Cost and Size of a Lego Minifigure Scale Earth

[drdesignz]

A Lego minifigure is 1.5 inches tall. Let's say the average human height is 5'-6". That means, considering height only, not size, a Lego minifig is 1:44 scale.

The mean radius of earth 6,371 km, or about 3,959 miles, so that's a diameter of about 7,918 miles with a surface area of about 196,939,900 square miles. That means a minifig scale earth at a scale of 1:44 would be about 180 miles wide, which is roughly the driving distancebetween New York City and Baltimore.

The surface area is (4)pi90^2, which equals about 101,788 square miles. That's about the size of the state of Colorado.

According to this calculator, it would take approximately 142 billion Lego bricks to cover a square mile, at a cost of 14.1 billion dollars (USD). So, for an entire Lego minifig scale earth, completely hollow, that would be about 14,453,896,000,000,000 Lego bricks.

That's nearly 14.5 quadrillion. Which, at the current rate of production of about 19 billion Lego elements per year, would take about a million years to produce. It is also about 30,000 times the total number of bricks produced since the company was started.

14.5 quadrillion Lego bricks has an approximate retail value of nearly 1.5 quadrillion dollars. That's roughly 700 times the USD monetary base, or over 20 times the entire world's GDP.

Edited October 24, 2012 by drdesignz

[Ferrik]

Interesting facts you have there. Now, I'd like to see someone build the Earth in lego form in actual Earth size.

[Hey Joe]

We need more Lego. Can you explain it to my wife? She just doesn't get it.

[PsyKater]

Thanks for the facts, drdesignz! They made me laugh a lot.

We need more Lego. Can you explain it to my wife? She just doesn't get it.

Edited October 2, 2012 by PsyKater

[L@go]

This is one of the best posts I've read in a long time. Funny, interesting and totally useless. Brilliant - thanks for the laugh!

[Pennas2000]

We need more Lego. Can you explain it to my wife? She just doesn't get it.

[CamelBoy68]

The surface area is (4)pi180^2, which equals about 407,150 square miles. That's about one and a half times larger than Texas, or how much land Bolivia has.

What about the inside...?

Also, are you just building the flat surface, you would need to add mountains and such like.....

Don't forget the Fjords.....[/slartibartfast]

[freakwave]

The only problem I see when you start constructing it:

How to tell NASA to move the ISS out of the way...

[purpleparadox]

...All that did for me was make me wanna buy more LEGO! Interesting read, though. Thanks!

[Aanchir]

Now the real question is, does enough crude oil exist on the planet to make that much ABS plastic, and how much would it end up costing TLG in raw materials to obtain it? Or would we have to go to Saturn's moons for this kind of endeavor?

Very neat observations. I've never seen people calculate this kind of thing. It almost makes some of the LEGO Star Wars dream projects, like a minifigure scale Executor, seem feasible by comparison.

[CamelBoy68]

Now the real question is, does enough crude oil exist on the planet to make that much ABS plastic, and how much would it end up costing TLG in raw materials to obtain it? Or would we have to go to Saturn's moons for this kind of endeavor?

Saturn moons have dead dinosaurs......

[JopieK]

I think the earth will also loose it's balance with such a large ball :)

[Bricktooth]

I find it interesting and yet incredibly hilarious that some people actually have time to get these numbers. I'm not saying this to offend anyone who worked on getting those numbers, but I can't help but laugh when someone calculates how many bricks it takes to build a minifig-scale Earth or Death Star (I remember someone did that as well).

BTW this topic should really run for the title of the most weird topic ever, it would have a great chance of winning. I'm interested in where this will get...

[spzero]

Great read thanks for the legwork. lol

[drdesignz]

I find it interesting and yet incredibly hilarious that some people actually have time to get these numbers. I'm not saying this to offend anyone who worked on getting those numbers, but I can't help but laugh when someone calculates how many bricks it takes to build a minifig-scale Earth or Death Star (I remember someone did that as well).

BTW this topic should really run for the title of the most weird topic ever, it would have a great chance of winning. I'm interested in where this will get...

It did not take very long, especially with online resources. I might do some graphics at some point later, too.

Here is the Death Star article, for anybody interested.

[Aanchir]

Saturn moons have dead dinosaurs......

No, but Titan has hydrocarbon seas. Though I suppose I was drawing a blank on my astronomy/chemistry, since those are things which in Earth's environment would be considered natural gases-- usable as fuel but probably not to make plastics in any environment.

You want to find dead dinosaurs in space, you'd have to look elsewhere.

[CamelBoy68]

No, but Titan has hydrocarbon seas.

So that will save a bit of cash, no need for drilling equipment.....

[davee123]

Hm... I get some different numbers. If you're assuming a minifig's height at 1.5" (38.1mm), and a ratio of 1:44, that should put the surface area at whatever the Earth's surface are is, divided by 1936 (44^2). Going by Wikipedia's estimate for the surface area of the Earth (510,072,000 km^2), that should be about 263,466.9421 km^2, or about 101,725.1551 square miles. (I think you took the diameter of 180 miles instead of the radius of 90 miles)

As for the bricks/square mile number? I'm not sure how that number came about-- I get that it would take 5,058,570,528 bricks to cover a square mile (5 billion rather than a whopping 142 billion). So, for the surface layer alone (assuming you could get all those rectangular edges to line up perfectly, which you obviously couldn't do), you'd need about 514 trillion 2x4 bricks (514,584,000,000,000).

I'm not sure how out-of-date the production numbers are per year-- That's always questionable to me, because nobody likes to source their data-- even the internal LEGO staff! They often just take the numbers that were published before, and use those, so the number that Gizmodo published in 2008 may have been a few years old at the time, which may-or-may not include Chinese and Mexican production. But at 19.1 billion per year, that's 26,941.56 years at the current rate of production!

... But that's to make just the surface-- it wouldn't hold together, and you couldn't really arrange the pieces evenly because of the curvature. What about if you filled it? The volume of the Earth is supposedly 1.08321 km^3, and the volume of a 2x4 brick is about 4915.2 mm^2 (excluding the studs, which will overlap inside of adjacent bricks). So you'd need about 2.6 sextillion bricks (2,587,100,000,000,000,000,000) in order to make the full sphere.

How much mass would it have? Assuming BrickLink's estimated weight of 2.32g per brick, that'd be 6 quintillion kilograms (6,002,080,000,000,000,000 kg), which is in the ballpark of 1/1000th of all the water on Earth.

Do we have enough oil? I don't know offhand. I once found a reference for roughly what percentage of ABS was oil (and it was something pretty small, like 1-5%). But a quick few Google searches haven't yielded me anything nice. Assuming my memory is correct at about 1%, we'd need 60 quadrillion kg (60,020,800,000,000,000 kg) of oil. However, I'm not sure that ABS actually uses crude oil-- IIRC it can use things like vegetable oil instead? I'm not sure. Call in the chemists!

DaveE

[drdesignz]

Hm... I get some different numbers. If you're assuming a minifig's height at 1.5" (38.1mm), and a ratio of 1:44, that should put the surface area at whatever the Earth's surface are is, divided by 1936 (44^2). Going by Wikipedia's estimate for the surface area of the Earth (510,072,000 km^2), that should be about 263,466.9421 km^2, or about 101,725.1551 square miles. (I think you took the diameter of 180 miles instead of the radius of 90 miles)

Thanks for checking the math. I'll check it again later and update the original post.

As for the bricks/square mile number? I'm not sure how that number came about-- I get that it would take 5,058,570,528 bricks to cover a square mile (5 billion rather than a whopping 142 billion). So, for the surface layer alone (assuming you could get all those rectangular edges to line up perfectly, which you obviously couldn't do), you'd need about 514 trillion 2x4 bricks (514,584,000,000,000).

That number came from the online calculator I linked to. It's simply a rough estimate. And it's not a flat surface, it's actual shape and structure. The calculator estimate considers the equivalent of bricks to build a one storey house, one square mile large. It seems like 5 billion would be a flat square mile surface, correct?

I'm not sure how out-of-date the production numbers are per year-- That's always questionable to me, because nobody likes to source their data-- even the internal LEGO staff! They often just take the numbers that were published before, and use those, so the number that Gizmodo published in 2008 may have been a few years old at the time, which may-or-may not include Chinese and Mexican production. But at 19.1 billion per year, that's 26,941.56 years at the current rate of production!

... But that's to make just the surface-- it wouldn't hold together, and you couldn't really arrange the pieces evenly because of the curvature. What about if you filled it? The volume of the Earth is supposedly 1.08321 km^3, and the volume of a 2x4 brick is about 4915.2 mm^2 (excluding the studs, which will overlap inside of adjacent bricks). So you'd need about 2.6 sextillion bricks (2,587,100,000,000,000,000,000) in order to make the full sphere.

How much mass would it have? Assuming BrickLink's estimated weight of 2.32g per brick, that'd be 6 quintillion kilograms (6,002,080,000,000,000,000 kg), which is in the ballpark of 1/1000th of all the water on Earth.

Do we have enough oil? I don't know offhand. I once found a reference for roughly what percentage of ABS was oil (and it was something pretty small, like 1-5%). But a quick few Google searches haven't yielded me anything nice. Assuming my memory is correct at about 1%, we'd need 60 quadrillion kg (60,020,800,000,000,000 kg) of oil. However, I'm not sure that ABS actually uses crude oil-- IIRC it can use things like vegetable oil instead? I'm not sure. Call in the chemists!

DaveE

Clearly the whole idea is preposterous! That's the point, it's just a fun idea to think about. But I would like the math to be as accurate as possible. Thanks for the feedback and additional information.

[Hrw-Amen]

Maybe NASA could use this model Earth as a space ship if it were hollow, could it be filled with a breathable gas? Also would if it were hollow stand up to its own mass, or would it collapse into a Black LEGO Hole sucking all other LEGO into it?

What we would need would be something like a King Midas, but for LEGO to go around turning everything instantly into LEGO bricks. Perhaps a King LEGOlas or something similar. That way you could create a full scale model Earth made out of LEGO just by getting him to roll around on the surface. You would have to make sure to stay out of the way yourself though or be turned in to a massive mini-fig!.

[davee123]

That number came from the online calculator I linked to. It's simply a rough estimate. And it's not a flat surface, it's actual shape and structure. The calculator estimate considers the equivalent of bricks to build a one storey house, one square mile large. It seems like 5 billion would be a flat square mile surface, correct?

Ahh, OK, that explains it. I thought 142 billion sounded rather off-- I think you may want to delve into that number more precisely rather than using the calculator, though, unless you know how it works. Does it (for instance) assume a 1-square-mile house has a floor, ceiling, and 4 1-mile walls? Or does it assume support structure (like interior walls) at regularly placed intervals? As is, it would be 28 bricks thick, which is probably sufficient to hold a lot of weight, but I don't know how much.

As for a flat vs. textured surface, I don't think it affects things too much. Probably affects the number by much less than 1%, considering that most of the surface is water.

Another interesting prospect would be just making the surface out of 48x48 baseplates, which would take 1.8 trillion (1,786,750,000,000) baseplates. Yikes!

DaveE

Edited October 2, 2012 by davee123

[drdesignz]

I think you may want to delve into that number more precisely rather than using the calculator, though, unless you know how it works.

That info is here: http://www.movoto.com/blog/novelty-real-estate/build-your-house-out-of-legos/

Here is some detailed information for Lego geometry: http://www.robertcailliau.eu/Lego/Dimensions/zMeasurements-en.xhtml

The bottom line is, it's impossible to come up with an exact quantity of Lego bricks for such a concept. Although, you could somewhat accurately calculate the number of bricks required for a large hollow sphere, if all bricks were the same size. A solid sphere would also be possible, I suppose. Either way the numbers are astronomical.

[davee123]

That info is here: http://www.movoto.com/blog/novelty-real-estate/build-your-house-out-of-legos/

Uh oh:

We came up with this figure by first figuring out the size of a standard eight-peg LEGO in inches. We found an excellent resource on LEGO brick dimensions and with some converting from millimeters to inches we had the size of a LEGO: about .26 x .62 x 1.22 inches.

Ouch.

A 2x4 brick measures 9.6mm x 16mm x 32mm. That translates to 0.378" x 0.630" x 1.260". They need a lesson in metric conversion, apparently!

After we figured this out we researched the standard size of a brick in the States: 2 1/4 x 4 x 8 inches. The end result: 359 LEGOs per brick.

That's about 12.7 studs x 25.4 studs x 5.9 bricks. If they went for "roughly-same-size-but-complete" brick, I'd go with about 12 studs wide by 26 studs long by 6 bricks tall. Using 2x4 bricks, I'd lay them out in rows such that they were 3 2x4's laid end-to-end to make up the width, then 13 side-by-side to make up the length, and stacked 6 tall. So, 3x13x6, or 234 per brick, not 359, which is off by quite a quite a lot, considering that this is going to be the base of their calculations! Otherwise, if you went for an average (as in, it'll average out over distance), it's about 240.04 per brick-- still off by a more than 100 bricks!

Then there's the fact that they seem to be basing their estimate for bricks based solely on the exterior walls of the house-- not including the floors/ceilings, roof, foundation, or interior structure.

[edit]Also, they're basing their information on some guy's response on Quora. He doesn't take mortar into account, and assumes a 1500 square foot house would be "for simplicity" 15'x100', which is 230' of perimeter, rather than something more realistic, like 30'x50', which would be 160' perimeter (the ratio matters quite a lot!). Also, the Quora post doesn't account for pitched roofs, windows, doors, or other things-- it's just some guy trying to estimate using math, without taking into account any features of reality. ... Not that it really matters for the purposes of making a LEGO house, since you may not WANT a pitched roof, and you DON'T want to include mortar (which just adds extra spacing).

FWIW, my guess for the Quora post is roughly 9,100 bricks, assuming 30'x50', 1 storey, hip roof, 0.5" mortar spacing, 12 windows, 2 exterior doors, based on a more-or-less standard floorplan layout. That's just under half of the answer given (18,400), which (if correct) means that the calculator is off by a factor of 2, just in the number of bricks needed, plus an extra 50% over-estimation based on the incorrect brick size. (I admittedly didn't take into account the overlap in corners, but that shouldn't add too much) So, about 250% overestimation for that calculator, if I'm reading it right.

The far better source for a LEGO house would be to assume that it would follow the "James May Standard", using the large-scale assembled bricks that they used. The math involved is simple enough-- why would they bother trying to trace it back to some extremely sketchy Quora post?[/edit]

Color me unimpressed with their calculator :(

The bottom line is, it's impossible to come up with an exact quantity of Lego bricks for such a concept. Although, you could somewhat accurately calculate the number of bricks required for a large hollow sphere, if all bricks were the same size. A solid sphere would also be possible, I suppose. Either way the numbers are astronomical.

Yeah, the practicality is so out-the-window that the exact figures don't make much sense-- but they can provide you with some idea of just how astronomically large such a construction would be!

DaveE

Edited October 2, 2012 by davee123

[drdesignz]

Well, I lost all of the calculation fixes and updates. I'll redo the work again shortly...

[Saberwing40k]

It might actually be easier to build a Star Destroyer than the entire planet, as I've seen some aircraft carrier models. It would still be pretty big, just look at this pic: