Converting Atmospheres to Pascals (atm to Pa)

Worked Pressure Unit Conversion Problem

Pressure applies to liquids, not just gases.
Pressure applies to liquids, not just gases. Reinhard Dirscherl / Getty Images

Atmospheres and Pascals are two important units of pressure. This example problem demonstrates how to convert the pressure units atmospheres (atm) to pascals (Pa). Pascal is a SI pressure unit that refers to newtons per square meter. Atmosphere originally was a unit related to the air pressure at sea level. It was later defined as 1.01325 x 105 Pa.

atm to Pa 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 pascals?

Solution:
Start with the conversion factor between the two units:

1 atm = 1.01325 x 105 Pa

Set up the conversion so the desired unit will be cancelled out. In this case, we want Pa to be the remaining unit.

pressure in Pa = (pressure in atm) x (1.01325 x 105 Pa/1 atm)
pressure in Pa = (99.136 x 1.01325 x 105) Pa
pressure in Pa = 1.0045 x 107 Pa

Answer:

The water pressure at a depth of 1 km is 1.0045 x 107 Pa.

Pa to atm Conversion Example

It's easy to work the conversion going the other way -- from Pascal to atmospheres.

The average atmospheric pressure on Mars is about 600 Pa. Convert this to atmospheres. Use the same conversion factor, but check to make certain Pascals cancel out so you get an answer in atmospheres.

pressure in atm = (pressure on Pa) x (1 atm/1.01325 x 105 Pa)

pressure in atm = 600 / 1.01325 x 105 atm (the Pa unit cancels out)

pressure on Mars = 0.00592 atm or 5.92 x 10-2 atm

In addition to learning the conversion, it's worth noting the low atmospheric pressure means humans couldn't breathe on Mars even if the air had the same chemical composition as air on Earth!