Conversion from Pounds per square inch to Pascals

Information about the Pound per square inch (psi)

The pound per square inch is a unit of pressure equal to 6894.76 pascals. Its symbol is psi. It is the force of one pound spread over one square inch, and it is the working pressure unit of the United States and of a great deal of equipment sold worldwide, because so much hydraulic and pneumatic machinery is designed to American specifications.

Its most familiar appearance is on tyres. A car is inflated to between 30 and 35 pounds per square inch, a bicycle tyre to 80 or more, and a heavy truck to around 100. Because the pressure and the contact patch together carry the vehicle, a small change in the figure changes handling, fuel consumption and tyre life, which is why it is printed inside the door of every car.

Compressed systems use the same scale. A workshop air line runs at 90 to 120 pounds per square inch, a domestic water supply arrives at 40 to 80, hydraulic machinery works at around 3000, and a full scuba cylinder holds 3000 or more. The convenient coincidence is that atmospheric pressure is 14.7 pounds per square inch, so a reading of 30 means roughly three times atmospheric in absolute terms.

That absolute distinction is written into the symbol. Engineers write psig for gauge pressure, measured above the surrounding air, and psia for absolute pressure, measured from vacuum. A tyre at 32 psig is at 46.7 psia, and confusing the two in a calculation of gas quantity or vessel strength produces an error of one atmosphere, which at low pressures is most of the answer.

Aviation uses it for cabin differential. An airliner maintains a pressure difference of about eight to nine pounds per square inch between cabin and outside air at cruising altitude, and the fuselage is designed and fatigue-tested against that repeated loading. The figure sets the effective cabin altitude and therefore how passengers feel at the end of a long flight.

Converting to metric is exact but not memorable, since a pound per square inch is 6894.76 pascals. The two rules of thumb worth carrying are that one bar is about 14.5 pounds per square inch and that one pound per square inch is about seven kilopascals; both are close enough for judging a gauge and neither is close enough for a design calculation.

One pound per square inch equals 6894.76 pascals, about 0.0689 bar, about 6.89 kilopascals, or about 0.068 atmospheres.

Information about the Pascal (Pa)

The pascal is the SI unit of pressure, written Pa. It is defined as one newton of force spread over one square metre, and it is named after Blaise Pascal, whose experiments with barometers in the 1640s established that air has weight and that its pressure falls with altitude. The General Conference on Weights and Measures adopted the name in 1971.

It is a remarkably small unit. Atmospheric pressure at sea level is 101,325 pascals, so the pressure everyone lives under is a six-figure number, and almost every practical use of the unit therefore carries a prefix. That awkwardness is not a design fault but a consequence of coherence: the newton and the square metre were fixed first, and the pascal is whatever falls out of dividing one by the other.

Acoustics is the field where bare pascals are natural. The reference pressure for the decibel scale is twenty micropascals, taken as the quietest sound a healthy young ear can detect, and ordinary conversation is around 0.02 pascals of sound pressure. The threshold of pain sits near 63 pascals, so the entire range of human hearing spans about six orders of magnitude in this unit.

Everyday objects give a sense of the scale. A sheet of office paper lying flat presses on the desk with about 0.8 pascals. A gentle breeze exerts a few pascals on a wall, and the pressure difference that drives ventilation through a building is typically between ten and fifty. Anything a person can feel as force is already in the thousands.

Prefixed forms carry the real work. Weather uses hectopascals, which are numerically identical to the older millibars, so a forecast reading of 1013 needed no relearning. Engineering uses kilopascals for tyre and fluid pressures, and materials science uses megapascals and gigapascals for strength and stiffness, where one megapascal is one newton per square millimetre.

The pascal also appears wherever a stress rather than a pressure is meant, since the two have the same dimensions. Young's modulus, yield strength and shear stress are all quoted in pascals or their multiples, which is why a single unit spans the pressure in a tyre and the stiffness of steel.

One pascal equals 1 newton per square metre, 0.01 millibars, about 0.0000099 atmospheres, or about 0.000145 pounds per square inch.