Converting Atmospheres to Pascals (atm to Pa)

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 an 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 canceled 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 10​⁵ 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. The low pressure of the Martian atmosphere also means water and carbon dioxide readily undergo sublimation from the solid to the gas phase.