How Many People Can the Earth Support?: Going Further 9–12

Eight billion and counting

For almost all of human history there were few people. Around 1800, after hundreds of thousands of years, the world reached its first billion. Then things sped up. Better farming, clean water, vaccines and medicines meant that far fewer babies and children died, while families stayed large for a generation or two. So the population grew faster and faster.

Figure 45.1 World population from 1700, with the year each billion was reached, and the United Nations’ projection to 2100 (dashed; World Population Prospects 2024, the middle of its range of projections).

You can measure how fast a population grows by its growth rate: how much it grows in a year, as a percentage of its size. The world’s growth rate was highest in the 1960s, at over 2 % a year. It has fallen since, to under 1 % a year (as of 2026), because families almost everywhere have become smaller. A woman in the world today has on average about 2.2 children; in the 1960s it was about 5. In Nepal the change has been even faster: about 6 children per woman in the 1970s, about 2.1 in 2022, which is just enough for each generation to replace the one before.

So the world is still growing, but more slowly each year. The UN expects the world to reach about 10.3 billion in the mid-2080s and then to shrink a little. That is a projection, not a fact: it depends on what millions of families decide.

Worked example

Nepal’s growth rate

Nepal’s census counted 26,494,504 people in 2011 and 29,164,578 in 2021. What was the average growth rate, in % a year?

Answer

Over ten years the population was multiplied by
$\frac{29\,164\,578}{26\,494\,504} = 1.1008$
If it grew by the same factor g each year, then g¹⁰ = 1.1008, so
$g = 1.1008^{1/10} = 1.0096$
The population grew by about 0.96 % a year. (The official figure, 0.92 %, is a little lower because it allows for the exact dates of the two counts, which were a little more than ten years apart.) It was the slowest growth Nepal’s censuses have recorded since 1941. (The first counts, from 1911 to 1930, show the population barely changing, but they are thought to have missed many people.)

A population growing by a fixed percentage each year doubles in a fixed time. A quick rule, the rule of 70, gives that doubling time: divide 70 by the growth rate in % a year.

The world’s population is still growing, but its growth rate has fallen from over 2 % to under 1 % a year. What does this mean?

Pick an answer to see why.

Why there is no single number

In Grade 8 you met the Earth’s carrying capacity, how much it can bear Grade 8: Principles of sustainable development: for any species, the most a place can support, year after year, without using up its resources. In How Many Tigers Can Chitwan Hold? how ecologists estimate it for tigers: count the deer, and work out how many tigers they can feed. Why not do the same for people?

Because people are not tigers. A tiger needs about 50 deer-sized animals a year, and always will. People change what they eat, how they cook, how they farm and how much they own. A person in Nepal and a person in the USA use very different amounts of the Earth. And people invent: a new crop variety, a better stove or a solar panel can change in a few years what the same land can give.

A story from science

A question 350 years old

In 1679 the Dutch microscope maker Antoni van Leeuwenhoek, the first person to see bacteria, tried to work out how many people the Earth could hold. Holland, he reckoned, had about a million people, and the Earth’s habitable land was about 13,400 times larger. If all of it were as crowded as Holland, it would hold 13.4 billion people.

In 1995 the American mathematician Joel Cohen collected every estimate he could find since Leeuwenhoek’s, and wrote a book with the same title as this topic. The estimates ran from less than 1 billion to more than 1,000 billion. They didn’t settle on one number as the years went by. Cohen’s conclusion: the answer depends on choices, about what people eat, how they live, what they leave for other species and what they are willing to risk, as much as on science.

Scientists sum up what a population takes from the Earth in a simple equation, written by the ecologists Paul Ehrlich and John Holdren in the early 1970s:

$I = P \times A \times T$

where I is the impact (the land used, the wood burned, the carbon dioxide given out), P the number of people (population), A how much each person uses (affluence, or consumption per person), and T how much impact each unit of use causes (technology). A better stove lowers T: the same cooked meal, less wood. A smaller family lowers P. A simpler life lowers A. The impact is the product of the three, so halving any one of them halves it.

The ecological footprint

One way to measure I is the ecological footprint: the area of land and sea needed to grow everything a person uses (food, wood, fibers such as cotton) and to soak up the carbon dioxide they give out. It is measured in global hectares (gha), hectares of land with the world’s average productivity. Against it is set the biocapacity: the area that is really there, able to grow back each year.

	Footprint per person (gha)
Nepal	0.9
India	1.1
world average	2.5
China	3.8
USA	7.1

The Earth’s biocapacity is about 12.2 billion global hectares: about 1.5 gha for each person alive (as of the 2025 accounts by Global Footprint Network and York University). The world average footprint, 2.5 gha, is about 1.7 times that. Humanity uses as much each year as about 1.7 Earths could grow back. It can do that only by using up stocks that took a long time to build: cutting forests faster than they grow, catching fish faster than they breed, letting soil wash away, and, above all, putting carbon dioxide into the air faster than plants and the sea take it back (about 60 % of the world’s footprint is carbon). Using more than the Earth regrows is called overshoot.

Choose how many people there are and how they live, then see how many Earths that would take. The slider lets farming and technology make the same land and sea give more.

People:

Everyone lives like:

Land and sea made to give more: +0 %

Earths needed: 1.7
People: 8.3 billion
Footprint per person: 2.51 gha
People the Earth could support, living so: 4.9 billion

More than one Earth: we would be using up stocks (forests, fish, soil) and piling up carbon dioxide faster than nature can take it back.

In I = P × A × T, a village replaces its open fires with improved stoves that cook the same food with a third less wood. Which factor has changed?

Pick an answer to see why.

A model you can build: a village and its forest

To see how the pieces fit together, scientists build a model: a set of rules, written as numbers, that stands in for the real thing. A model that a computer runs step by step, year by year, is a computational simulation. It can’t tell the future exactly, but it can show what follows from what: if people do this, then that happens.

Here is one small enough to build yourself, about something Nepal knows well: a hill village and its community forest. In many hill villages most families still cook on wood. Surveys in Nepal’s hills find that each person burns several hundred kilograms of firewood a year; our model takes 600 kg on an open fire, about 3 tonnes for a family of five. The forest gives that wood, and also shelter for birds, deer, leopards and orchids.

A woman walking along a dry, rocky mountain path, bent forward under a large basket piled high with split logs, held by a strap across her forehead — **Figure 45.2** Carrying firewood home in a doko in the mountains of Nepal. A family cooking on an open fire can burn about three tonnes of wood a year. Photo: Sergey Pashko, CC BY 3.0

The model has two stocks, things that build up or run down, and flows that change them each year:

Figure 45.3 The village-and-forest model. Boxes are stocks; thick arrows are flows that fill or empty them; dashed arrows show what decides each flow.

The forest. Its stock is the wood standing in it, in tonnes. Our forest is 100 hectares, and full-grown it would hold about 150 tonnes of wood on each hectare, 15,000 tonnes in all. Every year the trees put on new wood, its regrowth. A forest grows back like the tigers in How Many Tigers Can Chitwan Hold? (the logistic model): a nearly bare forest has few trees to grow, and a full forest has no room for more, so it grows fastest when it is about half full:

$\text{regrowth} = r \times W \times \left(1 - \frac{W}{W_{\text{full}}}\right)$

where $W$ is the wood in the forest now, $W_{\text{full}}$ the most it can hold, and r its growth rate when it has plenty of room; we take r = 0.08, 8 % a year.

The village. It starts with 600 people. The wood it needs each year is people × wood per person. Each year the number of people grows by a set percentage.

The link. Each year the village cuts the wood it needs, if the forest has it. The forest’s new stock is
$W_{\text{next}} = W + \text{regrowth} - \text{wood cut}$
If the wood cut is less than the regrowth, the forest grows; if more, it shrinks. The most that can be cut, year after year, without shrinking the forest, is its sustainable yield: here at most 300 tonnes a year, when the forest is half full.

Worked example

One year of the model

In 2026 the forest holds 7,500 tonnes of wood (half of its 15,000-tonne maximum) and the village has 600 people, each burning 600 kg of wood a year. Find a. the regrowth, b. the wood needed, c. the wood in the forest in 2027.

Answer

a.
$\text{regrowth} = 0.08 \times 7500\ \text{t} \times \left(1 - \frac{7500}{15\,000}\right) = 0.08 \times 7500 \times 0.5 = 300\ \text{t}$

b.Wood needed = 600 × 600 kg = 360,000 kg = 360 t.
c. $W_{\text{next}} = 7500 + 300 - 360 = 7440\ \text{t}$

The forest has lost 60 tonnes. That seems small. But next year there are more people, and a thinner forest grows back less, so the gap widens every year.

Doing this by hand for 75 years would take all day. A computer does it in a blink. Play with the model below: it is the same model, run from 2026 to 2100.

Choose how the village cooks, how fast it grows, and how much of the forest it protects (never cuts). The graph shows the forest and its species over the years; red marks the years the village can’t get all the wood it needs.

Cooking:

People grow: 1 % a year Forest protected: 0 %

Wood per person: 600 kg a year
People in 2100: 1,253
In 2100: wood needed / most it can regrow: 752 t / 300 t
Years short of wood: 38 of 75

The village cuts more than grows back. The forest thins, species are lost, and in the end there isn’t enough wood. Change a setting to make it last.

A model with round numbers, not a forecast: a 100-hectare forest, 600 people in 2026, the forest half full; nothing comes from outside.

Things to find out:

a.With open fires and 1 % growth a year, when does the village start to run short? What changes the outcome most: a better stove, slower growth, or both?
b.With the better stove, find the fastest growth at which the village still has enough wood every year to 2100. Is that growth sustainable after 2100?
c.Protect 30 % of the forest with open fires. What happens to the species, and to the people?

Activity

Build the model in a spreadsheet

You need: a computer or phone with a spreadsheet (Google Sheets, LibreOffice Calc or Excel).

Put the settings in column J: J1 the growth rate as a decimal (0.01), J2 wood per person in kg (600), J3 the most wood the forest can hold (15000), J4 the forest’s growth rate r (0.08).
In row 1 write the headings: A Year, B People, C Wood needed (t), D Forest (t), E Regrowth (t), F Wood cut (t), G Species kept (%).
Row 2 is 2026: A2 2026, B2 600, D2 7500.
In row 2 type these formulas (the $ signs keep a setting’s cell fixed when you copy a formula down):

Cell	Formula	What it works out
C2	`=B2*$J$2/1000`	wood needed, in tonnes
E2	`=$J$4D2(1-D2/$J$3)`	the forest’s regrowth
F2	`=MIN(C2, MAX(0, D2+E2-0.05*$J$3))`	wood cut: what the village needs, unless the forest is down to its last 5 %
G2	`=100*(D2/$J$3)^0.25`	species kept (explained in the next section)

Row 3 is the next year: A3 =A2+1, B3 =B2*(1+$J$1), D3 =D2+E2-F2. Copy C2, E2, F2 and G2 down into row 3.
Select row 3 and fill it down to row 76 (the year 2100). Make a line graph of columns D and G against A.
Change the settings in J1 and J2 and watch the whole future change at once. Add a column H, =C2-F2, for the wood the village couldn’t get.

What you should see

With the settings above, the forest shrinks slowly at first, then faster, and from the 2060s the village can’t get all its wood: the same as the widget. With J2 at 400 and J1 at 0, the forest grows back, to about 70 % of full by 2100, and settles where its regrowth matches the 240 tonnes cut each year. Your spreadsheet is a computational simulation, the same kind of model, much bigger, that scientists use for fisheries, forests and the climate.

In the model, why does a forest that is cut a little faster than it regrows lose wood faster and faster?

Pick an answer to see why.

People, resources and wildlife

The forest is not only wood. It is home to the birds, insects, orchids, deer and leopards of the hills. In Grade 8 you met the causes of biodiversity loss and the ways of conserving it Grade 8: Conservation of biodiversity. Here we put numbers on it: what happens to the species as the forest shrinks?

Ecologists have measured this on islands and in forests all over the world. A bigger area holds more species, but not in proportion: it follows the species–area relationship. A good rule is that the number of species is in proportion to the area raised to the power of about 0.25 (somewhere between 0.15 and 0.35, depending on the place and the group of living things):

$\frac{S_{\text{kept}}}{S_{\text{before}}} = \left(\frac{A_{\text{kept}}}{A_{\text{before}}}\right)^{0.25}$

Figure 45.4 The species–area rule, with power 0.25: the share of species a habitat keeps, against the share of the habitat left. The first losses of habitat cost few species; the last ones cost many.

Our village model uses the same rule, treating a thinned forest roughly like a smaller one (in a real forest, it depends on which trees are left). It shows two ways people and wildlife are linked. When the village overuses the forest, people and species lose together. But when the village protects part of the forest and still needs as much wood, the species are kept and the people go short. Protecting nature works best, for both, when it goes with ways for people to need less from it.

Figure 45.5 All the mammals and all the birds on Earth, by weight (estimates by Yinon Bar-On, Rob Phillips and Ron Milo, 2018).

The world’s wildlife has been squeezed the same way. Monitored populations of wild mammals, birds, fish, reptiles and amphibians have fallen by 73 % on average since 1970 (WWF’s Living Planet Index, 2024), mostly because their habitat has been turned into farms, and about a million species are at risk of extinction (IPBES, 2019).

Two plans for the village, which grows by 1 % a year: Plan 1 protects 30 % of its forest but keeps the open fires. Plan 2 gives every family a better stove but protects nothing. What does the model show by 2100?

Pick an answer to see why.

Try it in the widget. Protection keeps a core of forest, and with it about three-quarters of the species, but the village’s need doesn’t change, so the rest of the forest is cut bare sooner and people run short. The stove cuts the need by a third, which slows the loss of the whole forest, but the growing village still cuts more than grows back, and by 2100 only about 18 % of the forest is left. Each plan helps one side and not the other. Stoves, 20 % protected and a village that stops growing do both: enough wood every year, and by 2100 the forest has grown back to 60 % of full, keeping about 88 % of its species. Moving several levers together is what “managing” a resource means.

What changes the outcome

Every factor in the model is something people can change. These are the levers that decide how many people the Earth, or a village, can support, and how well:

How many people. Families become smaller when children survive, girls go to school, and women can choose. Nepal’s fall from about 6 children per woman to about 2.1 happened in two generations.
How much each person uses. A family that cooks with biogas, eats more grains and pulses and less meat, or keeps a phone for years, uses less land and energy. Meat is the big one: most of the world’s farmland is used to feed animals, which give back only a small share of the food energy they eat (see Where Does a Fallen Leaf Go?).
Efficiency and new technology. World cereal harvests per hectare have roughly tripled since 1961, thanks to new crop varieties, fertilizers and irrigation; without that, feeding today’s people would need far more forest cleared for fields. A better stove, a biogas plant, and electricity from rivers and the Sun do the same for energy.
The cost of getting resources. As a nearby resource runs low, getting it costs more: a longer walk for firewood, a deeper well, a farther mine. That cost is a signal, but often it comes late.
Conservation. Protected areas, now about a quarter of Nepal’s land, and community forests keep habitat for wildlife. Rules about when and how much to cut keep the harvest within the sustainable yield.
Planning towns and dealing with waste. A compact town with good buses uses less land and fuel per person than one that sprawls over farmland; waste that is sorted, composted or turned into biogas costs less land and pollutes less.

A smiling woman in a purple shawl bending to open a small red tap on a pipe coming out of the ground in a yard, beside a wooden animal pen — **Figure 45.6** Turning on the gas from a biogas plant in Nepal. Dung and toilet waste rot in a sealed tank underground, giving gas to cook with in place of firewood, and a liquid that fertilizes the fields. Photo: SuSanA Secretariat, CC BY 2.0

A story from science

The forests that came back

In the 1970s, experts warned that Nepal’s hill forests would be gone within a generation, cut for firewood and fodder by a growing population. It didn’t happen. From the late 1970s, and especially after the Forest Act of 1993, the government handed forests to the villages around them. Local community forest user groups, now more than 22,000 of them, made their own rules: when to cut, how much, who could graze animals, and who would guard the forest. Bare hillsides grew back, and many were planted with trees.

Researchers who compared forests across Nepal found that community forestry slowed the loss of forest and, in the same places, people’s poverty fell (a study in Nature Sustainability, 2019). Other things helped: many young people went to work in towns and abroad, and families bought gas cylinders for cooking. Every lever in the model moved at once: who manages the forest, how much wood each family needs, and how many people live in the village.

Tall, thin pine trees on a grassy hillside under a gray sky, with young broadleaf trees growing among them — **Figure 45.7** Badikhel community forest in Lalitpur: tall pines, with young broadleaf trees growing up among them. Pines were planted on many bare hillsides around the Kathmandu Valley in the 1970s and 1980s, as community forestry began. Photo: Shadow Ayush, CC BY-SA 4.0

A story from science

The bet

In 1980 the ecologist Paul Ehrlich, who had warned in his book The Population Bomb (1968) that hundreds of millions would starve, made a bet with the economist Julian Simon. Simon said people always find ways round shortages, so resources get cheaper, not dearer. Ehrlich chose five metals (chromium, copper, nickel, tin and tungsten) and bet that their prices, allowing for inflation, would be higher in 1990, as the world’s growing population used them up. By 1990 all five were cheaper: miners had found new deposits, and makers had switched to other materials. Ehrlich sent Simon a cheque for $576.07.

Who was right? Both, in part. Later studies found that in many other ten-year periods the bet would have gone Ehrlich’s way. And the big famines Ehrlich expected were prevented by new crops, while the losses he warned about came in other forms: forests, fish and wildlife, which no market sells back.

Think about it

How many people should the Earth support?

Some people say the Earth could feed 10 billion, if everyone ate less meat and farms were run well. Others say it already supports too many, because it is in overshoot and wildlife is disappearing. Can both be right? What would you need to decide before you could give one number?

Answer

Both can be right, because they answer different questions. “Can the Earth feed 10 billion?” is about food and technology. “Is today’s way of life sustainable?” is about footprints and overshoot. To give one number you would have to decide: how well should people live (food, energy, homes)? How much land should be left for other species? How much risk of a bad harvest is acceptable? What technology can we count on? Different answers to those give different numbers, which is why Joel Cohen found estimates from under 1 billion to over 1,000 billion. Science can tell you what follows from each choice; it can’t make the choices for you.

In short

The world passed 8 billion people in 2022. Its growth rate has fallen from over 2 % to under 1 % a year, and the UN expects a peak of about 10.3 billion in the 2080s. Doubling time ≈ 70 ÷ growth rate in % a year.
There is no single carrying capacity for people: it depends on how much each person uses and on technology, as well as on numbers. I = P × A × T.
The ecological footprint compares what people use with the biocapacity that grows back. Humanity uses about 1.7 Earths: overshoot, by running down stocks and piling up carbon dioxide.
A computational simulation (even a spreadsheet) runs stocks and flows year by year: forest + regrowth − wood cut. Use above the sustainable yield shrinks a resource faster and faster.
Species fall with habitat by the species–area rule, about (area kept)^0.25: losing 90 % of a habitat costs about half its species.
The outcome depends on all the levers together: population, use per person, efficiency, conservation and planning.

Questions

A population grows by 1.4 % a year. About how long does it take to double?

Pick an answer to see why.

A country’s population stays the same, but each person’s footprint doubles, and new technology halves the impact of each unit of use. By I = P × A × T, its impact

Pick an answer to see why.

a.

Why can ecologists estimate a carrying capacity for tigers in Chitwan, but not give a single carrying capacity of the Earth for people?

Answer

A tiger’s needs are fixed: it needs about the same amount of prey each year, and the prey a park can support depends on its area and plants. People’s needs are not fixed: how much each person uses (food, wood, energy, goods) varies more than seven times between countries, and technology changes what the same land can give (crop yields have tripled since 1961). People can also trade, bringing in resources from elsewhere. So the number of people the Earth can support depends on how they choose to live, what technology they have, and how much they leave for other species: different choices give very different numbers.

b.

In 2026 a community forest holds 6,000 tonnes of wood; full-grown it would hold 12,000 tonnes, and its growth rate r is 0.08 a year. The village has 400 people, each burning 600 kg of wood a year.

a.Calculate the forest’s regrowth this year.
b.Calculate the wood the village needs.
c.Is the village’s use sustainable? Explain with numbers.
d.Suggest two changes that would make it sustainable, and show that one of them works.

Answer

a.Regrowth = 0.08 × 6000 × (1 − 6000 ÷ 12,000) = 0.08 × 6000 × 0.5 = 240 t.
b.Wood needed = 400 × 0.6 t = 240 t.
c.Just about: the village cuts exactly what grows back, and the forest is half full, where regrowth is the largest it can be (240 t is the sustainable yield). So the forest stays the same, but there is no margin: if the village grows, or a dry year slows the trees, the forest starts to shrink, and then grows back less each year.
d.Any two of: improved stoves (about a third less wood: 400 × 0.4 t = 160 t, well under 240 t, so the forest would grow); biogas or LPG for some cooking; planting more trees on spare land; slower population growth. With stoves, the forest gains 80 t in the first year.

c.

Use the species–area rule (power 0.25) to estimate the share of a forest’s species that survive if 75 % of the forest is cleared. Why do conservationists say the last patches of habitat matter most?

Answer

25 % of the forest is left: 0.25^0.25 = 0.71, so about 71 % of the species survive (in the long run). The curve is steep near zero: the first half of a habitat lost costs about 16 % of the species, but the last 10 % holds more than half of them (0.1^0.25 = 0.56). So each hectare of the last patches protects far more species than a hectare of a large, intact habitat.

d.

Explain what “humanity uses 1.7 Earths” means, and how it is possible to use more than one Earth.

Answer

The ecological footprint of all the world’s people, the land and sea needed to grow what they use and to soak up their carbon dioxide, is about 1.7 times the Earth’s biocapacity, the area that can grow these things back each year. It is possible for a time by using up stocks: cutting forests faster than they regrow, catching fish faster than they breed, losing soil, and letting carbon dioxide pile up in the air and the sea instead of being taken back. Like spending a bank account’s savings as well as its interest, it can go on for a while, but the stocks shrink, and so does what they can give in future.

e.

A student runs the village model. With 1 % growth a year and open fires, the village runs short of wood from 2063. She finds three settings with which it never runs short before 2100: open fires with the village shrinking by 1 % a year (in 2100 it needs 171 t a year); better stoves with no growth (240 t); stoves and biogas with 2 % growth (520 t). The forest can regrow at most 300 t a year. What can she conclude about the relationship between population, consumption per person and the sustainability of the village’s resources? Are all three settings sustainable? What are two limitations of her model?

Answer

She can conclude that sustainability depends on the product of the number of people and the wood each one uses, compared with the forest’s sustainable yield: halving the wood per person allows about twice as many people, and faster growth needs a bigger cut in use per person to keep within the forest’s means. No single factor decides the outcome; several combinations work.
Not all three are sustainable, though. The first two need less than the 300 t the forest can regrow, so they could go on for ever. The third needs 520 t in 2100, far more than the forest can regrow: it reaches 2100 only by using up the forest’s stock, and it would run short soon after. Getting through a set number of years is not the same as being sustainable.
Limitations (any two): the numbers are rounded and assumed (a real forest’s growth rate, size and starting stock must be measured); people in the model can’t move away, buy gas or bring wood from elsewhere; the forest is treated as one block (in reality some parts are nearer and are overcut first); the species rule treats a thinned forest like a smaller one; nothing is random (no dry years, fires or landslides).

f.

Design a plan for a hill village whose forest is shrinking, using what you learned. Say which levers your plan moves, how you would know whether it is working, and what trade-offs it involves.

Answer

A good plan uses several levers together, for example: improved stoves for every family and help with biogas plants (lowers wood per person); a community forest user group with rules on when and how much to cut, and a protected core where no one cuts (keeps cutting under the sustainable yield and keeps habitat for species); planting fodder and firewood trees on terrace edges and bare land (raises the forest’s stock and regrowth); support for girls’ schooling and health posts (in the long run, smaller families).
To know whether it is working: measure the forest each year (sample plots: count and measure trees), record how much wood is cut, count birds or other species along a fixed path, and run the numbers in a spreadsheet model to see whether cutting is under regrowth.
Trade-offs: stoves and biogas plants cost money; a protected core means families lose some wood and grazing at first; rules must be fair, or poorer families who depend most on the forest are hurt; it takes years before the forest recovers.

Where to go next

How Many Tigers Can Chitwan Hold? The carrying capacity of a park for its tigers, and the logistic model that the forest in this topic uses.
Which Energy Should Nepal Use? Hydropower, solar or imported petrol, river sand or quarries: weighing the costs and benefits of each, for the land, the rivers and the air.
Why Do People Live Where They Do? How water, soil, hazards and climate shaped where Nepal’s people settle, from the Kathmandu Valley’s old lake bed to the Terai.