Conversion from Pounds per square inch to Gigapascals

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 Gigapascal (GPa)

The gigapascal is a unit of pressure equal to a billion pascals, written GPa. It is a thousand megapascals and ten thousand bar. It is the unit in which materials science states stiffness rather than strength, and in which the pressures inside planets and inside high-pressure laboratories are described.

Elastic modulus is its principal use. Steel has a Young's modulus of about 200 gigapascals, copper 117, aluminium 70, ordinary glass 70, concrete around 30, timber along the grain 10 to 15, and rubber less than a tenth of one. Those numbers describe how much a material stretches under load, not when it breaks, and they explain why a steel beam of the same strength as an aluminium one still deflects less.

Diamond marks the top of the ordinary scale. Its modulus of roughly 1200 gigapascals is the highest of any natural material, which is why it is used to make anvils for high-pressure work: nothing else can push that hard without deforming first. Synthetic diamond is made industrially at about five gigapascals and high temperature, in presses built specifically to hold that pressure.

The interior of the earth is described in the same unit. Pressure at the base of the crust is around one gigapascal, at the boundary between mantle and core about 136, and at the centre of the planet roughly 360. Laboratory diamond anvil cells now reach and exceed the central value, which allows the behaviour of iron and silicates under planetary conditions to be studied directly rather than inferred.

For contrast, the deepest point in the ocean exerts only about 0.11 gigapascals. That comparison is worth keeping, because it shows how much larger geological pressures are than anything associated with water: the bottom of the Mariana Trench is a thousandth of the pressure at the centre of the earth.

Below the gigapascal, the megapascal describes strength, and above it there is little except stellar and theoretical physics. The terapascal appears mainly in the elastic modulus of carbon nanotubes and in the interiors of giant planets, so the gigapascal is effectively the top of the range that laboratories and engineers work in.

One gigapascal equals 1,000,000,000 pascals, 1000 megapascals, 10,000 bar, or about 145,000 pounds per square inch.