One Weird Math Trick Estimates ANYTHING (Fermi problems) 

Police officer: Sir, do you know how fast you were going? Me: *Inhales*...

"You are technically correct. The best kind of correct."

"I've stood next to a large dump truck before" as Kyle halfway smirks at the camera.

I don’t know about anyone else, but my favorite part of each episode is the section after he says he doesn’t know what or how he’s going to fill the time as the Patreon names go by. It’s a very wonderful wrapup or behind-the-scenes moment for each episode that I really appreciate and look forward to

7:01 "This is going to be difficult, even Fermi"

I've been doing a version of this for so long but was never taught it or even knew what it was. Now that I know the process properly I feel more confident in my estimates and now it's even easier. Learning is great.

First time hearing or learning of Fermi calculations. Thank you. And thank you for mention South Africa 🇿🇦

Thanks for this episode. I loved it when you first demonstrated this on that livestream on a channel that shall not be named but was never able to find back what it was called. This is such a great tool, you're doing the basilisk's work with content like this.

I really enjoyed watching you think through the problems that you were working on. I’m a former teacher, and I really enjoy your channel. You are a great teacher, and I’m going to recommend you to a couple of my friends who have kids who are in school. I think that they would get a lot out of watching & learning from you. Thank you for what you do.

I used to have an 89 Titanium from 6th grade through AP Calc in 12th grade (the reason I passed, and only got a C [calculator/no calculator portions]) But for college I upgraded to TI's Nspire CX CAS when the batteries eventually leaked after the 89's long tour of duty. Still what I use to date when I need something more than a phone calculator, but doesn't warrant firing up MatLab. Hopefully the Li-ion battery never leaks! Step up your product placement Kyle if you want that brand deal! (having a jest here)

Fun fact: I use metric system and estimated 45 cubic meter for the dump trucks. 2m high, 4m large and 6 meter long + an extra 5 cubic meter of material from the lump. this is so close from your 6ft, 12ft and 18ft dump truck.

When you showed the result of the shark estimate I wondered how you came to this conclusion, but then I actually got to 972 using only the given numbers and I have to say I`m kinda proud of myself. As always thanks for the video and keep going my favourite science communicator.

I had a professor in orbital mechanics who could guesstimate distances, figures, orbital times, etc. this way *without a calculator* and be within 10%-20% of the real answer. It was very impressive.

It’s so weird bc I use this method like all the time without realizing it’s like a thing. Like if my mom wants to know “how much have we spent on fast food this month?!!” I start figuring: a fast food dinner generally costs about $10 per person, as does the average Starbucks breakfast. Assuming we haven’t had anyone else visiting that means about $20 per meal. If our average weekly consumption of fast food in the past week was about 6 meals (including Starbucks breakfasts and fast food dinners) (she usually says this when we’ve had a month of copious fast food eating), and there are 4 weeks in a month, then we’ve had 24 fast food meals in the past month. If each meal cost $20, then we spent about $480 on fast food in a given month. Which totally tracks since I remember we once looked at a list of all of the transactions on her credit card for budgeting purposes, and we had in that month spend $400 on fast food. I’ve been doing this for ages and never realized it was like an actual method of estimating

I use this all the time and just like you said on most things you can get well within one order of magnitute with numbers, you can do in your head. This is also why this is such and good tool to either estimate if something is possible or imposible. If a claim says something is well outside one order of magniture of you guesstimation it is likely not correct.

17:08 mans knew what he was saying

i tip my hat to the guy who somehow got his name put on the process of bullshitting an answer on a multiple choice exam

5:12 - "...No human's hair, laid end to end, would never reach the moon." Double negative is proof positive - all of us will, one day, have enough hair to the moon. Kyle says so. Cheers Kyle!

I do this all the time for fun and didn’t realize there was a name for it. I’m thinking 3 billion bricks in Baltimore, half a million pearl cous-cous in a bath tub.

I've been doing this on a smaller scale all my life and never realized there was an actual name for it.

So I’ve been doing this for the longest time and didn’t have a word for it. With the great white shark question, I figured that the Great White was endangered ( later found out i was wrong), i figured that the threshold for being endangered was 500 remaining members of a species, I figured that not all of them would be off the coast so I halved the number. My final guess was 250.

I use this all the time when people don't want to give time estimates - "how long will the task take?" "I don't know" "you must know the ballpark figure?" "No" "1 hour or 1 week?" "2-3 days" Good enough for me 🤷‍♂️

On the dump truck answer, alternatively, it would take just one dump truck to haul away Mt. Everest...in 6.4 billion loads.

Oh man, I'm using this with my kid's homeschooling! This is amazing!

I learned this in Navy nuke school, never knew Fermi came up with it. I use this method to answer people's random questions all the time. Yeah, if you look up some of your conversions you can calculate just about anything.

Discount Thor: "I've stood next to a really big dump truck before." Me: "Kyle, that's not a very nice thing to call Name-Brand Thor." 😆 But thanks for explaining this actual life hack. I've heard the term thrown around before and read alittle on it but I got critically confused, and no, I'm not being over dramatic or referencing Pokemon. Most online things on it just hurt my brainium so bad I lost interest in it. This is much more digestible. Thanks again.

So am I the only one who just estimated stuff like this naturally? I mean this is how I've always estimated things, and this is the first I'm ever hearing of a Fermi estimation.

You could’ve made an even more accurate guess if you had increased the great white sharks actually habitat. Austriallia is a good example.

Hears Kyle joke about 2kpm air in front of him. balks at the idea that 120 CFM is blowing past him and his hair isn't moving.

I know I'm real late to this video, but it made me feel really good that i picked up on the basketball mistake. I paused the video did my own calculations for it, and unpaused just for Kyle to pick up on the same error and calculate it the way I did. 🥰 I officially love this channel. 😀

How to solve basic math problems using basic math. Hey, I have 4 apples, and someone gave me another apple. Can Fermi help me figure out how many apples I have? 10 apples. Close enough. Thank you Fermi, and man in video.

So Fermi's big trick was the units management taught in physics 101?

I've always been good at guesstimating... always because I know "a little bit" about "almost everything".... So could guesstimate pretty darn close to any random thing I wanted to guess at..... Turns out I was using the Fermi Method in my head the whole time, but in an abstract way, instead of a pen&paper way. neato

Sharks exercise: I estimated there was around 300000 great white sharks in the oceans worldwide. I then guessed they had around a 10 percent chance of being within 50 miles of a coastline in the equatorial region, estimated that of total coastlines on earth california had probably 5 percent of equatorial coasts (which i defined in my head as between the tropics of cancer and capricorn). Came up to 200. Hair: my hair grows around an inch and a half a year, so my hair would probably be 110ish inches long if i lived to be 72 and never cut it. (Guessing roughly the multiplication since i don't wanna lose my comment so far) NBA: Probably 150000. Average NBA score is between 100 and 200, and there's around 100ish games a season. Trucks: using the volume of everest, and knowing a dump truck can haul around 2 to 7 cubic yards of rock, it would take around 2000000 loads to haul all of everest somewhere else assuming we use trucks capable of hauling the maximum of 7 yards each. This was all estimated while in the bathroom with no note paper

I have a question. I tried to find out the shape of our solar system and our galaxy and based on what I found on the RU-vid and the net was that the solar system and the galaxy are disc shaped rather than spherical. Why is that? As per my vague understanding of physics, I thought that the solar system and other celestial bodies would be in a arrangement similar to atoms where the bodies revolve around the center point in any plane essentially giving the galaxy a spherical appearance.

NBA points per season: Teams x games x team pts per game I know hardly anything about the nba but I have seen scores during my time. My guesstimate of an average team score is about 80 points. American major leagues seem to have 32 teams that never change apart from when one team moves to the other side of the country. I rounded down to 30 to make the mental calculation easier. I looked up nba records at one point out of curiosity and the most games played by one player is around 1500 - or at least only a couple of people have played more than that. I think Kareem Abdul Jabbar was one of those few and he played about 20 seasons (maybe a couple more but 20 years is pretty much an upper limit for a sporting career). 1500/20 = 75 games per season so that was my games per season estimate. 80 x 75 x 30 = 180000 so pretty damn close to the actual figure.

This was such a fun video! I am fairly certain that there are WAY more than 10,000 hairs on a human head. I once heard 110,000 as an average. You still wouldn't get to the moon, though.

Didn't know a calculator could run out of battery, I thought it was impossible hahaha. In my almost 25 years of life I haven't seen even one calculator run out of battery (not even scientific ones)

If you considered Australia as another shark habitat you would have been even closer

huh, when we discussed fermi problems in uni, calculators were strictly forbidden

Thanks for the lesson!

Thor teaching us about maths is awesome.

I've been doing this for years and calling it slop math, for math with estimates will have play, and I get a range

I guessed 500 sharks just with a general understanding of their declining population in the ocean!

renthead: 525,600 minutes.... 🎶

bro! you should have Fermi estimated the volume of mount Everest. I got close by pretending it was a 5 mile tall cone ^_^

Formless and emotionless void? Wow Nerdist must be really bad.

Okay, but how many marbles are in the jar? Guess and win the prize.

I got almost almost the exact answer for the hair (10.6 meters) and that is because I was off on average life a little. the fact that I get 12 inches of hair cut off every two years means I have a lot of confidence in the rate of hair growth.

Wow! I'm actually surprised with this ngl. For the portion where you did it on camera, I tried the hair length problem before I watched you try to solve it. And I came up with 10.16 meters! My process was as follows - I know the average lifespan to be around 80 years - I know it takes about 2 years for a buzzcut to grow to shoulder length, and id imagine that being around 10-12 inches. I played it safe and said 10 inches. I simply multiplied the inches that hair grows in a year, by the average years in a life to get 400 inches. 400 inches to meters is 10.16 meters Sadly I didn't attempt the rest because I had no clue about any numbers whatsoever for those

I infered the great white shark population correctly. Cool

That's so few sharks! I thought you were an order too small because 900 is so small to maintain a species, assuming the populations don't meet.

This man is Thor if he was a scientist

How accurate does it sound that in a whole highschool year I see 45 000 girls obviously counting repetition?

Is that the same method that Drake used for his famous equation named for himself?

My estimate on the sharks was more accurate because of Australia.

Am I the only person who has done this all their life, and thought it was something everyone already did?

I really enjoyed this video

From what I can ascertain your correct answer for the NBA question is off. 186000 points in an nba season/ 30 teams/82 games equates to each team averaging about 75 points per game. However the lowest scoring team in the nba last season averaged 103 points per game. So the correct answer though I cannot definitively find it is closer to you estimation than the correct answer given in the video. Being a fan of the NBA and us in Fermi I estimate the correct answer is probably closer to 260,000

I knew hair wasn't 5mm a week, I always heard is was about 5-10mm a month

For the sharks, my method was to guess that you could expect an average of 1 shark for every 2 or so miles of coast and assumed the coast was about 1000 miles so I guess 500-600 and I was so close

If it's ok to look up the volume of mount Everest surely by that (cheating) logic you can also look up the volume a dump truck can hold?!

So could you use this method to estimate how long until the emergence of AI super intelligence?

It takes 1 dump truck to move Mount Everest, plus a lot of time.

Thanks Kyle, now I can get every question on my math tests almost right.

As a middle school science teacher, I use fermi estimates ALL THE TIME to answer crazy questions from my students that I have no way of 100% correctly answering on the fly

I remember doing these kinds of exercises in school. My dad calls these SWAGs: Scientific Wild A$$ Guesses

"The air's moving around at around 2 KpH in here by the way." Two Kyles per Hill? WHERE IS THIS OTHER KYLE?

I love how the Drake equation is simply a Fermi estimate, jumbo sized.

Title: How to estimate anything Me: All non-infinity numbers round to zero

"Is that a firm estimate?" "No, it's a Fermi estimate." "Isn't that what I just asked?"

"what's 9+10?" Enrico Fermi: "21"

"A few years ago when I was trapped in a formless, emotionless void-". Ah, so working on Because Science

That "Texas Instruments, sponsor us" at the end made me laugh my ass off. I'm sitting at work, on break, at a Texas Instruments facility in TX at this very moment

The best part of a Fermi estimation is that once you've done it, you have an incentive to check your work, providing yourself with even more points of confidence.

"How many great white sharks are swimming off the coast of california?" All of them, you don't swim on a coast

What’s even more fun is using the right answer to triangulate, cross reference, and analyze my guesstimation biases

Kyle, you were actually even closer on the NBA question if you're counting the points scored in a normal season. The last two seasons were shortened due to covid so the totals were lower but 2018-2019 there were about 275,000 points scored. I know the point is just getting close by fermistimating but gotta give you the credit you deserve you total sports guy. Love the channel, keep it up

"No this isn't cheating, this is using what we have available." So are you saying that I can just google answers instead of using this method?

Fermi guesses are PERFECT for making sure your "precise" calculations make sense. The funniest example I found of it is "How many piano tuners work in Chicago?" The author looked up the population of Chicago, and then guestimated their way to within 5% of the right answer. It was pretty impressive, NGL. Great work, as always!

I can guesstimate within a few cents all of my grocery bills with admirable regularity. Does that count?

I really think this should be taught in more courses than just physics. I was a physics major for 5 minutes before switching to engineering and my physics classes were the only ones to teach Fermi estimations. The thing is, this technique doesn't require any specific vault of knowledge, it just requires that you be taught how to think. Any student could learn this, regardless of major. It also would be super helpful for those annoying job interviews where someone asks you "How many pianos are in New York"?

What’s fun about this is once you have tour guesstimation next to the actual number, you can reverse engineer your estimations to find where you were off and posit why you where over/under on a number. Like the dump trucks- the truck might be 2 Kyles tall but the bed starts 1 Kyle up which makes it only 1 Kyle deep overall. Run that calculation and you’d be closer to the actual number. Fun!

Dude this is so freaky and cool. When Kyle was doing the guesstimations for sharks I did my own even shoddier, even more imprecise measurements going “Yeah that sounds about right”. I guesstimated knowing the distance from my home in Vegas to the coast of California which is 300 or so miles (and I only know due to visiting family on the coast) then went “I think the coast is about two of that distance”, doubled it since I think I recall miles to km being vaguely “double the miles = km” (only just now remembering thats just for metric WEIGHT and I have no clue if that actually applies to distance) then asked from my experience at beaches and very vague knowledge of shark inspired beach hysterics if one shark per kilometer sounded right, then if two sharks per km sounded right - and it did So I ran the Fermi estimate numbers, 1 shark per 2km divided over 600km of coast = about 300 sharks off the coast right now. I sat there waiting to see how insanely off I was because no way my estimate is within a mile of this super smart science man with tons of statistics and figures (vs me, a highschool dropout who, yeah, LOVES hearing about the results of science but struggles to even sorta comprehend the processes and math involved in getting those results 95% of the time) yet LO AND BEHOLD. I WAS MORE SPOT ON THAN HIM This is the only situation in math I have ever heard of where less precise data and figures have been a boon, and I can only assume its due to the fact that he had a lot of precise and neutral numbers, with big and heavier numbers, resulting in a net skew towards larger estimations. Meanwhile my dumbass (probably, I havent checked) way underestimated the distance of the coast and (again, probably) way over estimated the amount of great white sharks that exist on the coast and so those both balanced out to a way more neutral number. I know no one cares or will read this but I just needed to write it down somewhere because this was such a wild and mind blowing experience for me. Never before have I truly experienced and utilized the sheer power and magic that is MATH to this insane degree, all thanks to Kyle. Thank you Kyle this is amazing stuff

"within a value of 3" " you gotta be impressed by that... unless you're a seal." I may be wrong, but if I was a seal and I knew there are less than imagined i'd be pretty happy.

That's how me and my dad solve discussions when we drink

"My TI is out of battery". This is the story of my engineering life

I feel like this should be properly taught in school. Over in Australia I’ve never once heard of this. Just feels like it’s a great way to get people to think about a problem instead of knowing the answer to a problem

My mind has been corrupted. Every time I hear “dump truck” I can’t help but to think about rear ends lol

"But this is going to be difficult....... even Fermi."

At a physics competition in high school that I took part in, there was a special section of problems to solve: estimation challenge. They didn't give any parameter values, we had to estimate them best we could. That was certainly out of my comfort zone, because all the problems would always have precise "here is X and Y, figure out what's Z". It was an interesting experience for sure! Good times :) Not to flex, but I managed to be a laureate on this thing, which gave me an easy entrance to a good university, and I work as a scientist now, and estimation is a very important part of my job!

I use this process everyday just for fun, I didn't even realize it had a name.

I sincerely appreciate the segment showing how you did these in real time AND that you got one wrong and went back and fixed it. So often we only see the polished, finished product on RU-vid tutorials and it can be intimidating when you try to replicate it yourself. Thank you SO MUCH for showing that process!

As a Guitarist in front of Whole Foods in Birkenstocks... I feel personally attacked...

I’d be interested to see a detailed breakdown of Fermi’s actual estimate from the blast

"i've stood next to a large dumptruck before" **remembers the vampire's mommy video**

My freshman Physics teacher told me that you can even estimate how physical equations look like. Start from gathering as much as seemingly relevant input parameters and try to arrange them in an equation in a manner where the units cancel out until they matches the unit of the output.

So apparently I've been using Fermi estimates all my life without knowing they had a name. Neat, I think.

Video title "How to Guesstimate Like a Genius" Uploaded: 1 minute ago Me: I'm already 4 parallel universes ahead of you

I am a pharmacist and use dimensional analysis all the time while working, but it applies in so many areas of life. It’s probably the single most useful mathematical tool I’ve ever learned.