Pressure calculator
Enter a force and an area, get the pressure.
How do I calculate pressure?
Pressure = force ÷ area. 1,000 newtons on 0.5 m² is 2,000 pascals (2 kPa).
What is a pascal?
One newton per square meter — a small unit. Atmospheric pressure is 101,325 Pa, or 101.3 kPa.
How do I convert pascals to psi?
Divide by 6,894.76: 101,325 Pa is 14.70 psi.
Why does a sharp knife cut better?
The same force on a much smaller area makes a much higher pressure.
Is this gauge or absolute pressure?
Neither on its own — it is the pressure from the force you enter. Tire gauges show pressure above the surrounding air.
How do I convert tire pressure from psi to kPa or bar?
Multiply psi by 6.894757 for kPa and divide kPa by 100 for bar (1 bar = 100 kPa exactly). A tire gauge reading of 34 psi is 234.4 kPa, or 2.34 bar. That is a gauge value, measured above the surrounding air; the absolute pressure is the gauge reading plus atmospheric pressure, 34 + 14.7 = 48.7 psi or 336 kPa (OpenStax University Physics, Volume 1, section 14.2, Eq. 14.11).
How much pressure does water add with depth?
At depth h in a fluid of constant density the pressure is p = p₀ + ρgh, with p₀ the pressure at the surface (OpenStax, section 14.1, Eq. 14.4). For fresh water at 20 °C, ρ = 998.2 kg/m³, so 10 m of depth adds 998.2 × 9.80665 × 10 = 97.9 kPa, or 14.2 psi, about 0.97 atm. That is why the pressure at 10 m is nearly double the 1 atm at the surface.
The formula and what it assumes
Pressure is the force pressing perpendicular to a surface divided by its area, p = F ÷ A (OpenStax University Physics, Volume 1, section 14.1, Eq. 14.3). The SI unit is the pascal, 1 Pa = 1 N/m². The calculator turns the force into newtons and the area into square meters and then shows the result in Pa, kPa, psi, atm, bar and mmHg, using 1 psi = 6,894.757 Pa, 1 atm = 101,325 Pa and 1 bar = 100,000 Pa. Only the part of the force perpendicular to the surface counts, and the calculator assumes it is spread evenly over the area, so the answer is an average.
Worked example: boots and snowshoes
A person weighing 150 lbf is 667.2 N. Standing on two boots with a total contact area of 60 in² (0.0387 m²), the average pressure on the snow is 667.2 ÷ 0.0387 = 17.2 kPa, or 2.50 psi. On snowshoes with 240 in² the same weight gives 4.31 kPa, or 0.625 psi, one quarter as much, because four times the area carries the same force.
Common mistakes
The unit of force is the first trap: pounds-force and newtons differ by a factor of 4.448, and a mass in kilograms is not a force until it is multiplied by 9.80665. The second is the area unit. Psi means pounds-force per square inch, and a square foot holds 144 square inches, so 100 lbf spread over 2 ft² is 100 ÷ 288 = 0.35 psi, not 50. The third is the kind of pressure. A gauge reads relative to the air around it, so a flat tire reads 0 psi gauge while still holding air at about 14.7 psi absolute.
Sources: OpenStax University Physics, Volume 1, section 14.1 (density and pressure, Eq. 14.3–14.4; Table 14.1) and section 14.2 (gauge and absolute pressure, Eq. 14.11; Table 14.3 of pressure units); the pound-force, psi, atmosphere and bar factors are from NIST SP 811, Appendix B.8. Related: pressure converter, force calculator, density calculator and head pressure calculator.