Converting Atmospheres to Bars

Worked Pressure Unit Conversion Problem

The pressure units atmospheres and bars may be used to calculate underwater pressure as well as atmospheric pressure.
The pressure units atmospheres and bars may be used to calculate underwater pressure as well as atmospheric pressure. Jeff Rotman, Getty Images

This example problem demonstrates how to convert the pressure units bar (bar) to atmospheres (atm). Atmosphere originally was a unit related to the air pressure at sea level. It was later defined as 1.01325 x 105 pascals. A bar is a pressure unit defined as 100 kilopascals. This makes one atmosphere nearly equal to one bar, specifically: 1 atm = 1.01325 bar.

Problem:

The pressure under the ocean increases roughly 0.1 atm per meter.

At 1 km, the water pressure is 99.136 atmospheres. What is this pressure in bars?

Solution:

1 atm = 1.01325 bar

Set up the conversion so the desired unit will be canceled out. In this case, we want ​the bar to be the remaining unit.

pressure in bar = (pressure in atm) x (1.01325 bar/1 atm)
pressure in bar = (99.136 x 1.01325) bar
pressure in bar = 100.45 bar

Answer:

The water pressure at a depth of 1 km is 100.45 bar.