Fermi Questions – Activity Directions
Enrico Fermi (1901-1954) was an Italian physicist who made significant
discoveries in nuclear physics and quantum mechanics. In 1938, he received
the Nobel Prize in physics for his discovery of nuclear reactions caused by
slow neutrons. This mechanism led directly to the development of atomic
bombs and nuclear fission reactors. After receiving his Nobel Prize, he
emigrated with his family to the United States to escape the fascist regime
of Benito Mussolini, where he soon began contributing to the Manhattan
Fermi was famous for being able to make good estimates in situations
where very little information was known. When the first nuclear bomb was
tested, Fermi was nearby to observe. To get a preliminary estimate of the
amount of energy released, he sprinkled small pieces of paper in the air
and observed what happened when the shock wave reached them. (Being so
close to the bomb on this and many other occasions exposed Fermi to
dangerous radiation that led to his death by stomach cancer at the age of
53. Fermi was aware of the danger, but chose to work on this project anyway
because he believed that the work was vital in the fight against Fascism.)
Fermi often amused his friends and students by inventing and solving
whimsical questions such as "How many piano tuners are there in
A "Fermi Question" asks for a quick estimate of a quantity that seems
difficult or impossible to determine precisely. Fermi's approach to such
questions was to use common sense and rough estimates of quantities to
piece together a ball-park value.
For example, one way to estimate the number of piano tuners in
Chicago is to break the process into steps: estimate the population;
estimate the number of households in the population; estimate the fraction
of households that have pianos; estimate how often each household has its
piano tuned; estimate the time it takes to tune a piano; estimate how many
hours a piano tuner would work each week.
In this case, it is possible to check the estimate by looking in the
phone book to see how many piano tuners are actually in Chicago.
Fermi Questions in Everyday Life
Here are a few examples of practical Fermi Questions.
- In business: "How many teens within a 30 mile radius of our proposed radio station?"
- In environmental policy: "By how much would the amount of trash in
landfills be reduced if it became illegal to throw away plastic grocery
- In educational policy: "If the school district reduces the maximum
class size to 20 students, how much would it cost to hire the extra
- In public health: "A virulent strain of influenza is spreading and
everyone in our county needs to be vaccinated by a qualified health care
professional. How quickly can this be done?"
- Personal finance: "I am going to work in a fast food restaurant to
cover my college tuition, books, and living expenses. Will I need to
take out a loan? Will I have enough study time?"
- Event planning: "Our city is organizing a parade with a mile-long
route. About 150 organizations have expressed interest in being in the
parade. For how much time will the streets need to be closed along the
It is empowering to cultivate your ability to think about these kinds of
big picture questions. Thinking this way can enable you to dream big and
accomplish your goals. Practicing this skill can equip you to identify
opportunities and dangers that are not apparent to most people.
Fermi Questions Lab
Record your answers to each question on another page. Be sure to write
your team name, list the members of your team, and write out the Fermi
question you are investigating.
- Question: State the question and discuss how you will interpret it.
- Wild Guess: What is your answer without any calculating?
- Educated Guess: List the pieces of information you will need to
answer this Fermi question more precisely. Estimate the value of each
quantity in your list. Based on your estimates, what is your solution
to the Fermi question? Show all your steps and use words to explain
- Variables and Formulas: Choose variable names for each quantity that
you estimated. Write a series of formulas or a procedure that explains
how you used the quantities to find the solution. Try to simplify the
process into a single formula that answers the Fermi question if
- Gathering Data: Perform experiments, conduct surveys, make
measurements, or search for information that would help you to obtain a
more precise estimate. For each quantity, identify the smallest
possible value, the largest possible value, and the most likely value
(you will have to use your best judgment to estimate these
values). Then use the formula you found in the previous step to find
the smallest likely answer to the Fermi question, the largest likely
answer to the Fermi question, and the most likely answer to the Fermi
question. Show your work!
- Conclusions: State your final answers to the question. Explain some
possible sources of error in your procedure. List any interesting facts
that you learned while seeking the answer to the Fermi question.
Finally, describe a further direction that you could pursue if you
wanted to extend your investigation into this topic.
Sample Fermi Questions
- In Bendix Woods near the old test track, the word STUDEBAKER is
spelled out in pine trees so that it is visible from the air (check
out the satellite image online). How many pine trees were required?
- What would it take to fill this room with popcorn?
- If you prepared a tank with all of the air you need to breathe
in one day, how large would it be?
- How many people in the world are talking on their cell phones at
- If all the people of the world were crowded together, how much
area would we cover?
- If everyone in our city donated one day's wages to a good cause,
how much money could be raised?
- How many dump trucks would it take to cart away Mount Everest?
- How many people would be required to surround this city if they
- How large a landfill would our county need to store 100 years of
- How many square miles of paved surfaces are there in our city?
- How much gasoline does a typical automobile use during its lifetime?
- How many people are airborne over the US at any given moment?
- How much money could the city of South Bend save this year by
shortening the work day of all city employees by one hour?
- How many port-a-potties should be planned for the next million-man-march?
- How many blades of grass are in a typical lawn in your
- How big is the local market for home-made gourmet dog treats?
- How many musical notes are played on your favorite radio
station in a given year?
- How many gallons of water move down the Mississippi River in one day?
- How far does a bumblebee fly each day?
- If there were no traffic, how quickly could a race car travel
from Washington D.C. to Los Angeles?
- How long would your hair be if it never broke or was cut from
the time you were born until now?
- How many dollars worth of pennies would you need to stack to
equal your height, the height of the school, the tallest building in
the world, Mount Everest, outer space?
- What is the current population of mosquitos in our county?
- How much milk is produced in the United States each year?
- How many pencils would it take to draw a straight line along the
entire Prime Meridian of the Earth (assuming that a suitable drawing
surface could be placed along the entire route)?
- If you took the thread from all the uniform shirts of the Notre Dame
football team and laid them end-to-end, how many times could you wind
it around the football stadium at Notre Dame?
- If all the pizzas eaten by students in your school last year were laid out next to each other, what area would be covered?
- How many people attend Art Beat in South Bend each year?
- How many grains of sand are there on the beaches surrounding
- If you posted an advertisement on a billboard on Lincolnway for
one month, how many people would be likely to see it?
- How many desks occupy 7th grade math classrooms in the state of Indiana?
- How many plastic flamingos still exist in the United States?
- Of all classified mentally ill persons, how many are diagnosed
with schizophrenia (world wide)?
- What is the total number of shots taken in one NBA season
(including the tournament)?
- How many yards of thread in a shirt?
- How many sheets of toilet paper in the school?
- How many sheets of copy paper in the school?
- How many ceiling tiles in the room?
- How many blades of grass in a football field?
- How many minutes does the average student play video games per
day, week, year?
- What is the cost of food for the children in the Family Literacy
program for one year?
- What is the cost of transportation for the Family Literacy
program for one year?
- How many screws would it take to put the floor down for the
Boston Celtics at the Garden?
- How many hot dogs are bought at all the Major League Baseball
games for one season?
- How many water droplets make up fog? Stratus clouds? Cumulus
clouds? Cumulonimbus clouds?
- How many hours of sleep will I have in my lifetime?
- What is the graduation rate of students I have taught over the
past 22 years?
- How many texts does the average student send per year?
- How much food waste does the school have in a month?
- Not counting the hours when you are asleep, how does the amount
of time you are in school compare with the amount of time you are
out of school?
- What is the average lifetime of a pencil?
- How much popcorn is popped at the movie theater on an average
- If you played your favorite song continuously for a whole year,
how many times would it play?
- How many times does your heart beat per day? Per week? Per year?
- How many marshmallows would it take to cover your desk?
- How many M&Ms would it take to cover the floor?
- How many hours of tv will you watch in your lifetime?
- How many pennies in my jar?
- How many times would my 22 inch rims go around if I could drive
around the equator of the Earth?
- How many calories does a student burn while switching classes?
How does this compare with the number of calories in a school lunch?
- How many steps would I need to climb to burn as many calories as
there are in a bag of potato chips?
- How many laps would I need to make around our classroom to go a
- How many laps around our school would burn enough calories to
lose a pound?
- Do you burn more calories using stairs?
- How many pizza boxes would we need to cover the classroom floor?
- How many sticky notes would it take to cover the chalkboard?
- What would it take to make a paper chain long enough to go down the main hallway at school?
- What is the weight of a building?
- How many sheep would it take for every person in the world to
have a wool sweater?
- What is the average number of bricks used to build a building?
- How many gum balls would it take to reach from the Earth to the
- How many strands of hair do you have on your head?
- How many snowflakes would it take to completely cover a driveway?
- How many trees would need to be planted to lower the average
global temperatures by one degree?
- How many nerd ropes would it take to go around the Earth?
- How many cells would fit in a gallon?
- How many drops of lemon juice should be added to a liter of water
to reach a pH of 5?
- How many electrons would flow through an iPod in one day?
- How many sailors would it take to sink an aircraft carrier?
- How many hole punch pieces would fit in a backpack?
- How much water is wasted by a leaky faucet in one day?
- If the amount of the national debt were represented with a stack
of $1 bills, how far would the stack reach?
- I am planning to buy a new car. One car is $5,000 cheaper and
gets 25 miles per gallon of gasoline. The other option gets 35 miles
per gallon of gasoline. How long would I need to own the car to
recover the $5,000 cost difference?
- How much energy would be saved at our school each year if the
lights were replaced by energy-efficient alternatives?
- How many bees are needed to polinate an orchard?