How many people can you feed per square-kilometer of farmland?

Question

Questions about how to feed a large population keep popping up on this website quite frequently. One obvious option is farming. But how many people can you feed per square-kilometer of farmland?

Interesting would be a comparison depending on the farming method used:

• prehistoric methods
• medieval methods (irrigation and simple tools)
• modern methods (powered machines, industrial fertilizer and pesticides, applying findings from biology and agriculture as a science)
• high-tech methods (hydroponics, genetically-modified crops and other high-tech methods which are currently working under lab conditions but not yet widely used for food production).

I believe it would also be useful to compare farming efficiency depending on climate, because I think that this will have a great effect, especially on low-tech methods.

I tried to find sources for this using search engines, but was unable to find a reliable one.

Answer 1

Conventional Farming

According to this source, the highest caloric density food is sweet potatoes, which provide 70,000 kcal/ha/day. (with potatoes providing 54,000 which is roughly in line with what ArtOfCode calculated.) This involves fairly intensive farming, so we'll need to let the land lie fallow for about a third of the time, reducing our long-term average to around 47,000 kcal/ha/day for our most dense food crop (in terms of kcal.ha/day). This is achievable with fairly primitive technology. This corresponds to 4,700,000 kcal/km²/day, which can feed 2350 people on a 2000 kcal/day diet of pure sweet potatoes.

Hydroponics

Now let's see how we can increase that yield. The first thing we can do is to employ hydroponics. According to this source, hydroponics will increase our raw yield by around 280%. In addition, we won't have to let our fields lie fallow, since we no longer have any soil that we're growing plants in. This increases our base of 70,000 kcal/ha/day to 266,000 kcal/ha/day, which will feed 13,300 people per square kilometer.

Aeroponics

Currently, individuals are researching an even better way of growing crops: aeroponics. In an aeroponic farm, nutrient rich water is vaporized to form a mist that is then sprayed onto the roots of crops. This source found that, with the correct nutrient solutions, they were able to increase yield over conventional hydroponics by between 50% and 270%. Assuming that, with further refinement, the upper end of this can be realized, we should be able to increase our sweet potatoes to 98,420,000 kcal/km²/day, which can feed a total of 49,210 people on a 2000 kcal/day diet of sweet potatoes.

What else could we do to increase this?

So far, all of this has been constrained by sunlight: we can only grow one layer of crops if our crops get energy from the sun. Of course, if we can fire up a fusion generator to illuminate our crops with artificial, light, we can stack layers of crops on top of each other. In this case, a better measure might be kcal/km³/day. A sweet potato is about a meter tall, so we can grow 1000 layers of them in a 1km³ densely packed fusion powered green house. Our cube, using aeroponics, would produce 98,420,000,000 kcal/km³/day and could feed a population of 49,210,000 people. Genetic engineering might be able to increase this even further, but this is about the right order of magnitude.

Answer 2

The question is way too broad, since there are many crops, land types and soil fertility levels, climate zones, technological levels, amounts of labor and capital that is available. These will dramatically affect what you get from given area. Moreover, there are many ways of transforming those crop calories into foodstuffs. For instance, do you eat the cereal or do you feed it to livestock, and then eat the livestock? Or perhaps you choose to distill your cereal and make bourbon... This could easily be a whole essay.

For now, I'll restrict myself to modern era practices, since they range from essentially medieval tech to the most modern methods, so a cross-section through space is, in a sense, also one through time in this case.

Crop yield varies a lot by crop, and is defined in two ways. The first is a ratio of seed to harvest, for instance 20:1 would mean that for every grain planted, you get 20 grains of harvest.

The second definition measures output per area, and there are a myriad definitions, but the most common in modern times is yield in kg per hectare. As there are 100 sq. hectometers in a sq. km, one needs to simply multiply the answers by 100 to get your final answer. There are a multitude of sources on this for the modern world. Perhaps the easiest is the World Bank. I've linked the cereal yield. Obviously you can have mushroom yield, fruit output per hectare of orchard, etc.

As you look through the table linked above, you'll see an astonishing amount of variation, which has partially to do with climate variation, but mostly with the degree of mechanization and the size of farms (smaller farms tend to be less efficient and less mechanized). Low development countries in the present day have low yields, sometimes significantly under a ton per hectare (barely above replacing the seed grain!), while countries like France, US and Belgium have yields in the 6-10 ton/ha range.

And this is just grain. Potatoes, on the other hand, not only grow in hilly and rocky areas where you can't grow grain, but under careful cultivation and with pest-control, can currently deliver something like 80 tons/ha, whereas the first varieties that were introduced in Europe (this is after a few thousand years of Andean selection) only gave 13tons/ha.

Finally, hydroponics can increase yields for a large variety of plants anywhere from 6 to 30-fold. Howard Resh has a book called Hydroponic Food Production.

Identical cucumber plants produced 7,000 pounds per acre in soil but 28,000 pounds per acre when grown hydroponically and tomato yields that ranged from 5 to 10 tons per acre in soil but 60 to 300 tons per hydroponic acre. The reported results are typical for practically any plant. Said another way, to produce the total number of tomatoes consumed annually in Canada (400 million pounds) requires 25,000 acres of soil. Hydroponically, it would require only 1,300 acres.

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Now one kg of wheat is about 3400 Calories. A human needs about a million Calories per year (2700 Cal/day for 365 days), so that would be 294kg, (ignoring varied dietary needs for a sec). So one modern, say Belgian cultivated (yield 9t/ha) hectare of wheat would feed 30 people. So one sq. km would meet the calorie needs of about 3000 people. Obviously you will want meat, and other fruits and vegetables, so you could cut that to about a third (wheat --> meat has relatively low efficiency), so you could easily feed 1000-1500 people from a sq. km. of fertile modern-tech cultivated land. With hydroponics or other green-house style tech, and providing your own light, you could go a lot higher. If you covered the Earth in arcologies and dedicated a significant fraction to climate and light-controlled greenhouses, you could support trillions of people on Earth.

Answer 3

You might well be interested in my answer to this question, as it details minimum requirements. In it, I do some calculation to find out that to feed one average human for a year, you need 5110 potatoes and 460 square metres of space.

That takes care of one year, but if you plant potatoes again the next year you need to plant them somewhere different next year. That means you need 920 square metres per person per two years. You can cycle between two different locations with potatoes so that's all you'll need. So:

There are $ 1000^2 = 1,000,000 $ square metres in one square kilometre.

There are $ \frac{1,000,000}{920} = 1086.9565 $ 920-square-metre plots in a square kilometre, so you'd just about squeeze 1087.

So, you can feed a maximum of 1087 people per square kilometre (ppsk) if they all live on nothing but potatoes. You would of course also need living space for all of them.

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That gives a bit of an estimate to what you can do. Let's compare that with population and see what the ratio of living space to farmland is.

A decent size, single person house is around 50 square metres floor space. If you have 1087 people and a square kilometre of farmland, that means you're going to need:

$$ 1087 \times 50 = 54350 $$

square metres of living space. That's 0.054 square kilometres. Therefore the ratio is:

$$ \text{farmland} : \text{ living land} $$ $$ 1 : 0.054 $$ $$ 18.8 : 1 $$

That's quite a large space requirement. If you have a 5km radius city, it needs a 21km wide farming zone around it to fully support all its inhabitants. This is possible, but inefficient - this is why much of our food is imported from other countries with lower population and more farming space.

Answer 4

With current farming technology as actually practiced in the United States about 10 acres of land (40,000 square meters) is used to produce food for each average person.

This itself represents are remarkable improvement in agricultural productivity in the last half century or so.

Between 1950 and 2000, during the so-called "second agricultural revolution of modern times", U.S. agricultural productivity rose fast, especially due to the development of new technologies. For example, the average amount of milk produced per cow increased from 5,314 pounds to 18,201 pounds per year (+242%), the average yield of corn rose from 39 bushels to 153 bushels per acre (+292%), and each farmer in 2000 produced on average 12 times as much farm output per hour worked as a farmer did in 1950.

Globally, we use about a third as much land to product the same amount of food as we did fifty years ago, and agricultural productivity per land area has increased steadily year in and year out.

The highest cereal yields per acre in the world in Kuwait and some Caribbean islands (in both cases, where arable land is at a premium) are about three times as great as in the U.S.

Still, farming in the U.S. is organized to optimize dollars of food output per dollar of food production cost, not to optimize caloric output per square meter of land (as you might want to in a space colony or starship or biosphere), because the U.S. has vast amounts of arable land available to it.

The easiest way to maximize calories per square meter per year relative to the status quo would be to replace lots of meat with lots of plants in the average person's diet.

Soybeans for example use about 5% as much land to generate the same number of protein calories as cows.

Soybeans produce at least two times more usable protein per unit area than any other major vegetable or grain crop, except for hemp which can produce up to 33 g/m2 (290 lb/acre). They produce 5 to 10 times more protein per unit area than land set aside for grazing animals to make milk, and up to 15 times more protein per unit area than land set aside for meat production.

And, how much meat does the average American eat?

In 2012, the average American consumed 71.2 pounds of red meat (beef, veal, pork, and lamb) and 54.1 pounds of poultry (chicken and turkey), according to the U.S. Department of Agriculture. The average amount is likely a bit higher. The USDA doesn’t take into account vegetarians, who consistently represent about 5% of the population, according to Gallup polls.

And meat and dairy and fats, all of which usually have animal sources, make up almost exactly half of the average American's diet.

Now not all plants are as efficient sources of protein in particular, or calories in general as soybeans, and eating soybeans all the time gets old (and doesn't supply all of the ammino acids needed to live by itself). But, it is fair to say that you could reduce the land footprint of the food an average person eats by about 45% (90% of the half from animals) by switching to an almost purely vegan diet.

This is still a lot of farmland per person, about 5.5 acres per person (about 22,000 square meters). And, exactly how much improvement you could get with higher technology approaches like hydroponics, twenty-four hour grow lights and so on, isn't exactly clear.

Assuming that an enclosed environment could at least match the peak productivity of cereal crops per land area relative to the U.S., it might be possible to reduce the amount of farmland per person required to a bit less than 2 acres per person (about 8,000 square meters, which is 125 people per square kilometer if one is answering the title question).

Allegedly, hydroponic farming could significantly improve on even this 80% reduction from the status quo in food produced per acre, as the posts above note. But, estimates of 500-1000 square meters per person do seem unrealistic given current technology.

Answer 5

TL;DR answer: 111 people per square kilometer

Explanation:

A simple way of looking at this question is to divide the total amount of agricultural land worldwide by world population. This equation ignores waste and people who are starving, assumes humans don't eat fish from the oceans, and assumes farming methods worldwide are equally efficient (they aren't). Regardless, this answer is far closer to reality than the other answers provided.

36,480,000,000 acres - Total land mass of Earth
13,497,600,000 acres - Land used for agriculture (37% in year 2,000)
6,082,966,429 - World population (year 2,000)

So if we divide 13,497,600,000 acres by 6,082,966,429 humans, we can say that each human on the planet requires 2.218 acres of land in order to eat. Since a square kilometer is roughly 247 acres, that much land can feed 111 people.

Answer 6

My ex is a gardener and I read an article that stated that you could feed a person (vegan only, no meat) on only 800 m² in a temperate climate (Sweden in this case) using no hi-tech methods just planting things close and having several harvests per season. The crops used are potatoes, broad beans, carrots, parsnips, cabbage, onions and apples.

Keep in mind that a hobbyist can plant things much denser than in industrial farming since the latter is focused on one crop and needs more space for the machines to work.

Answer 7

No matter how you tack the problem, you will be bound by physical limits. So I will restrain my answer to the physical aspects of the problem :

Solar irradiance

No matter how effective the agriculture methods, you cannot yeld more energy per square meter than the ammount that reaches the soil. For one, according to this map, the solar irradiation is approximately 1900 kWh/M² on NE Brasil. Provided that the region is fertile, and it is, and has access to water, wich it does (this is one of the regions of Brazil where Sugar Cane is produced to later be transformed into alchool and become vehicle fuel) your limit on productivity will be roughly proportional to the efficiency of the plants at photosynthesis.

Photosynthesis efficiency

Modern sugarcane is one of the the most efficient plants at converting solar rays to sugar. It can reach efficiencies of 8%. This means that one square meter of sugar cane will, at the indicated area on the surface of the earth, produce

E = 5 kWh/Day * 0.08 = 400 Wh/day of sugar, or 1440 kJ of energy.

Glucose is the main sugar produced by sugarcane, wich holds 3000 kJ of energy per mol, circa 700 kcal/mol. This means that, each day, each square meter of crop area will produce

M = 1440 kJ / 3000kJ/mol = 0.48 mol of Glucose

Wich when converted to grams means

W = 0.48 mol * 180 g/mol = 86 g of sugar per day.

Aknowledging that your daily intake of food per day is not solely composed by sugar, all other plant material is the product of a subsequent transformation of this sugar into other materials, or, the energy provided by this sugar is used to cause chemical reactions that will produce those other substances. If the substance is not produced by the plant itself, it will be produced using this energy (protein, fat etc are produced at the expense of sugar by the plant itself or by animals that eat that plant and are subsequently eaten by humans). In other words, no food will ever hold, or spend being produced, more energy than this total ammount of sugar that the sugarcane produces per square meter.

The normal male adult should eat 10500 kJ of energy per day,

A = 10500 kJ/day / 1440 kJ/day/M² = 7,29M²

wich means that 7.29 square meters of land should be cultivated in order to produce enough energy to sustain it, this, using the most efficient plant available, and expresed as pure calories (fat or sugar, but no vitamin or other regulatory food). This means that by a purely physical standpoint, using the most efficient plant available, by the most efficient method available, you need at least ~7 square meters of land to produce enough for a single adult male. Real world figures will be higher due to various inefficiencies.

Food production and distribution is a complex activity and more than sugar is needed to sustain an human being, meaning that less efficient plants are needed in order to produce all nutrients needed. Meat is produced by feeding livestock with plant produced by the same process as sugarcane (photosynthesis), but each change of trophic level imples a certain loss of energy, so the meat produced by a certain ammount of land will be less than of those directly consumed as sugarcane. And so on.

tl;dr

With current types of crop, you will need at least ~7 square meters of land per adult male, no matter wich cultivation process, type of plant, meat or veggie, etc. This is a physical limit implied by photosynthesis limits. The only way around is increasing photosynthetical efficiency of plants by genetic manipulation.

Answer 8

Vertical hydroponic farms (doable with current technology):

If you build a 100 floor hydroponic farm skyscrapper next to some massive water source on 1 square kilometer of land, you can basically feed an entire city. That would be an economic disaster and be unprofitable but it's technically doable.

Vertical farming is not science fiction and is already being experimented now in some cities like Singapore.

It s not really economically profitable since conventional farming is still super cheap but for some countries with limitied land like Singapore, having vertical structure using some advanced hydroponics (no soil needed) allows them to stack farmland vertically. Singapore is doing it to not depend too much on food import (policital reasons).

Assuming energy and building cost become cheap enough or that arable land becomes rare enough, that would become economically viable.

Answer 9

I personally think it depends on the plant. Certain foods, such as corn, grow only one or two ears per stalk, whereas a tomato plant may grow 15 or more tomatoes throughout the season. Either way, you would need to rotate your crops every few years in order to be able to grow anything, so you'd have to be careful on what you did grow. I think what you'd really want to pay attention to is A) How much food does the plant produce and B) How healthy is the plant for the soil and C) What sort of vitamins will people gain from them.

In my personal experience, grapes, tomatoes, green beans, carrots, and other foods that have take up minimal space will allow for more food overall, so I would say at least 10-25 acres, at minimum, more if you have the space. I don't know how helpful this really was, but I do hope it gave you some insight.

Answer 10

I draw fictional maps, and I did do these calculation. According to my calculation and assumptions, 1m2 of wheat field will produce 1x 700g (approx 1lb 8oz) loaf of bread. This assumes medium fertility of about 5 tons of grain per hectare. Herbivores eat 2% of their body weight per day, and a cow would require about 2/3 of a hectare per year (allowing the grass to grow back). My research shows that a meat animal is about 50% efficient: only half of the animal's weight can be converted to edible meat.

Answer 11

Under natural circumstances and farming organically without fertilizers and artificial chemicals or using GM technology, you cannot produce more than 500kg of grain (using wheat as an example) and that is just about enough to feed a person per year.

Considering the vegetables, spices, and other condiments that must be cooked to be eaten with the bread, chapatis, or whatever else people make with flour to be eaten with the vegetables, we need an additional of about 3 hectares of land. That means 4 hectares per person per year under natural farming conditions. As there are 100 hectares in 1km^2, this amount of land can feed only about 25 people very well with a bit left over for comfort.