The Computed Limit of Human Population

Executive summary:
  1. Human population reached 8.0 billion in November 2022 (click: view current total; note that humanity adds another billion every 11-12 years). But the total effective total should include the sum of "number of humans" plus "beasts of burden" plus "air-breathing machines".
    Recall that an automobile consumes more O2 (oxygen) and energy in one hour than its owner would consume in 21 days. Also consider how much oxygen is consumed by the worldwide population of boats (cargo carriers, tankers, cruise liners), airplanes, locomotives, cruise liners, farm equipment, construction equipment, 18-wheelers, etc.
    On a lesser note: (1) consider the 9 carrier strike groups operated by the USA which include up to 70 other vessels each; (2) the number of SAC bombers that are always flying; (3) consider the super yachts run by the world's millionaires and billionaires.
  2. Atmospheric O2 levels have been falling ever since scientists began continual measurements in 1990. This is because atmospheric O2 is combined with C (carbon) to produce CO2 (carbon dioxide) during chemical combustion as well as animal respiration. Even though CCS (carbon capture and storage) technology promises to reduce CO2 emissions by pumping CO2 underground, O2 levels will continue to fall due to burning.
  3. There simply isn't a sufficient amount of photosynthetic life on Earth to compensate for all the fossil fuels being burned by humanity.
    Fact: Oceans, plants and animals emit about 780 gigatons of carbon annually and absorb nearly all of it. Human activities emit 29 gigatons of carbon per year but absorb almost none of it (so it ends up in the atmosphere). We can see this principle in action through the Keeling Curve which indicates a constant growth of atmospheric CO2 ever since measurements began in 1958. More update-to-date atmospheric measurements can be seen at NOAA. Did you notice the small "sine wave" oscillating on the rising line? This annual fluctuation in CO2 is caused by seasonal variations in "carbon dioxide uptake" by land plants. Since many more forests are concentrated in the Northern Hemisphere, more carbon dioxide is removed from the atmosphere during "Northern Hemisphere summer" than "Southern Hemisphere summer".
  4. Humanity is reproducing too quickly:
    1. Pick your preferred starting date before thinking about our current problem:
      1. Science provides these dates for your consideration:
        1. the current mammalian growth spurt begins 65 million years ago after an asteroid strikes Earth at Chicxulub causing the dinosaurs to become extinct.
        2. anatomically modern humans first appear in the fossil record 250,000 years ago in Africa
        3. the current human growth spurt begins 11,700 years ago after the end of the ice age (estimated population: between 5 and 10 million)
      2. Abrahamic religions teach the world is ~ 6,000 years old (starting population: one mating pair)
    2. Despite disease, war, and natural calamities, human population reached 1 billion in 1804. This required ~ 11,500 years (or ~ 5800 years)
    3. Despite disease, war, and natural calamities, human population reached 2 billion in 1930. This required an additional 126 years.
    4. Despite disease, war, and natural calamities, human population reached 6 billion in 1999. This required an additional 69 years. So, in 69 years, humanity repeated six times what required all history (before 1804) to only do once. Clearly, the current human population (which is still growing at a rate of 1 billion every 11-12 years) is too large and will soon outstrip planetary resources. Even if we destroyed all our machines and attempted to live like the Amish, there are still too many of us. In order to support the current population humanity will need to shift to non-combustible renewable energies.
    5. Clearly, Homo sapien has morphed into Homo technologicus

This page began "Thinking about Communicable Disease"

CAVEAT: the following effort was created before the COVID-19 pandemic. Numerous scientists said that a large pandemic was inevitable while most politicians ignored the warnings.

Influenza articles like these...

... tell us that the Influenza Pandemic of 1918 was triggered by soldiers living in close proximity during World War I. British medical archives tell us that an unknown disease (now known as The Flu) started in 1916 and then returned in 1917, 1918 and 1919. Apparently, diseases often reach pandemic proportions after three iterations.
I started thinking that communicable disease would certainly exterminate all of humanity if we lived in similar proximity to World War I soldiers, and I wondered what that number would be. But all of humanity can't live like soldiers because we need (at the very minimum) to "set aside farm areas to provide us with food" and "industrial areas to provide us with clean water while processing our detritus". While it is true that tall buildings allow urban peoples to live more densely than field soldiers, human population will ultimately be limited by the area of land required to support life. And I wondered what that number would be.

Population-Limit Calculations

The current size of human population is billion. Earth's mean radius is km so applying the formula (4 • pi • r^2) yields a surface area of xxx square km. Since % of the Earth's surface is composed of water then the surface area of the land is xxx square km.  Many estimates place the percentage of farmable land at only % of the total land surface which yields xxx square km. (caveat: references like this one say to use a lower percentage).

Agriculturalists inform us that hectares of modern farmland are required to support one person (low-tech farms are less productive so would require a larger area; scientists like William Rees think 2.1 hectares might be closer to the mark). However, higher temperatures due to climate change are already reducing the productivity of farmland which means that more will be required to support every person. Also remember that the shift from summer to winter causes a large fraction of farmable land to go offline every year (since a slightly lower amount goes online each year, perhaps we should compute the total area then divide it in half). On top of all this, let's not forget that farmable land is permanently lost to other uses like roads, residential housing, airports, industrial areas, office complexes, as well as other civil support structures like schools, theaters, legislatures, libraries, court houses, prisons, etc.

Hectares Acres Square
Supported Population


  1. When you compare any two lines (e.g. "0.6 hectares" to "0.7 hectares") there does not seem to be a safe margin of error. All you would need is one bad agricultural year to nudge humanity over the top.
  2. Many human societies require beasts-of-burden (horses, oxen, elephants) for farming and/or transportation. Each one of these larger animals requires agricultural land to support their biological needs so the Maximum Supported Population tabled above should include the total of "humans and domesticated animals". In this case humanity may have already exceeded Earth's resources.
  3. Not every society on the planet is using western agricultural techniques -AND- climate change is limiting agricultural productivity worldwide. I think it is safe to say that some projections showing humanity successfully growing to nine billion are just a marketing fantasy. Eight billion may be out of the question as well. If we ignore these risks, I am fairly certain that nature will produce some nasty diseases to limit our efforts. Perhaps the civilized thing to do is to accept seven billion as an upper limit with an intention of shrinking back to six billion or lower.
  4. Work published by William Rees uses different numbers which require urgent action.
    1. For example, his calculations state that the world average amount in 2007 was 2.1 global hectares per person.
      Quote: For 2007, humanity's total ecological footprint was estimated at 1.5 planet Earths; that is, humanity uses ecological services 1.5 times as quickly as Earth can renew them
      NSR Calculations:
      • estimated population in 2007:
        • population in 1999 was 6 billion.
        • population grows ~ 83 million per year.
        • total = 6 billion + ((2007-1999) * 83 million)
        • total = 6 billion + 664 million.
        • 6.664 billion.
      • correction factor for unity (where 100% of Earth's resources can sustain humanity):
        • 1 / 1.5 = 0.666
      • target human population:
        • 6.664 x 0.666 = 4.42 billion
    2. The typical U.K. citizen requires 4.9 global hectares per person.
    3.  The typical American requires 8.0 global hectares per person.
      • for everyone on the planet to have the same quality of living as an American, total population size must be reduced below one billion.
    4. Proceeding forward humanity must do one or more of the following right now:
      1. richer countries need to lower their standard of living.
      2. families need to reduce size.
      3. individuals need to delay reproduction.
      6. (the population clock is unnerving)

Supporting Data

Current Official Population Densities (2011-12-29)

This table provides a starting point for comparative purposes (note: I'm not sure if they are using total area or agriculturally usable area).

Videos (to learn more)

Unit Conversions (and other stuff)

Caveats (prompted by a few emails I've already received about this web page)

How large is one billion?

Number augmentative suffix number of zeros confusing alternate
1,000 thousand 3  
1,000,000 million 6  
1,000,000,000 billion 9 milliard
1,000,000,000,000 trillion 12  
1,000,000,000,000,000   15 billiard

Loss of Biological Productivity

C3 Photosynthesis (efficiency drops as temperature rises)


Further Research (C4 Photosynthesis and CAM)

World Losses in Productivity (is it one degree Fahrenheit or Celsius?)

I have always been looking for publications which would say that an overall 10% loss is due to an increase of one degree Fahrenheit or one degree Celsius but have had no luck to date.

Considering all these points:

I am going to speculate that Celsius is correct figure when considering world-wide losses in biological productivity. 

Flowering of Rice (blocked at high temperatures)

Tree growth is slowed by heat

Oceans cannot be relied upon to pick up the slack.

Have We Already Passed the Tripping Point? Maybe.

Talking Point #1
CO2 Levels as Mauna Loa Observatory

Some people tell me "humanity has nothing to worry about because CO2 is good for plants". Supposing that this statement is not a naive over simplification then we must ask: when can we expect plants to react to the excess CO2? Referring to the Keeling Curve for a moment, it looks like CO2 has been on a constant rise ever since Charles Keeling started taking official measurements in Hawaii starting in 1958. The rising line looks fairly straight and you would have thought we might see the results of an explosion of plant life to compensate for all the additional CO2. More update-to-date atmospheric measurements, charts, and datasets can be retrieved from NOAA's GMD (global monitoring division) site. Raw data in csv format (can be imported into MS-EXCEL) can be retrieved here:

year  CO2 1958
2011 391 315 24% increase over 53 years
2019 410 315 30% increase over 61 years

Perhaps higher atmospheric temperatures (due to higher CO2 levels) are preventing plant life (at least C3 plant life) from exploding into the role of "environmental savior" because the atmospheric temperature chart seems to have grown continually since 1878 when the International Meteorological Society began daily world-wide measurements. One thing that is certain is this: additional deforestation by humans probably hasn't helped. Especially if it was done by slash-and-burn techniques.

Talking Point #2

Some people tell me "higher levels of CO2 will force plants to grow". This is a gross oversimplification for the following two reasons:

  1. Almost all biological systems are pull-based rather than push-based. For example, a human body-builder will lift weights to force his body to "require" more dietary protein. This causes an increased amount of dietary protein to be pulled into the body from the digestive system which, if you think about it, is really outside the body but I digress. Attempting to push-in nutrients does not induce muscle growth (but a lack of it will be a problem if not enough is present when required).
  2. A primary grade school explanation of photosynthesis tells the young student that "CO2 is converted into O2". Sometimes a very simplified chemical formula is provided like this one:
    CO2 + H20 + energy = (CH2O) + O2
  3. Secondary-school biology classes introduce more details including a properly balanced chemical formula similar to this one:
    6CO2 + 6H2O + photons = C6H12O6 + 6O2
    diagram of photosynthesis
  4. College courses in molecular biology fill in the missing intermediate steps which show that O2 is only liberated by the photolysis of water (the original research was done using radioactive tagging). So rather than saying: During photosynthesis, "CO2 is converted into O2" it is more accurate to say "H2O is split by photolysis into O2 and H with the O2 discarded to the atmosphere; later in the process, H is combined with atmospheric CO2 to produce glucose"
    A few more details 
    • The left-hand side of the diagram was previously known as The Light Reactions but most publications this side of Y2K refer to it as Light-dependent Reactions
      • Light induces photolysis (splitting of water into hydrogen and oxygen) which liberates an electron along with a small amount of energy to power other chemical reactions (see: electron transport chain for details)
        • one liberated electron is used to bind phosphorous (+P) with ADP yielding ATP (the power transfer molecule of most biological systems including humans)
        • energy is used to bind atomic hydrogen (H) to NADP+ yielding NADPH (to transport hydrogen to the other side of the diagram)
        • some energy is used to bind atomic oxygen (O) into molecular oxygen (O2) which is released to the atmosphere
      • observation: You might wonder why Photosystem II is before Photosystem I. These labels relate to the order in which they were discovered and were not changed because this would conflict with previously published literature. 
    • The right-hand side of the diagram was previously known as The Dark Reactions but most publications this side of Y2K refer to it as Light-independent Reactions  
      • hydrogen (from NADPH) is combined with atmospheric CO2 to produce glucose
      • the whole thing is powered by converting ATP back into ADP (which frees a +P to be used in the next turn if the cycle)
    So we now know that sunlight (input 1) and H20 (input 2) are more important than CO2 (input 3) because the photolysis of water in Photosystem II (on the left-hand side of the diagram) powers the Calvin Cycle (on the right-hand side of this diagram). We already know that too much sunlight, or too much water, will kill a plant so pushing in additional carbon-dioxide makes little sense (but each ingredient is considered a limiting factor to maximum productivity). But because increasing atmospheric CO2 is driving up atmospheric temperatures, we can expect increased evaporation. This will result in less bio-available water to plants.
    Speculation: to avoid a CO2 run-away effect, humanity may need to engage in world-wide terraforming of Earth just to get the rising CO2 problem under control. Fat-cat business men will try to make a buck out of this crisis but this might be something that everyone on Earth will be pressed into to doing just to save humanity and human culture (which Earth's biosphere couldn't care less about)
Talking Point #3 - Fact: Atmospheric Oxygen is Falling
atmospheric oxygen in decline

I recently stumbled onto this article at John Cook's Skeptical Science site which states "Atmospheric O2 (oxygen) is decreasing by the same amount that CO2 (carbon dioxide) is increasing".

Googling this phrase: atmospheric oxygen depletion
yields documents like these:

Yikes! I think I made a fairly strong case at the top of this page for the area of farmland being the main limiting factor to the human population but it now looks like humanity is using more oxygen than is being replenished by photosynthesis.

The article also states "Atmospheric Oxygen is so abundant at about 20.9% (209,500 parts per million or ppm) that we are in no danger of running out". But I think we need to realize that our planet has "turned a corner" which means humanity cannot continue previous behavior.

While it is true that 7 billion humans are busy inhaling O2 and exhaling CO2, no one has mentioned the elephant in the room: automobiles. Like large animals engaged in respiration, automobiles (which experts number at slightly over 1 billion) are responsible for a large amount (perhaps 20%) of O2 being converted in CO2. Really large machines like locomotives, tankers, cruise ships, and jet air craft, consume way more O2 than a car, but there are far fewer of them compared to automobiles. So at the very least, the automobile population needs to be included when computing the maximum population of human and large animals at the top of this page. We all know that humanity has no intention of giving up personal transportation so I think I have just convinced myself of the need for electric cars powered by renewable energy from hydrological, wind and solar technologies.

NSR Comments:

Parable of the Bacteria in a Bottle

Developed by Al Bartlett, professor of physics at University of Colorado
The Set-up
You place a single bacterium in a nutrient-filled bottle at 11:00 am. It grows and divides into two bacteria at 11:01. These two bacteria each grow and divide into 4 bacteria at 11:02, which grow and divide into 8 bacteria at 11:03, and so on. (i.e., doubling time of 1 minute.)
Bottle is full, nutrients gone, all the bacteria die.
  1. When was the bottle half-full?
    Hover Mouse Here to View Answer:
  2. You are a mathematically-sophisticated bacterium, and at 11:56 you recognize the impending disaster. You immediately jump on your soapbox and warn that unless your fellow bacteria slow their growth dramatically, the end is just four minutes away. Will anyone believe you?
    Hover Mouse Here to View Answer:
  3. Just before disaster strikes… a bacterial space program discovers three more bottles in the lab. With a population redistribution program, how much time do the 3 new bottles buy the colony?
    Hover Mouse Here to View Answer:

NSR Comments:

French Lily Pond Riddle

This story is told to French school children to impart the power of exponential growth

  1. One lily pad in a pond
  2. The next day it doubles: two lily pads
  3. The next day it doubles: four lily pads
  4. The next day it doubles: eight lily pads
  5. After 29 days, the pond is half filled
  6. One day later, the pond is full

NSR Comment:

Video Lectures (to Learn More Details)

diagram of photosynthesis

Free 10-minute video lectures from Khan Academy

A refresher on photosynthesis

A refresher on cellular respiration

Internal Links

External Links

Assertion: One U.S. Gallon of Gasoline meets the energy requirements of one human for 21 days

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Neil Rieck
Waterloo, Ontario, Canada.