Converting pressure from PSI/BAR to BAR/PSI

However, Pascal is not the only unit used for pressure: 

The bar is originally a British unit, and 1 bar roughly corresponds to the average air pressure at sea level (although 1 atmosphere (atm) is a better description). The bar is defined as 100,000 Pa, or 100 kPa. This unit is pretty much the standard reference when it comes to pressure. 

History: Bar was once introduced by Vilhelm Bjerknes, a Norwegian meteorologist who was at the forefront of modern weather forecasting. The term “bar” comes from the Greek word “baros,” meaning weight. 

Current usage: Although bar is the unit of pressure, it is not accepted by the International System of Units (SI) and is even disapproved in some areas. The International Bureau of Weights and Measures, while indicating that authors are free to use bar, has not included it in the permitted list of the SI. 

Millibars (symbol: MB) is also commonly used to describe atmospheric pressure. Where atmospheric pressure equals 1013.25 mbar (101.325 kPa). Meteorologists and weather forecasters worldwide use this unit, as an expression in Pascal would lead to much longer numerical results.

The atmosphere corresponds more closely to the average air pressure at sea level, and is defined as follows: 1 atm = 101.325 Pa; so just over 1 bar. Air pressure is also regularly expressed in millibars or hectopascals. In this case, 1 millibar is exactly equal to 1 hectopascal. 1 atmosphere is therefore 1013 millibars and 1013 hectopascals.

The PSI is an American unit and stands for Pounds per Square Inch. The pressure that a Pound delivers depends on gravity which is not the same everywhere on earth. Because it is not the same everywhere, you cannot simply apply a conversion factor to convert PSI to Pa or bar. To be able to do this anyway, an average approximation is always used. 

Definition: A PSI is a unit used worldwide.  It is defined as the pressure created when a force of one pound-force is applied to a surface of one square inch. One PSI is approximately 6.895 Pascal (N/m2).

History: This unit finds its history in the imperial and American system of units of measure. It is based on the avoirdupois system, a system that uses weights in terms of the avoirdupois pound, which was standardized in 1959. The system came into use in England about 1300 and was used primarily in the international wool trade. 

Current Use: PSI is used worldwide to measure a lot of pressures. From tire pressure to gas pressure and quite a few others. Although the Pascal is used more in the scientific context, PSI is used more day-to-day. Especially in the Anglo-Saxon countries.