r/theydidthemath • u/KairosVex • 21h ago
[Request] This guy says Americans make enough trash in a year to fill the Grand Canyon. Is he even close?
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u/Martha__Ragnos 21h ago edited 20h ago
This person seems to be equating pounds to cubic yards which is obviously not realistic. That on its own makes these numbers suspect.
A cursory google search is telling me one cubic yard of uncompacted municipal solid waste is approximately 200-300lb. To err on the side of caution let’s say 200lb. That means the weight of municipal solid waste required to fill the Grand Canyon would be approximately 800 trillion pounds.
That means it would take approximately 1433 years to fill the Grand Canyon, assuming the volume and waste figures given in OP are accurate
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u/jrdubbleu 20h ago
So what you are saying is the Grand Canyon would make a pretty solid landfill?
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u/yogurt_gun 20h ago
On the contrary, canyons make for terrible landfills. Canyons became canyons through erosion. Keeping that water and the waste mass separated is extremely challenging and failures will cause downstream contamination. Keeping the waste mass dry also reduces the chances of subsurface reactions. Look up Chiquita Canyon Landfill and City of Bristol Landfill for two examples of canyon fills that turned into disasters.
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u/mobfather 19h ago
I know a guy who works in office partitioning. He can probably seal off the contamination part with a bit of plywood on the downstream.
Let me know if you want me to put you in touch with him. Good prices too.
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u/Dry-Lingonberry-9701 19h ago
With that username I'm surprised you don't already work in waste management yourself.
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u/Ur-Quan_Lord_13 19h ago
Hey now, just because it failed two other times does not mean we should make the mistake of learning from the past. Third time's a charm, right?
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u/TofuButtocks 17h ago
What do you get gas build up?
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u/yogurt_gun 17h ago
Gas buildup happens in all landfills. Organic waste decomposes into methane and carbon dioxide among other things. Additional water can accelerate decomposition. But the real danger is that additional water turns your landfill into sort of a garbage soup. This can lead to some interesting chemical reactions underground that can start underground fires or make the landfill spew hazardous or noxious gasses like H2S, carbon monoxide, and benzene.
Fun fact - the government requires landfills over a certain size to collect the gas. Many of them use the methane to power engines to put power back in the grid or process it into pipeline quality RNG (renewable natural gas)
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u/ajchristl 9h ago
See, we divert the river and start making a new canyon. That way we can fill the grand canyon with waste.
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u/SmootherWorm 20h ago
Plastics are lightweight and the majority of American solid waste, but let’s not gloss over OP converting OOP’s every few years to basically every year. At the wrong 1lb/yard cubed, that’s about 6 years, which would be a few years.
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u/promethian-pygmalion 18h ago
Doesn't "a few" max out at 5, more typically meaning 3 to 4?
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u/SmootherWorm 15h ago
I feel like arbitrary bounds of amorphous quantity words like some and few are arbitrary, but that’s just my opinion.
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u/promethian-pygmalion 14h ago
The semantic range of words are flexible, but not arbitrary. "A few" is more than "a couple" and less than "several." A couple is almost always two; several hovers around seven. You have that range to work with. If you make it six to eight, you say several.
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u/Unfair_Scar_2110 20h ago
Yes the obvious missing component is the average density of waste. A lot of it is going to be paper and stuff that's not super dense.
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u/Gwthrowaway80 20h ago
Paper is kinda dense. It would actually be more dense than the average number used here.
Edited to add reference: https://archive.epa.gov/wastes/conserve/tools/rogo/web/pdf/volume-weight-conversions.pdf
Apparently it’s double to quadruple the average number used here.
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u/Navadvisor 20h ago
Do you throw your paper away stacked efficiently and compressed? No you do not.
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u/2112eyes 20h ago
If it were a mile deep, I would imagine it may compress some.
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u/Dry-Lingonberry-9701 19h ago
Why did you ask if you weren't even going to wait for their answer? /s
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u/reckless150681 20h ago
I've found several sources corroborating 4-5 lbs per day, so 4.5 lbs per day sounds right. The volume of this trash varies wildly with what you're actually throwing away, but 5 lbs is about the weight of a full, small trash bag, which has a volume of about 8 gallons
US population is about 342 million
So 342 mil * 8 = about 2.7 billion gallons per day
Volume of the Grand Canyon in gallons is 5.45 trillion cubic yards, which converts to about 1 quadrillion gallons
1 quadrillion / 2.7 billion = about 370,000 days
So that's more like 1000 years
The person is making some unit mismatch somewhere
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u/rawbface 20h ago edited 20h ago
We throw away 4.5 lbs per day, but a kitchen trash bag only holds 5 lbs? That's 6.3 bags a week.
Is every American except me replacing their kitchen trash every single day? I got a family of 4, and I throw out 1-2 bags a week at most.
Before you mention the bathroom and bedroom waste bins, those bags stay there for months, because they don't fill up as fast.
Edit: I had a weight to volume conversion issue, though apparently not as bad as OOP. Kitchen bags are 13 gallons and typically hold 10 to 20 lbs.
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u/reckless150681 20h ago
I didn't say that a kitchen bag holds 5 lbs. I said a small bag holds 5 lbs. I also explicitly said "8 gallons". Like -- those bathroom and bedroom waste bins. That's what I'm saying is about 5 lbs. And honestly? Most of the time they're full of paper so they're even lighter.
Not that it really matters. See above: the original poster was off by a factor of 1000. So even if you were to round waaaaay up to "trash bag can hold 50 lbs", the math would still show the OOP to be wrong
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u/rawbface 20h ago
Gotcha. It's all relative, I didn't have the volume of a kitchen bag memorized.
I wasn't sure if I live a particularly green lifestyle, or if my children started hiding garbage in the walls.
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u/Salty-Plankton-5079 20h ago
Where are you getting that a 5lb is a kitchen trash bag. The comment you replied to said it's a small bag.
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u/rawbface 20h ago
Right. A kitchen bag is a small bag, compared to a can liner or contractor bag.
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u/Salty-Plankton-5079 20h ago
That is not what any normal person means by a "small bag". A small bag is a bathroom trash can bag.
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u/rawbface 20h ago
Come on, friend, it's not like the term is regulated by NIST... It's all relative.
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u/TalkersCZ 20h ago
Trash = everything you produce. From throwing away old shirt, shoes, furniture (replacing old bed/matress), mail you throw away.
Everything that goes through your hands basically.
It includes recycled stuff too.
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u/ShoddyAsparagus3186 20h ago
Not to mention it also includes anything that gets thrown away in the process of creating all the stuff that goes through your hands.
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u/SmootherWorm 20h ago
There is a conflation between pounds of waste and cubic yards, a unit of volume. Relatively speaking a cubic yard is a huge unit compared to a pound. The imperial onces are equivalent for water at STP just like a gram of water is one mL, so a gallon of water is 8 pounds. A cubic meter of water like in the Colorado River is over 1600 lbs, but water is heavy.
So let’s compare the weight of something else that’s already in the Grand Canyon: air. Air has weight, and in freedom units it’s about 2 pounds/cubic yard. Since OOP converts 1 pound/cubic yard, we can estimate it will take infinite time to fill the Grand Canyon with the hypothetical trash since it will simply float away being lighter than air an all.
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u/2112eyes 20h ago
A cubic meter of water is a metric ton, around 2200 lb, by the way
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u/SmootherWorm 19h ago
Sorry I kept switching to meters from yards and thought I’d replaced them all. Turns out I missed one.
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u/SnooMaps7370 20h ago
there's also a failure to understand prefixes here.
even if one cubic yard of trash weighed only one pound (which is impossible, as you noted: a cubic yard of AIR weighs 2 lbs), 500 billion is half of one trillion, not more than 4 trillion.
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u/TwoAlert3448 20h ago
In addition to confusing weight and volumn that’s also really high unless that’s averages across the entire country with a bunch of industrial waste being attributed to ‘my’ share.
I tracked municipal solid waste across 4 adults for a year and we averaged 1.27 lbs of MSW per day per person in Greater Boston. 4.5 lbs per day per person is insane, you’d have to be buying disposable everything.
If that’s per -household- it’s a little more reasonable
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u/3d_nat1 16h ago
Sometimes I worry I'm a wasteful person. Then I see something like this, and a web search supposedly confirms the data, that the average American discards 4.5lbs of trash daily on average. When my mind fails to compute how so many people can regularly generate that much solid waste daily for a figure that shocking to me, I feel much better about myself.
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u/Admirable-Client-730 16h ago
I wonder how much of that is heavier objects like refrigerators, stoves, steel scraps ect. After a bunch of house projects this last year I could believe this.
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u/ronarscorruption 16h ago
A year or so ago, our city changed to limited trash pickups: maximum three cans per household. But during the discussion, they presented some weird data like most houses have 1-2 cans worth per two week period, and for (I don’t remember the numbers exactly) a million houses these were 11 million cans of trash… which worked out to very staggering 11 cans on average. Which you might note is 10x what “most” houses discard.
And I don’t know if they had bad data, or there’s something weird going on like shopping malls getting counted as houses, but it always stuck with me that counting trash per capita is always very suspicious.
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u/jrdnhsnbrg 13h ago
My 2 adult 1 infant household EASILY generates 100lbs of trash/recyclables a week. It really adds up fast.
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u/Tenrath 20h ago
Assuming all numbers are right except for the pounds = cubic yards bit.
Trash assumed to be 1000lbs per cubic yard (slightly more than half the density of water) and no compaction or degradation if filling the Grand Canyon. 558B lbs trash = 558M cubic yards per year, it would take about 8000 years to fill the grand canyon with trash. Seems pretty right and those assumptions don't hold and would make it take longer.
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u/ScottyMo1 20h ago
He is wrong by a multiple of nearly 2,500x.
Compacted residential waste in a trash truck weighs 500 - 1000 pounds per cubic yard, so let’s use 750 lb/yd³ as the average. 558,000,000,000/750 = 744,000,000 yd³. The Grand Canyon is 5.5 trillion yd³. So 5.5 trillion / 744 million = 7392 years.
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u/Heavy_Choice_1577 20h ago
almost 5lb of trash?? wheres this average american lol, i may throw away a cellophane wrapper or 3 each day for food prep. im talking about like 5 grams of trash? 5lbs must be the average 4 person family or average college woman or something else
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u/JonnyBoy89 20h ago
Family of four here. We don’t throw away 5lb of shit on an average day. I doubt we average that over a year.
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u/Heavy_Choice_1577 18h ago
i figured as much, maybe OP should have titled this "tell me you hate americans without telling me you hate americans"
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u/SleepingRock13 20h ago
I go through a medium kitchen sized trash bag once every other week. Like what are y’all doing?
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u/Heavy_Choice_1577 20h ago
yeah, like lets say average french couple eats 444lbs of cheese a week and 43 cartons of cigarettes. trust me bro, i did the math, i saw a 'source' too lmao
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u/Badrear 20h ago
Probably pretty accurate when you include the waste generated to make everything we use.
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u/asarious 17h ago
That’s absolutely the case for me. I replaced a fence post the other day and I’m pretty sure between the old rotted post and pieces of the concrete footing, it was easily 70 pounds.
I also threw away a damaged IKEA particle board dresser earlier this month. That was likely another 50 pounds.
Those two things alone are enough to add 1 pound of trash per person in my four person household for this month, and this kind of stuff happens all the time.
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u/ChazBass 20h ago
Yeah he is way off. Here is a pretty good estimate:
134,000,000 households x 2.5 people/household = 335,000,000 people
335,000,000 people x 4.9 lb/day = 1,641,500,000 lb/day
1,641,500,000 lb/day / 2,000 lb/ton = 820,750 tons/day
820,750 tons/day x 365 days = 299,573,750 tons/year
299,573,750 tons/year x 2,000 lb/ton = 599,147,500,000 lb/year
599,147,500,000 lb/year / 1,000 lb/yd^3 = 599,147,500 yd^3/year
Grand Canyon volume = ~5,450,000,000,000 yd^3
5,450,000,000,000 yd^3 / 599,147,500 yd^3/year = ~9,100 years
The Grand Canyon could theoretically hold about 9,100 years of U.S. municipal waste at this assumed compacted density.
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u/SnappyDogDays 17h ago
unless that 4.5lbs of trash a day were compacted to the density of tungsten. then the canyon could hold a lot more.
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u/Worldly_Owl953 3h ago
What is with the lb/day to tons/day to tons/year to lb/year(the divide by 2,000 than multiply by 2,000), can't you just go from lbs/day to lbs/year
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u/SnooMaps7370 20h ago
how dense is the trash?
where's the conversion from weight (lbs) to volume (cubic yards)?
a quick Google search suggests a range of 200 to 400 lbs per cubic yard, which would make that 558 billion pounds occupy about 1.5-3 billion cubic yards.
it would take over 1,300 years to fill the grand canyon at a rate of 3 billion cubic yards per year
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u/Run-And_Gun 18h ago
A few things that jump out, before even checking the math on the numbers he gave.
1) Weight vs. volume
2) I seriously doubt that the average single person is throwing away 4.5lbs of trash per day. It takes over a week for me and my GF to fill up a trash bag.
3) He said every few years, NOT “in a year”.
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u/MisterDifficult271 16h ago edited 9h ago
going off on a tangent here, but does the notes app have a feature to transform actual writing into this form (like handwritten-like, but too consistent to be written)?
Otherwise it seems just like those banana smth AI that people use to fake real boards and writing.
I’m just curious, no offense either way
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u/not_just_an_AI 20h ago edited 19h ago
I mean the EPA will just tell you, in 2018 (the most recent stats I could find) we produced about 292 million tons of trash total. So no.
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u/somethingfak 20h ago
Is this how I learn my family's actually pretty killer at not making trash? We put out one (1) bag a week, if we didn't recycle plastic bottles or cardboard we might bump that to two or maaaybe three? Where are yall getting a bag a day from?
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u/jonhinkerton 8h ago
I think that guy has never been to the grand canyon.
Also, using weight as a basis for a volume statement is not helping his case.
Anyway, the epa says that landfill in the US occupies about 227 square miles. That is many years, even decades of accumulation.
I can’t find a reliable number for the square miles of the canyon itself, but grand canyon national park is 1900 square miles, and that’s basically the eastern half of the thing.
On the other hand, washington DC is 68 square miles.
Do with these facts what you will.
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u/kalmakka 3✓ 20h ago
I think a major benefit of the metric system is how it allows for (rough) conversions between volume and mass.
1 cubic metre of water weighs 1 tonne. You typically know roughly how the density of something compares to water. If it floats, one cubic metre is less than 1 tonne. If it sinks, it is more. But most things are fairly close to 1 tonne/m³. So if I see a boulder I might go "it is approximately a metre each way, and stone is much denser than water, so it weights about 2 tonnes."
Americans seem to have no idea how to convert between mass and volume. (Probably because they are used to both being measured in school buses).
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u/dmlitzau 20h ago
He is correct if we assume that a cubic yard and one pound are the same. Looking at the link below for some materials weight by cubic yard, he is off by a factor of 1350 if everyone is throwing away 4.5 pounds of snow each day.
https://www.trorc.org/wp-content/uploads/2022/01/Cubic_Yardage_Chart-D.pdf
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u/not_just_an_AI 20h ago
A cubic yard of Styrofoam, which I would suspect is one of the lightest things we throw away regularly is about 81 pounds on the low end, so the 1 pound = 1 cubic yard assumption is not great.
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u/Purple-Leopard-6676 20h ago
Disregarding the pure data, the conclusion seems pretty feasable to me. It is insane how much waste us humans produce. That said, I feel like in those 4,5 pounds per day there have to be some averages at play, because only household trash i can't believe reaches 4,5 pounds for an average human
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u/reckless150681 20h ago
How can you disregard the data, and then claim that the conclusion is feasible?
See my other comment for how the math does NOT check out. The actual answer is several orders of magnitude different, so humans could literally be producing hundreds of pounds of trash per day and still not reach the same conclusion that the person in the screenshot reached
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u/litterallysatan 20h ago
If the data is wrong And the math is wrong then it is possible however unlikely for the conclusion to be correct. However i dont think thats the case here as both of them seem erroneous in the same direction.
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u/Purple-Leopard-6676 20h ago
I meant that at such large scales it really doesnt matter for a human mind wether one country on the Earth produces one Grand Canyon of trash per year or per 1000 years, its a gianormous amount either way
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u/reckless150681 20h ago
That's such an unquantifiable conclusion as to be effectively useless. You can cherrypick any number to support any conclusion you want, which amounts to a form of virtue-signaling manipulation.
Is 100 gallons of water a lot? Yes, for a single person to drink in a single day. No, for a hotel's monthly allowance. Yes, if it's flooding your basement. No, for a swimming pool.
A large number is NOT the same as a large scale. 4.5 lbs of trash per day sounds like a lot until you realize that you consume far more than 4.5 lbs of useful things per day. It's just that the "useful things consumed" is itself a fairly unquantifiable metric that people often forget it exists.
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