Verify results from laboratory work on force and area. Enter the measured force and area to confirm the predicted pressure, or solve for area to check calibration.

• Entering area in cm² instead of m²: The formula uses SI units. An area of 100 cm² is 0.01 m², not 100. Entering 100 instead of 0.01 gives a pressure 10,000 times too low.
• Confusing weight and force: Weight is a force (in newtons) not a mass (in kilograms). To convert mass to force, multiply by 9.81 m/s². A 10 kg object exerts about 98.1 N downward.
• Ignoring atmospheric pressure for gauge readings: If your pressure sensor reads gauge pressure, the true (absolute) pressure is the gauge reading plus atmospheric pressure (101,325 Pa at sea level). Many engineering formulas require absolute pressure.
• Using inconsistent unit systems: Mixing SI and imperial values (e.g., force in pounds-force with area in m²) produces incorrect results. Convert everything to SI before using this calculator.

1. 1Select which quantity you want to calculate: pressure, force, or area.
2. 2Enter the two known values. Force is in newtons, area in square metres, pressure in pascals.
3. 3For pressure: the calculator divides force by area and converts the result to kPa, psi, and atm.
4. 4For force: it multiplies pressure by area and converts to kilonewtons.
5. 5For area: it divides force by pressure and converts to square centimetres.
6. 6All inputs must be positive; dividing by zero would give an infinite result and is caught as an error.

• Convert kg to N before using the force field: Multiply mass in kilograms by 9.81 to get force in newtons. For quick estimates, use 10 N per kg (introduces less than 2% error).
• Standard atmosphere is a useful reference: One atmosphere (atm) = 101,325 Pa = 101.325 kPa = 14.696 psi. Keep this in mind when interpreting results. A result of 0.5 atm means half of atmospheric pressure.
• Pressure does not depend on direction in fluids: In a static fluid, pressure at a given depth is the same in all directions (Pascal's principle). The P = F/A formula applies to the normal (perpendicular) force component only.
• Use kPa for most engineering work: Pascals are small. Most practical pressures fall in the kPa or MPa range. Divide the Pa result by 1000 to work in kPa, or by 1,000,000 for MPa.