Could the air you just breathed in contain air someone exhaled long ago?
― The number of molecules in one breath, and how many breaths Earth's atmosphere adds up to, are almost the same number
The answer is "yes." And nearly every time. Just one breath, exhaled by someone 1,000 years ago — its molecules, on average, are estimated to be mixed one or two at a time into the breath you're taking right now. That's because two "absurdly large numbers" happen to be about the same size.
One morning, you open a window and take a deep breath. Cool air fills your chest.
That air was just outside the window a moment ago. Before that, where was it? Over the ocean? In a forest in another country? Did it ever pass through someone's chest, centuries ago?
You might think, "Surely it's diluted away to nothing by now." But when you actually count it up, the story turns out to be the exact opposite.
Only two reasons old breaths still reach us today
One quiet breath is about 0.5 litres. It contains 1.2 followed by 22 zeros' worth of molecules. No matter how much it's diluted, the starting number is so huge it never fully reaches zero.
A breath you exhale is carried by the wind, and is said to spread from the Northern to the Southern Hemisphere in about a year. Nitrogen molecules, which make up nearly 80% of the air, drift on almost unchanged for millions of years.
"There's a huge amount" and "it mixes evenly." Put these two together, and someone's breath from long ago stays dissolved thinly and uniformly throughout Earth's atmosphere. Let's look at the numbers, step by step.
The molecule count in one breath, and how many "breaths" Earth's air adds up to, are about the same
First, let's count the molecules in one breath. Gases share a property: at the same temperature, pressure, and volume, any gas contains the same number of molecules, regardless of type. Using this, we can calculate that 0.5 litres of air contains about 1.2 followed by 22 zeros' worth of molecules.
Next, let's see how many times Earth's entire atmosphere can be divided into "0.5-litre breaths." The total weight of the atmosphere is roughly 5.1 million trillion tonnes. Converting this to a molecule count and dividing by the number of molecules in one breath gives about 8.8 followed by 21 zeros.
Look at Figure 1. At the top, "the number of molecules in one breath," and at the bottom, "how many breaths Earth's air adds up to," line up at almost the same position on the scale.
What happens when these two numbers are about the same? Suppose a single breath from long ago mixed evenly into Earth's atmosphere. Then the number of "molecules from that breath" in your breath right now can be estimated as follows.
Divide the number of molecules in one breath by the number of breaths Earth's air adds up to. Dividing 1.2 with 22 zeros by 8.8 with 21 zeros gives about 1.4. That works out to roughly one or two molecules mixed in, from any single breath, by anyone, from any era.
Over a lifetime of breathing, the number grows further. A person is said to breathe about 550 million times in a lifetime. So the molecules exhaled over an entire lifetime by one person who lived 1,000 years ago would amount to roughly 700 million of them mixed into your breath right now.
How fast does air actually mix across the whole planet?
This calculation assumes the air is "well mixed." So how long does it actually take for an exhaled breath to spread across the globe?
Look at Figure 2. Air mixes quickly east-west, but slowly north-south. Circling all the way around a single band of latitude takes about two weeks. Spreading across the entire Northern Hemisphere takes one to two months. Because air exchanges less across the equator, reaching the Southern Hemisphere is thought to take about a year.
In other words, a breath from more than a few years ago has already mixed almost uniformly across the whole planet. What matters here is that the molecules themselves don't break down. Nitrogen, at about 78% of the air, and argon, at about 1%, barely undergo chemical change. They keep drifting as the same molecules for centuries.
Oxygen and carbon dioxide, on the other hand, are constantly exchanged with plants and the ocean. So you can't say the oxygen from an old breath is still around unchanged. Still, nitrogen and argon alone make up nearly 80% of the air, so the broad estimate of "one or two molecules" doesn't really change.
Suppose you counted the molecules in one breath at a rate of one per second. Finishing the count would take about 30,000 times longer than the time that has passed since the universe began. That's why, in Figure 1, there's a gap of 5 zeros between the age of the universe in seconds (17 zeros) and the molecules in one breath (22 zeros).
The number of water molecules in a single glass of water is said to be far greater than the number of glasses it would take to hold all the water in Earth's oceans. So a glass of water poured into the ocean, once well mixed, would leave more than 1,000 of its molecules in any glass of water you scoop up.
Summary
The number of molecules in one breath is about 1.2 followed by 22 zeros. The number of times Earth's atmosphere can be divided into single breaths comes out to almost the same figure. Air mixes across the whole planet within a few years, and nitrogen and argon molecules survive intact. As a result, one or two molecules from any breath ever exhaled by anyone, in any era, are estimated to be mixed into your breath right now.
Air is a single shared resource that people all over the world
have been breathing in and out, in turn, for thousands of years.
For the story of how a tiny fraction of the air can have an outsized effect, see Carbon dioxide is only 0.04% of the air — so why does it change the temperature?, and for the story of a component making up 1% of the air that went unnoticed for over a century, see Why did it take over 100 years to discover argon?
- Watching a clock, count your breathing rate for one minute as normal. For an adult, this is typically 12-20 breaths.
- Multiply that number by the minutes in a day (1,440) and the days in a year (365). Now you know roughly how many times you breathe in a year.
- In one corner of a room, open a scented hand cream. Time how many seconds it takes someone in the opposite corner to notice it. Then turn on a fan and time it again.
Without a breeze, a scent takes a long time to travel. Left to move on their own, molecules mix very slowly. Stirred by wind, mixing speeds up dramatically. Earth's atmosphere mixing within a few years is likewise the work of large-scale wind currents stirring it.
Want to go deeper? ― terms, formulas, and where this fits in the curriculumEach level, from middle-school science to university specialist courses, is labelled explicitly
- MSCovered in middle-school science
- HSCovered in high-school "Basic Chemistry" / "Chemistry"
- HS+Advanced high-school content, or textbook sidebar material
- UnivContent not taught in high school — university-level specialist courses (probability & statistics, atmospheric chemistry)
- ResearchNot yet settled even at university level — an active area of current research
MSTerms: this phenomenon has names
- Molecule: the smallest particle that still has a substance's properties. Air is a mix of nitrogen molecules, oxygen molecules, and others, all flying around independently.
- Avogadro's law: at the same temperature, pressure, and volume, any gas contains the same number of molecules, regardless of type.
- Atmospheric circulation: the large-scale wind currents that circle the globe, carrying air quickly east-west and slowly north-south.
MSHSCheck it with formulas: how many molecules from an old breath are in today's breath?
Large numbers are hard to work with directly, so we calculate using "10 to the power of something" as a unit. For example, if we take "10^23 molecules" as one unit, then 0.12 units is the number written as 1.2 followed by 22 zeros.
| In symbols | N = ( V ÷ Vm ) × NA k = N × ( N ÷ Na ) |
| In words | Molecules in one breath = (volume of one breath ÷ volume of 1 mole of gas) × Avogadro constant. Molecules from an old breath present in today's breath = molecules in one breath × (molecules in one breath ÷ total molecules in Earth's atmosphere) |
| Where the formula comes from | The first half is Avogadro's law (a gas's volume is proportional to its molecule count). The second half is the idea of uniform mixing: "if well mixed, the proportion is the same wherever you sample." We multiply the fraction that the old breath represents of the whole atmosphere by the molecule count of today's breath. |
Symbol meanings: N is the number of molecules in one breath, V is the volume of one breath (litres), Vm is the volume of 1 mole of gas (litres), NA is the Avogadro constant, Na is the total number of molecules in Earth's atmosphere, and k is the number of molecules from one particular past breath present in today's breath.
| Volume of one quiet breath | about 0.5 litres |
| Volume of 1 mole of gas (25°C, 1 atm) | about 24.5 litres |
| Avogadro constant | about 6.0 per mole (taking 10^23 molecules as one unit) |
| Total weight of Earth's atmosphere | about 51 (taking 10^20 grams as one unit; about 5.1 million trillion tonnes) |
| Weight of 1 mole of air (average) | about 29 grams |
| Lifetime breath count (15 breaths/min over 70 years) | about 550 million |
| Moles in one breath | 0.5 ÷ 24.5 ≒ 0.020 |
| Molecules in one breath (10^23 as one unit) | 0.020 × 6.0 = 0.12 |
| Moles in Earth's atmosphere (10^20 moles as one unit) | 51 ÷ 29 ≒ 1.76 |
| Total molecules in Earth's atmosphere (10^43 as one unit) | 1.76 × 6.0 ≒ 10.6 |
| Earth's air = how many breaths (10^21 as one unit) | 10.6 ÷ 1.2 ≒ 8.8 |
| Molecules from one past breath present in today's breath (taking the breath's molecule count as 12 in 10^21 units) | 12 ÷ 8.8 ≒ 1.4 |
| Molecules from one person's lifetime of breathing present in today's breath (in hundreds of millions) | 1.4 × 5.5 ≒ 7.7 |
Because the molecule count of one breath (1.2 with 22 zeros) and the number of breaths Earth's air adds up to (8.8 with 21 zeros) are nearly equal, dividing one by the other gives a value near 1. Limiting this to just nitrogen and argon still leaves about 80%, so over a lifetime that's roughly 600 million molecules.
HSHS+Amount of substance, and the north-south gap in carbon dioxide
HSIn basic chemistry, particle counts are measured using "amount of substance" (moles). One mole is 6.02214076 followed by 23 zeros' worth of particles, and since 2019 this figure itself has been the defined value. The volume of 1 mole of gas is about 22.4 litres at 0°C and 1 atm, or about 24.5 litres at 25°C.
HS+The slow north-south mixing of air also shows up in carbon dioxide observations. Because more carbon dioxide is emitted in the Northern Hemisphere, its concentration there is slightly higher than in the south. The reason this north-south gap doesn't disappear is thought to be that crossing the equator takes about a year.
Univ"An average of 1.4" doesn't mean exactly 1.4 every time
How many molecules from an old breath end up in today's breath varies each time. The spread you get when counting rare events over many trials is described by the Poisson distribution. When the average is 1.4, the probability of getting zero is about 25%. In other words, roughly three times out of four, at least one molecule is present. In atmospheric chemistry, the average time a molecule stays in the atmosphere is called its "residence time." For nitrogen this is estimated at several million years or more, while for oxygen it's estimated at around a few thousand years.
📖 For the derivation of the formulas and further reading: Avogadro constant (Wikipedia) / Poisson distribution (Wikipedia)
ResearchWhat's still not fully understood
- How "old" is the air high above us? Observation and modelling estimate that stratospheric air left the surface a few years ago. But whether this "age" is shifting as warming changes atmospheric circulation is still debated among researchers.
- How much exchange happens with the ocean and soil? Even nitrogen partly dissolves into the ocean or gets taken up by microbes. Exactly how much time any individual molecule spends outside the atmosphere is still not precisely known.
- Is it really "uniform"? Some places, like over cities or at the bottom of valleys, don't exchange air easily. Precisely modelling how air mixes at a fine, local scale remains a difficult problem even today.
So the content of this article, too, reflects "the explanation as currently understood." The figure of "one or two" is an estimate of the average under well-mixed conditions.
How this connects to the curriculum (by level)
| Level | Subject / unit | Where in this article |
|---|---|---|
| MS | Science Field 1, "The nature of matter"; Field 2, "Weather and its changes" | Molecules, composition of air, large-scale wind currents |
| HS | Basic Chemistry, "Amount of substance" | Moles, Avogadro constant, volume of 1 mole of gas |
| HS+ | Earth Science, "Atmospheric circulation" | North-south gap in carbon dioxide |
| Univ | Probability & statistics, atmospheric chemistry | Poisson distribution, residence time |
| Research | Atmospheric transport, material cycles | Age of air, molecular exchange |
| ― | Everyday connections | Ventilation and how air mixes, intuition for huge numbers |
- International Bureau of Weights and Measures, "The International System of Units (SI)," 9th edition (2019) ― the defined value of the Avogadro constant
- National Astronomical Observatory of Japan (ed.), Rika Nenpyo (Chronological Scientific Tables), Maruzen Publishing (国立天文台編『理科年表』丸善出版) ― composition and mass of the atmosphere
- Sam Kean, Caesar's Last Breath: Decoding the Secrets of the Air Around Us, Little, Brown and Company, 2017
- Japan Meteorological Agency, "Long-term trend of atmospheric CO2 concentration" (気象庁「二酸化炭素濃度の経年変化」)
- Wikipedia, "Avogadro constant" (ウィキペディア「アボガドロ定数」)
※This article is a general-audience science explainer. The figures given are approximate, meant to convey the underlying mechanism. They are average estimates assuming well-mixed air, and actual numbers will vary by location and time.