It is lunchtime at school, and Pema is looking at the hill of bhat on her plate. “I wonder how much rice the whole of Nepal is eating today,” she says.
Her friend Sujan shakes his head. “Nobody can know that. Nobody stands at every kitchen with a scale.”
He is right that nobody counts it. But Pema doesn’t need a count. She needs three numbers she can guess from her own kitchen, and one multiplication. In this topic you will find that a careful guess, built from small guesses, usually lands within a factor of two of the truth: between half and double. That is close enough to plan a country’s food.
Guess first, without working anything out.
About how much uncooked rice does everyone in Nepal eat together in one day?
Pick an answer to see why.
Now build an estimate of your own. You only need three guesses: how many people live in Nepal, how many meals of rice each person eats in a day, and how much uncooked rice goes into one meal.
Breaking the question into pieces
“How much rice does Nepal eat?” is a question nobody can answer in one go. But it is made of three questions anyone can answer roughly:
| Question | A rough guess | What it’s based on |
|---|---|---|
| How many people? | 3 crore | The 2021 census counted 2,91,64,578 people. |
| Rice meals a day? | 2 | Our guess: dal bhat in the morning and again in the evening, as in many homes. |
| Uncooked rice in one meal? | 150 g | Our guess: a 1 kg packet makes about 6 or 7 plates. |
Multiply them:
About 9,000 tonnes a day. What this means: 3 crore people eating two plates each is a lot of plates (6 crore of them), but each plate is small, and the answer is a number you can picture, about nine thousand tonnes, or 3,60,000 sacks of 25 kg.
Each guess here is rough. Not everyone eats rice twice a day: some families eat dhido or roti for a meal instead, and a baby eats far less than a farmer. A plate in one house may have twice the rice of a plate in the next. You might think these doubts make the answer worthless. The surprise of this topic is that they don’t.
Your friend guesses 3 meals a day but only 100 g a meal. You guessed 2 meals of 150 g. Whose estimate for Nepal is bigger?
Pick an answer to see why.
Is the answer right? The real figures
Nobody weighs every plate, but the country does count its rice in two other ways. Each gives a figure we can compare with.
Counting what is grown and bought
FAO, the United Nations’ food agency, reported that Nepal’s farmers harvested about 57 lakh tonnes of paddy in 2025 (5.7 million tonnes). Paddy is rice still in its husk. A survey of 41 rice mills in Nepal found that the mill gives back about 70% of the paddy’s weight as white rice (66.2% whole grains and 3.4% broken ones); the rest is husk and bran. Nepal also buys rice from abroad: FAO expected about 650,000 tonnes (6.5 lakh) to come in during 2026.
Divided by the 365 days of the year, that is about 12,650 tonnes a day. This is all the rice there is. Some of it never reaches a plate: it is kept as seed, fed to animals, spoiled in storage, or made into drinks. So the rice people actually eat must be a little less. (Of those 46 lakh tonnes, imports are about 14%. FAO’s own report says that imports of all cereals, mostly rice, cover “about 15 percent” of what the country needs, so the two fit.)
Counting what people eat
The Ministry of Agricultural Development published another figure: each person in Nepal ate about 87.75 kg of rice a year in 2011–13. With the 2021 census’s people:
This figure is more than ten years old, and Nepal’s population and diet have changed since. So the real number for today sits somewhere between about 7,000 and 12,650 tonnes a day.
Look at those two official figures. They count different things in different years, and the bigger is 1.8 times the smaller: even careful counting leaves an uncertainty of almost a factor of two. Our 9,000 tonnes, built from three kitchen guesses, lands between them.
Our estimate gives each person 300 g a day. What is that in a year, and how does it compare with the ministry’s 87.75 kg?
Pick an answer to see why.
What’s going on: why rough guesses add up to a good answer
A question like Pema’s, answered by breaking it into pieces you can guess and multiplying them, is called a Fermi problem, and the answer a Fermi estimate, after the physicist Enrico Fermi (his story is below). Nobody expects the exact answer. The aim is the right order of magnitude: the right power of ten. Is it about a thousand tonnes, ten thousand, or a lakh? (You met orders of magnitude in How Long Is a Crore Seconds?.)
Within a factor of two
Two numbers are within a factor of two of each other if the bigger is no more than twice the smaller. So an estimate of 9,000 tonnes is within a factor of two of any true answer from 4,500 to 18,000 tonnes. It is a way of saying how close, by “how many times” instead of “how many more”: an estimate 5,000 tonnes out is a bad estimate of 6,000 tonnes and a good one of 5 lakh tonnes.
Now think about what happens to the guesses’ errors when you multiply them. Suppose each of your three guesses is off by up to a factor of two, either way. The worst that can happen is that all three are too big, by the full factor: 2 × 2 × 2 = 8 times too big. That sounds terrible. But how often does it happen?
The arrows show what goes on. A guess that is too big pushes the estimate to the right; one that is too small pulls it back to the left. Since too big and too small are equally likely, most chains have some of each, and they cancel, partly or wholly. To end far out, the guesses must nearly all go the same way, and all by a lot, which is rare.
The exact chances, if every error from half to double is as likely as any other, counted the way the widget’s line is marked (×1.5 as likely as ÷1.5), worked out with a little more maths than this topic uses (and matching what the widget finds after a few thousand estimates):
| Guesses multiplied | Worst case | Ends within a factor of 2 | Ends within a factor of 4 |
|---|---|---|---|
| 1 | 2 times out | always | always |
| 2 | 4 times out | 75% of the time | always |
| 3 | 8 times out | 67% of the time | 96% of the time |
| 4 | 16 times out | 60% of the time | 92% of the time |
With three guesses, each up to a factor of two out, the estimate ends within a factor of two two times in three, and within a factor of four 24 times in 25. The worst case, eight times out, almost never happens.
Counting in zeros
A Fermi estimate is easy in your head if you write each guess as a number times a power of ten (Grade 8’s scientific notation) and handle the two parts separately:
The powers of ten add (7 + (−1) = 6), and 3 × 2 × 1.5 = 9 is small enough to do in your head. 9 × 10⁶ kg is 9 × 10³ tonnes. Even rounding 150 g to 100 g (10⁻¹ kg) gives 6 × 10⁶ kg: the same order of magnitude.
Powers of ten also answer “how many times more?” at a glance. FAO expects the world to use about 559.1 million tonnes of rice in 2026/27, about 5.6 × 10⁸ tonnes, while Nepal uses about 4.6 × 10⁶ tonnes a year:
About 120 times as much. What this means: the world uses in about three days the rice Nepal has for a whole year.
When you have no idea: guess between your limits
Sometimes you can’t guess a number at all, but you can say what it surely isn’t. How many rice grains are in a kilogram? “More than 1,000, surely, since I can’t count a kilogram in a minute; fewer than 10 lakh, since a grain isn’t dust.” Which number between 1,000 and 10,00,000 should you guess?
Not the middle, 5,00,000. That is 500 times the lower limit but only half the upper one. Instead, go halfway in zeros: 1,000 has three zeros and 10,00,000 has six, so guess a number with about four and a half zeros, between 10,000 and 1,00,000. Then you are the same number of times above the lower limit as below the upper: 31,623 is about 32 times 1,000, and 10,00,000 is about 32 times 31,623. (The real answer: a thousand grains of Nepali paddy weigh about 18 g, so a grain of white rice, its husk and bran milled off (about 70% of the weight is left), weighs roughly 13 mg, and a kilogram holds about 79,000 grains. Within a factor of 2.5 of the guess. How Much Rice Is on the Chessboard? used a round 20 mg a grain, nearer a grain of paddy in its husk, which is why it gets fewer grains to a kilogram.)
You are sure a number is more than 100 and less than 10,000. Halfway in zeros, what should you guess?
Pick an answer to see why.
How precise to be
Our estimate came out at exactly 9,000,000 kg. Should we say “9,000,000 kg”? No: the seven digits pretend to an accuracy the guesses never had. Our guesses were good to perhaps a factor of two each, so only the first digit means anything: “about 9,000 tonnes”, or “about 10,000”. Say an answer with as many digits as you trust, and no more.
Harder puzzles
How many grains?
Back to the chessboard
The twist: when Fermi estimates go wrong
The guesses cancel only if their errors are really as likely to go one way as the other. Three things break that.
Errors that all go the same way. Suppose you estimate Nepal’s rice from your own family, and your family has two growing teenagers who eat a lot. Your rice meals a day and your rice in a meal will both be too big, and nothing pulls the other way. The roll of the dice is gone: your errors pile up. A Fermi estimate is only as good as the honesty of its guesses; a guess pushed one way in every step can end far out.
A guess you have no feel for. In 1961 the astronomer Frank Drake wrote the number of civilizations in our galaxy that might send radio signals as a product of seven factors: how many stars form each year, how many have planets, how many of those planets get life, and so on. Some of those factors are known well. Others, like the chance that intelligent life develops on a planet with life, or how long a civilization goes on sending signals, nobody knows even to a power of ten: estimates range over many orders of magnitude. One factor unknown by a factor of a million makes the whole answer unknown by a factor of a million. No amount of canceling can save it.
A missing piece. If Pema had counted only the rice Nepal grows and forgotten the rice it buys, her figure for all the rice in the country would have been 14% too small. When an estimate is far out, the first thing to ask is not “which guess was wrong?” but “what did I leave out?”
Where this is used
- Planning a country’s food. Nepal’s Ministry of Agriculture has worked out whether the country grows enough food by a Fermi-style product: the population times a need of 191 kg of cereals for each person in a year, compared with what was harvested, as reported in 2013 when it found a rice shortfall of 9 lakh tonnes. FAO estimates each year how much grain Nepal will need to import in the same way: what the country needs, minus what it grows.
- Science and engineering. Before they measure or build anything, scientists and engineers check what size of answer to expect. Universities teach it: MIT’s course The Art of Approximation in Science and Engineering, and others at Caltech, Berkeley and Toronto, some with “order of magnitude” in their titles. A Fermi estimate that disagrees badly with a careful result is a warning that something was left out.
Questions
Which of these is a Fermi estimate?
Pick an answer to see why.
About how many plates of rice are eaten in Nepal in a day, if 3 crore people eat 2 plates each?
Answer
An estimate of 9,000 tonnes is within a factor of two of which of these?
Pick an answer to see why.
Estimate how many times your heart beats in a lifetime of 70 years, at about 70 beats a minute. Give the answer as a power of ten, and in Nepal’s number names.
Hint
Answer
How many grains of rice do you eat in a year, if you eat 300 g a day and a gram of white rice has about 79 grains? Round your answer sensibly.
Answer
You are sure the number of buses in Kathmandu is more than 100 and less than 1,00,000. Halfway in zeros, what should you guess?
Pick an answer to see why.
Your estimate of Nepal’s rice is 9,000 tonnes a day. Your friend’s is 36,000. You both used 3 crore people. What could your friend have guessed differently, and how would you find out who is closer?
Answer
Make a Fermi estimate of how many liters of tea people in Nepal drink in a day. Write down each guess and why. Then say which of your guesses you trust least, and how much it could change the answer.
Hint
Answer
Where to go next
- How Long Is a Crore Seconds? Powers of ten, lakh and crore, million and billion, and a feel for how far apart they are.
- How Much Rice Is on the Chessboard? Doubling, and a number of grains no country could grow.
- What Does an Average Hide? One number for a whole country, like our 300 g a person, and the people it leaves out.
- Is the Answer Roughly Right? Rounding to check a calculation in your head.
- Can 1,000 People Speak for 3 Crore? (Grades 9–12) How a survey of a few people can tell you about a whole country.
- How Much Rain Falls on the Kathmandu Valley? (Grades 9–12) A bigger estimate from a map and a rain gauge.
- How Do You Count Tigers You Can’t See? (Computing, Going Further) Estimating a number nobody can count, with cameras and a computer. (Coming soon.)
Where these facts come from
- Every number in this topic (the chains, the real figures per day, the factors, the chances in the table, the grains, the questions’ answers): computed in
checks/textbooks/math-further-6-8/29/tmp/rice_numbers.py. - Nepal’s 2025 paddy harvest, 5.7 million tonnes; rice imports of 650,000 tonnes forecast for 2026; cereal imports, mostly rice, covering “about 15 percent of the national consumption needs”; FAO estimating Nepal’s cereal import requirements: FAO GIEWS Country Brief, Nepal, 18 August 2026, read October 2026.
- Milling recovery in Nepal, 66.2% head rice and 3.4% broken rice, from 41 mills in 19 districts, and the Terai growing about 75% of Nepal’s rice: K. P. Pant and M. Aryal, “Varietal effects on price-spread and milling recovery of rice in Nepal”, The Journal of Agriculture and Environment 15 (2014), read October 2026.
- Rice consumption of 87.75 kg a person a year in 2011–13, from the Ministry of Agricultural Development’s journal: Sangam Prasain, “Nepalis eating less rice compared to a decade ago”, The Kathmandu Post, 17 January 2018, read October 2026.
- The ministry’s food balance with 191 kg of edible cereals a person a year, and the 900,000-tonne rice deficit: “Nepal to face rice deficit of 900k tonnes this year”, ShareSansar (from The Kathmandu Post), 11 June 2013, read October 2026.
- Nepal’s population at the 2021 census, 29,164,578: Wikipedia, “2021 Nepal census”, read October 2026.
- World rice utilization forecast at 559.1 million tonnes for 2026/27: FAO Cereal Supply and Demand Brief, 2 October 2026, read October 2026.
- A thousand grains of paddy weighing 18.09 g on average (17.33 to 23.00 g across varieties): U. Sah, S. K. Sah, S. Marhatta and M. P. Neupane, “Effects of varieties and fertilizer levels on yield and economics of hybrid rice at Hardinath, Nepal”, Journal of Agriculture and Forestry University 5 (2022), read October 2026.
- Fermi problems, the piano tuners of Chicago (the article doesn’t say who first asked it), overestimates and underestimates canceling, the Drake equation as a Fermi estimate, and courses (MIT’s The Art of Approximation in Science and Engineering, Caltech, Berkeley, Toronto): Wikipedia, “Fermi problem”, read October 2026.
- The Trinity test on 16 July 1945 in New Mexico; Fermi’s paper scraps, the blast about 40 seconds after the explosion, moved about 2.5 m, his estimate of about 10,000 tons of TNT; the first radiochemical yield of about 18.6 kilotons and the accepted yield of about 25 kilotons (24.8 in a 2021 re-analysis): Wikipedia, “Trinity (nuclear test)”, read October 2026.
- Fermi’s life (1901–1954), his Nobel Prize in Physics in 1938, leaving Italy that year because of the racial laws that threatened his wife Laura Capon, and the Trinity yield of about 18.6 kilotons given there: Wikipedia, “Enrico Fermi”, read October 2026.
- The Drake equation (1961, seven factors, some ranging over many orders of magnitude): Wikipedia, “Drake equation”, read October 2026.
- Farming beginning about 11,700 years ago, after the last Ice Age: Wikipedia, “Neolithic Revolution”, read October 2026.
