## Have you ever wondered how much breathable air is on Earth?

#### This article is part of a series

In this article, I will demonstrate how to calculate the mass of oxygen in the atmosphere. Calculating how much oxygen in the air is relatively easy. The challenge is that atmospheric science is complicated, and the numbers are estimates based on current theories and knowledge. If you want to skip the math, you can see the answers highlighted in yellow below. Afterward, we’ll explore nine reasons why the accepted amount of oxygen in the atmosphere might not be accurate, including my favorite — the fishbowl theory.

For the record, we will measure only the breathable oxygen in the atmosphere, also known as molecular oxygen, which is two molecules of oxygen — O_{2}. After iron, oxygen is the second most abundant element on Earth. It is part of almost half the upper crust of the Earth and more than half of the sea, but, of course, we can’t breathe dirt or water.

Our calculation will be in two steps. 1) We need to know how big the atmosphere is. 2) Then, we can figure out the percentage and mass of the atmosphere’s different gases.

Okay, let’s get started.

## What is the mass of the Earth’s atmosphere?

Because the atmosphere is composed of gases and the volume of gases changes with temperature, we will calculate the mass of the atmosphere instead. To arrive at this number, all we need to do is calculate the Earth’s surface area and then multiply that by the pressure the atmosphere exerts on the surface. This simple formula will get us very close to the accepted value, which according to the National Center for Atmospheric Research, is 5,148,000,000,000,000,000 kilograms. We’ll discuss this number more below.

First, we need to calculate the surface area of the Earth. We can use simple high school geometry.

The formula for the area of a sphere is 4 x pi x radius squared. A search online gives the Earth’s radius as 6.371e6 meters. Plugging this into our formula gives:

A = 4 x π × (6.371e6)^{2}

Area of the Earth = 5.100644e14 m^{2}

Again, I’m using CalculatorSoup to help. (More about how I do my math.) And I double-check all my answers with reputable sources online. Wikipedia says that the surface area of the Earth is “about 510 million km^{2},” which is the same number. This assumes the Earth is a perfect sphere, but it is squished a little, like someone sitting on a yoga ball. I’m assuming the difference in surface area is insignificant. Still, it is the first hint of something being off.

Now we need to know what the atmospheric pressure is at sea level. We are under tremendous pressure. 14.696 pounds of pressure per square inch. Imagine putting a 15-pound weight on one square inch of your body. It would leave a big dent. Fortunately, we don’t notice because the pressure is equal all over inside and out.

Anyway, we need to convert that number to something more useful. We can measure the atmospheric pressure as pounds per square inch, Pascals, bars, millimeters of mercury, et cetera, etc. (The hard part of all this math is converting the numbers and units. Sheesh! If only humanity could agree on something.) Cheating a little bit and looking it up online, the unit of measure and the number I need is Newton/meter^{2}.

So, converting 14.696 psi, the pressure the atmosphere exerts on the Earth’s surface = 101,325 Newton/meter^{2}.

But that is the pressure at sea level; the pressure on top of mountains is much less. Now, let’s do a rough calculation of the average elevation of both land and sea. If I trust the internet, the average elevation of all the continents is 841 meters, and the Earth is covered by 71% ocean and 29% land. So:

841 meters × 29% = 244 meters

The average elevation of the Earth = 244 meters

The atmospheric pressure at that elevation per this website equals 98,416 N/m^{2}.

So, the total force the atmosphere exerts on the surface of the Earth is:

98,416 N/m2 × 5.100644e14 m^{2}

= 5.019849e19 Newtons

To convert force (Newtons) to mass (kilograms), we use the equation for the force of gravity.

Force = mass × gravity. Solving for mass gives:

Mass = Force ÷ gravity

Mass = 5.019849e19 N ÷ 9.81 N/kg

Mass of the atmosphere = 5.117073e18 kilograms or 5,117,073 gigatonnes.

Double-checking this number again, Wikipedia says the mass of the atmosphere is about 5.1480e18 kg. So, my number is very close. Far less than a 1% difference. And, now that we know the mass of the Earth’s atmosphere, we can calculate the mass of its parts.

## How much oxygen is in the atmosphere?

Below is a chart of the five most common gases in our atmosphere. You’ll notice almost all of it is oxygen and nitrogen. Carbon dioxide, the gas everyone is worried about, is not even close. (To be fair, it may not seem like a lot of CO2 but if it doubles, that’s a big problem.) And, the water vapor varies greatly, so it is subtracted before measured.

Gas | Symbol | Volume % | Molar Mass | Weight % |

Nitrogen | N_{2} | 78.084 | 28.013 | 75.52 |

Oxygen | O_{2} | 20.946 | 31.999 | 23.14 |

Argon | Ar | 0.934 | 39.948 | 1.29 |

Carbon Dioxide | CO_{2} | 0.04 | 44.010 | 0.06 |

Neon | Ne | 0.001818 | 20.18 | 0.0013 |

Here is something I didn’t know: it is commonly said that oxygen is 21% of the air. That means oxygen is about 21% of the volume or 21% of the number of molecules, but oxygen is about 23% of the atmosphere by weight. Confusing? Yes!

So the mass of oxygen in the atmosphere is:

0.2314% × 5.117073e18 kilograms (mass of the atmosphere per my math)

= 1.184090e18 kilograms or 1,184,090 gigatonnes

Again, I am shockingly close. Online estimates for the mass of atmospheric oxygen vary from 1,080,000 gigatonnes to 1,185,000 gigatonnes to 1,200,000 gigatonnes. That’s a huge number!

That’s pretty good for an artist. Maybe I should have been an atmospheric scientist. But, seriously, how can it be this simple to figure out how much oxygen is in the atmosphere? It makes me wonder if something is wrong.

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## Double checking my accuracy

Okay, I was so surprised at my accuracy that I had to consult a real research scientist. They didn’t seem surprised. They said, “This is how science works. Doing science is like following a recipe. Anyone can duplicate the process and arrive at the same answer.” They also said that hundreds if not thousands of scientists came before me to help make this process very easy, like Newton and Avogrado. That being said, if one theory, one scientist or one piece of data collected is wrong, our recipe fails. The good news is that science is meant to be scrutinized. If a theory breaks, that is an opportunity to see how the world really works.

## How is oxygen measured by scientists?

I was going to stop here but I wanted to learn how oxygen is actually measured.

It’s complicated. For starters, oxygen is measured either by concentration (percentage) or by partial pressure. The percentage of oxygen in our atmosphere is theoretically the same everywhere (except at extreme altitudes) but the partial pressure changes. So, at high altitudes, the percentage is the same at about 21%, but there are fewer molecules. So, it gets harder to breathe.

The Scripps O2 Program is the organization that collects air samples from 9 locations worldwide and measures changes in atmospheric oxygen concentration. (Per their data, oxygen is going down step by step, matching the rise in carbon dioxide.) Two points interest me:

One) Per their website: “Measuring the changes in O2 is challenging because the changes are so small. The data reported on this website are measured using a technique developed by the project leader (R. Keeling) as part of his Ph.D. thesis back in the 1980s. The technique involves detecting changes in the refractive index of air via a very precise measurement method known as interferometry. The data are reported as changes in the O2/N2 ratio in ‘per meg’ units.”

Two) Then, they compare this ratio to a sample of air they collected in the mid-1980s.

Okay, wow! So, the reference sample of oxygen is only about 35 years old. This is well after the industrial revolution when fossil fuels began being burned. What’s more surprising is that the Scripps Institute only measures a change in the ratio between oxygen and nitrogen, not a change in the actual amount of oxygen.

### This raises so many questions:

- How did they measure the total mass of oxygen? (Their measure is almost the same as mine and presumably also 35 years old.)
- Was this method accurate in the 1980s?
- Where does nitrogen come from or go? (If this has changed, then the ratio is off.)
- And, not only are water vapor and pollutants subtracted from the equation but so are three of the top five gases, argon, carbon dioxide and neon.
- I had so many questions that I now list then below as possible errors in measurement.

Well, figuring this all out could take a long time!

## Possible errors in measurement

This section got so big that I made it an article all by itself. Please see: 10 reasons why global oxygen measurements may be wrong. Topics include:

- Oversimplification
- Weight versus volume
- The water vapor problem
- Air pollution
- Measuring non-breathable forms of oxygen
- Atmosphere shape and size
- Doldrums and dead zones
- Fishbowl Theory
- Oceans warming and glaciers melting
- CO2 fertilization
- And more if I find them.

## Summary

Okay, whew! We calculated the mass of the atmosphere to be about 5,117,073 gigatonnes and the mass of the oxygen to be 1,184,090 gigatonnes. We can feel — given the current understanding of climate science — that these numbers are fairly accurate. Then we discussed ten reasons why there might be less oxygen than believed. This is part of my series exploring the theory that it is actually oxygen depletion NOT carbon dioxide emissions that is the major factor in climate change.

If you find any flaws in my thinking, please leave a comment below. Thanks.

**Footnotes**

See links in the above article. Plus the following:

The Mass of the Atmosphere: A Constraint on Global Analyses.