Pressure Calculator

Pressure is force per unit area acting perpendicular to a surface: P = F/A, where P is pressure, F is force, and A is area. In SI units, pressure is in pascals (Pa); 1 Pa = 1 N/m². So the same force over a smaller area gives higher pressure (e.g., a sharp knife). Our calculator can compute pressure from force and area, or solve for force or area when the other two are known, and convert between common units (Pa, kPa, bar, atm, psi, torr).

Hydrostatic pressure is the pressure in a fluid at rest due to the weight of the fluid above: P = ρgh, where ρ is density, g is gravitational acceleration (9.8 m/s² on Earth), and h is the depth (height of the fluid column). So pressure increases with depth—e.g., at 10 m underwater it is about twice the pressure at 5 m. This formula applies to liquids and to gases over small height ranges; it is used in engineering, diving, and hydraulics.

The ideal gas law is PV = nRT. Rearranged for pressure: P = nRT/V. So for a fixed amount of gas (n constant), pressure is proportional to temperature (T) and inversely proportional to volume (V). Compressing a gas (smaller V) or heating it (higher T) increases pressure. R is the gas constant, 8.314 J/(mol·K). This relationship is used in chemistry and physics for gases at moderate conditions; real gases deviate at high pressure or low temperature.

Atmospheric pressure drops with altitude because the weight of air above you decreases. In an isothermal approximation, pressure decreases exponentially: P = P₀ e^(−h/H), where P₀ is pressure at sea level, h is altitude, and H is scale height (about 8,400 m for Earth). So at 5,500 m (around 18,000 ft) pressure is roughly half of sea level. That is why aircraft cabins are pressurized and why cooking and boiling points change at high elevation.

Common units are pascals (Pa, SI), kilopascals (kPa), bar, atmosphere (atm), psi (pounds per square inch), and torr (mmHg). Standard atmospheric pressure at sea level is 101,325 Pa = 101.325 kPa = 1.01325 bar = 1 atm ≈ 14.696 psi = 760 torr. Tire pressure is often in psi or bar; blood pressure in mmHg; vacuum and some science in torr or Pa. Our calculator converts between these so you can enter one unit and get results in another.

Our pressure calculations use the definition P = F/A and the standard conversions between Pa, kPa, bar, atm, psi, and torr, consistent with the International System of Units (SI) and common engineering and science references. Hydrostatic and barometric formulas follow standard fluid mechanics and atmospheric physics. For precise work, refer to NIST or similar standards for exact conversion factors.