One psi is exactly 6,894.757293168361 pascals. Every digit is definitional, because the pound-force and the inch are both exactly defined in metric terms — the pound-force through standard gravity fixed in 1901, the inch through the 1959 agreement.
About the units
Psi stands for pounds per square inch, and the pounds in question are pounds-force, not pounds of mass. That distinction is the one thing worth being careful about in this pair. A pound-force is the force exerted by gravity on one pound of mass under standard gravity of exactly 9.80665 m/s², which works out to 4.4482216152605 newtons. Divide that by a square inch of 0.00064516 m² and the pascal figure follows. The pascal, one newton per square metre, is the SI unit and needs no such chain.
The exact factor
The derivation is 4.4482216152605 N ÷ 0.00064516 m² = 6,894.757293168361 Pa, exact. In more practical units that is 6.895 kPa or 0.06895 bar. Two variants of the unit appear in engineering documents and mean different things: psig is gauge pressure, measured relative to the surrounding atmosphere, and psia is absolute pressure, measured from vacuum. They differ by about 14.7 psi, and a specification that says only psi is ambiguous — in most industrial contexts it means gauge.
Where you meet this conversion
American engineering throughout: hydraulics, pneumatics, plumbing, pressure vessels and compressed air. Material strength is quoted in psi or ksi, thousands of psi, where structural steel yields around 36,000 to 50,000 psi. Converting an American specification into an SI calculation runs through this number every time. Scuba and industrial gas cylinders in the United States are rated in psi where the rest of the world uses bar, so a 3,000 psi cylinder is a 207 bar cylinder.