Pressure Calculator
Compute pressure P = F/A with force in N and area in m². Result in Pa, kPa, bar.
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Pressure: P = F/A
Pressure is force per unit area: P = F/A, measured in pascals (1 Pa = 1 N/m²). Standard atmospheric pressure is 101,325 Pa = 1 atm = 760 mmHg = 14.7 psi = 1,013 hPa. The smaller the area, the higher the pressure — that's why a high heel (≈1 mm² contact) supporting 70 kg generates ≈70 MPa, far more than a car tire (200 kPa ≈ 30 psi). Blood pressure is reported in mmHg (systolic/diastolic, e.g., 120/80). Hydrostatic pressure follows P = ρ·g·h — every 10 m of water adds about 1 atm, which is why divers must equalize. Pascal's principle (pressure transmits fully through a confined fluid) underlies hydraulic presses and brakes.
Applications
Meteorology (hPa on weather maps), tire pressure, pressure cookers (≈1.8 atm), aviation (altimeters infer altitude from pressure), foundation engineering, hydraulic systems, scuba diving, and medical instruments (sphygmomanometers, ventilators).
FAQ
Why does a sharp knife cut better? Same force on a much smaller area means much higher pressure — the blade concentrates force into a thin edge.
Pa, bar, psi, atm — which to use? SI is Pa; bar (10⁵ Pa) is common in industry; psi in the US/tires; atm in chemistry. 1 bar ≈ 1 atm (within 1.3%).
Is pressure a vector? No — pressure is a scalar. The force it produces on a surface is a vector, always normal to the surface.
Related Tools
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Calculate the minimum thickness of a pressure-vessel hemispherical head by the ASME Section VIII formula, t = (P·r) ÷ (2·S·E − 0.2·P), from the internal pressure P (MPa), internal radius r (mm), allowable stress S (MPa) and joint efficiency E. Heads close the ends of a pressure vessel's cylindrical shell, and their shape is decisive for structural efficiency. The HEMISPHERICAL (half-sphere) head is the MOST EFFICIENT of all: since the sphere distributes pressure equally in all directions (uniform membrane stress), the hemispherical head needs only about HALF the thickness of the cylindrical shell of the same radius and pressure (compare the '2·S·E' in the denominator with the shell's 'S·E'). So it is the choice for high-pressure vessels. The drawbacks are costlier fabrication and greater height (more space). For moderate pressures and costs, elliptical (2:1) or torispherical heads, intermediate, are used. The head-type choice is a trade-off among thickness/material (cost), space and fabrication ease. This formula is fundamental in the complete vessel design, combining shell and heads. Enter the pressure, internal radius, allowable stress and joint efficiency.
Rope-Pulley Contact Pressure
Calculate the contact pressure between a wire rope and a pulley (or drum) groove, p = 2·T ÷ (d·D), from the rope tension T (N), the rope diameter d (m) and the pulley diameter D (m); the result is in kPa. When a tensioned wire rope wraps a pulley, it presses the pulley groove with a contact pressure depending on tension and geometry. This pressure is a critical WEAR factor of the rope and pulley: high pressures (highly tensioned rope, small-diameter pulley, thick rope) accelerate abrasive wear of the rope's outer wires and the pulley groove wear, shortening both lives. Contact pressure is INVERSELY proportional to pulley diameter — so larger pulleys and drums extend rope life (besides reducing bending fatigue). Codes and makers specify allowable pressures per pulley material (steel, cast iron, polymer) and rope. With the D/d ratio (governing bending fatigue), contact pressure sets the rope-pulley system durability. Controlling contact pressure — using adequate pulleys and keeping tension within limits — is essential for the service life and safety of cranes, elevators and cableways. Enter the rope tension, the rope diameter and the pulley diameter.
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Hemispherical Head MAWP
Calculate the maximum allowable working pressure (MAWP) of a pressure-vessel hemispherical head, MAWP = (2·S·E·t) ÷ (r + 0.2·t), from the allowable stress S (MPa), the joint efficiency E, the available thickness t (mm) and the internal radius r (mm). Each pressure-vessel component has its own MAWP — the maximum pressure IT withstands with its available thickness — and the WHOLE vessel's MAWP is the SMALLEST among all its components' MAWPs (shell, heads, nozzles), since the vessel is as strong as its weakest component. This formula gives the hemispherical head's MAWP, the inverse of that head's thickness calculation. The factor 2 in the numerator (versus 1 in the shell) reflects the greater efficiency of the spherical form: for the same thickness, radius and material, the hemispherical head withstands about DOUBLE the cylindrical shell's pressure. So in a well-designed vessel with hemispherical heads, the cylindrical SHELL is usually the component governing the vessel's MAWP (the weakest), and the heads have margin. Comparing the components' MAWPs identifies the weakest link and guides repairs and reinforcements. Recomputing MAWP with the remaining thickness measured at inspection is part of vessel integrity management. Enter the allowable stress, efficiency, thickness and radius.
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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.