One megapascal is 145.0377377302 psi. This is the conversion of materials engineering: strengths, moduli and hydraulic ratings are quoted in MPa in metric documentation and in psi or ksi in American, and the two describe the same steel.
About the units
A megapascal is a million pascals, equal to 10 bar or 1 N/mm² — that last identity being the reason mechanical engineers like it, since stress calculated from a force in newtons over an area in square millimetres comes out directly in megapascals with no conversion at all. The psi is pounds-force per square inch, and its thousand-fold multiple, the ksi, is standard in American materials specifications. Both express stress, pressure and elastic modulus, which are dimensionally the same quantity even though they describe different physical situations.
The exact factor
The exact relationship is 1 MPa = 145.0377377302092 psi, which follows from the psi being exactly 6,894.757293168361 Pa. The approximation of 145 is good to three parts in ten thousand. Reference values that make the scale legible: mild structural steel yields at about 250 MPa or 36,300 psi; high-strength steel at 700 MPa or 101,500 psi; concrete compressive strength runs 20 to 40 MPa, which is 2,900 to 5,800 psi; and the elastic modulus of steel is 200 GPa or 29 million psi.
Where you meet this conversion
Materials specifications, structural calculations and hydraulic system design. Comparing a European steel grade to an American one requires this conversion, and getting it wrong by a factor rather than a rounding produces a structure that is either wildly overbuilt or unsafe. Hydraulic systems are rated in MPa or bar in metric equipment and psi in American, with typical working pressures of 20 to 35 MPa, which is 2,900 to 5,000 psi. Injection moulding, hydroforming and pressure testing all cross the same boundary.