It is funny to watch Neil deGrasse Tyson. I think the does a really nice job even when speaking around politics. Ok, inspect out this video from actual Time v Bill Maher:

Not that ns don't to trust him, but I guess: v I want to check. Would one trillion dollar (1 dollar bills i assume) stack to the moon and earlier four times?

## How special is one dollar?

I don't usually bring cash in my wallet, however when I perform I measure up it. There were 5 bills. Ns measured the thickness of just one, climate two and so forth. ~ all 5 were stacked, I started folding them over. Here is a picture.

You are watching: How tall is a stack of 1 billion dollar bills

Yes, this would be complicated to measure through a ruler. The maker above is a micrometer. Ok, what around the data. Below is a plot of the measured thickness (in mm) vs the variety of bills. Oh, ns am assuming that a 5 dollar bill is the very same thickness as a 1 disagreement bill.

I included a direct regression line v the data. It has actually a steep of 0.1 mm/bill. So, I will certainly go v that value.

## How tall would certainly a sunshine dollar stack be?

First, what is one trillion of anything? Sadly, no everyone agrees. In the USA, one trillion is 1,000 billion or 1012. In some various other countries, one trillion means 1018. (see Wikipedia's page on brief scale vs. Long scale)

So, if ns stack 1012 bills, exactly how high would certainly it be? First, let me assume the the bills don't obtain compressed. Why am ns assuming that? i don't know. The height of this stack would certainly be:

The distance from the earth to the Moon is about 4 x 108 meters. Okay, now there is a problem. Follow to mine calculations, the ridge of one sunshine dollar bills would go one fourth of the way to the moon. Neil claimed it would go there and back four time (which would certainly be 32 x 108 meters). His calculation of the elevation of the stack is 32 time too big (or mine is also small).

Let me shot one various other thing. If one trillion dollars goes to the moon and ago four times, just how thick would certainly it have to be?

3 mm thick bills would be fairly awkward. So, ns think Neil messed up. It's ok. It happens to united state all. Just don't make a habit of that (although the did acquire the explanation for the tides wrong also). Anyway, the whole point would have been ruined. Might you imagine Neil speak this:

*"Oh, and also I would just like to allude out something around a trillion. Go you understand that if you stack one trillion dollar bills, it would make it one 4th of the way to the moon?"*

Oh well, what various other things can we do with one sunshine dollars?

## Stacking and stability

Suppose you might stack the bills perfectly. As the stack gets greater and higher, it would be more likely to loss over native a slight nudge. Let me start with a block.

For each stack, the red period represents the center of mass. If the stack is tilted such that the center of mass goes over the edge of the base, the stack falls over. Yes, i am suspect the receipt stick together. But you have the right to see that the taller the stack gets, the smaller the "tilt" angle would certainly be for it to autumn over.

If the basic of the bill has actually a broad *w* and also length *t*. For tipping towards the diluent side of the bill, we have a best triangle.

Solving because that θ:

Now, suppose the broad of the disagreement is 6.6 cm. Would would a plot the this "tipping angle" as a function of height look prefer for a stack from 1 meter tall to 10 meters tall.

So a 10 meter tall stack that bills would certainly only should be tilted 0.37° because that it to be at the tipping point. Here is a plot for heights indigenous 100 meter to 10,000 meter stacks. I had actually to make the vertical range a log-plot.

Ok, what if i take this as much as 106 meters tall? That would certainly be a tipping edge of 3.8 x 10-6°. And a trillion dollar stack (assuming the was all in a continuous gravitational field - which it wouldn't be) that would have a tipping edge of 3.8 x 10-8°. Simply for a comparison, Alpha Centauri A (a star) has an angular diameter of 1.9 x 10-6 °.

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## Is the even feasible to stack paper this high?

Suppose you could stack the bills and also they wouldn't autumn over (and again assuming consistent gravitational field). Would certainly the bills at the bottom that the stack be able to maintain this weight? Ok, so ns already collection up something prefer this because that the compressive strength of absent (when talking about the height of pyramids) Essentially, the paper can only take so much pressure before bad stuff happens. The allude where bad stuff wake up is dubbed the compressive strength. I don't know about paper, however wood has a a compressive strength from 3 to 27 MPa. Because that this case, ns am just going come randomly pick 20 MPa as the compressive strength of a bill.

What is the push at the bottom the the stack? Well, that would certainly be the weight of the stack over the area of a bill. Suppose a bill has actually area of 6.6 cm by 15.6 cm. This means the pressure at the bottom would be: