Conversion from Pounds per square inch to Micropascals

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 Micropascal (µPa)

The micropascal is a unit of pressure equal to one millionth of a pascal. Its symbol is µPa. It is one of the smallest pressure units in practical use, and it owes its place to a single number: 20 micropascals, the reference pressure against which every sound level in air is measured.

That figure is the threshold of hearing — roughly the quietest sound a healthy young ear can detect at a frequency of about 1,000 hertz. When acousticians defined the decibel scale for airborne sound they needed a fixed pressure to compare against, and they chose that threshold. Zero decibels means a sound pressure of 20 micropascals; every decibel figure quoted for a road, a machine or a concert is a ratio to that number.

The scale that follows is steep. Twenty decibels is ten times the reference pressure, 200 micropascals. Sixty decibels, ordinary conversation, is a thousand times it, or 20 millipascals. A hundred and twenty decibels, the threshold of pain, is a million times it: 20 pascals. The ear covers a range of a million to one in pressure, and the micropascal sits at the bottom of it.

Underwater acoustics uses the same unit but a different reference. Sound in water is referred to 1 micropascal rather than 20, because the threshold of human hearing is meaningless in the sea. That difference matters enormously: a level quoted in decibels underwater is not comparable to one in air, and the gap between the two conventions is about 26 decibels before any other correction. Sonar figures, whale-song measurements and shipping-noise studies all carry the re 1 µPa qualifier for that reason.

Outside acoustics the micropascal appears in vacuum science. A good high vacuum is around 100 micropascals, and ultra-high vacuum, the regime used for surface physics and particle accelerators, runs from a few micropascals down to nanopascals. Pumping a chamber to that level takes hours of baking to drive adsorbed gas off the walls.

The unit also shows up in radiation pressure and in the very small pressure differences that laboratory instruments resolve. Anything measured in micropascals is a measurement rather than a force anyone would feel, which is exactly what makes the reference-level convention so useful.

One micropascal equals 0.000001 pascals, 0.001 millipascals, 1,000 nanopascals, or about 0.000000000145 pounds per square inch.