# A quart of quarters = ??? \$\$\$

Going to the US Mint website, the dimensions of a quarter are:
24.26 mm diameter and 1.75 mm thickness.
This would make a cylinder volume of 808.93 cubic millimeters.
One US Quart = 946,350 cubic millimeters and so
1 quart = 946,350 / 808.93 = 1,170 Quarter volumes.
Obviously we are not going to get 100% packing efficiency with quarters and so there will be some spaces between the quarters. I remember when I had to do a huge amount of coin rolling, I wanted to make rough estimates too. I found (and feel free to debate this) that even the tightest packing of coins would only result in about 50% of the theoretical volume.
So, even though a quart contains 1,170 Quarter Volumes, allowing for air spaces between quarters, this would reduce the figure to 585 quarters or** \$146.25**.

I think this would be in rough agreement with Joey P’s \$200 estimate.

Si Amigo, are you going to post the results you get? Even if you say a cup of quarters is worth \$36.50, that would be a start.

For some reason, the OP reminds me of a (possibly apocryphal) Civil War story:

A general was on a riverbank, discussing with his staff how deep the river might be, while his troops waited to cross. The whole operation was at a standstill while the officers debated the question. George Custer, then a junior officer, rode his horse into the water and yelled back, “It’s this deep, General!”

Just count the damn quarters.

spoke-
Yeah, that’s what I thought (hence the last paragraph in my previous posting).

At least count a cupful of the damned things and let us know that.

Sunday I was too lazy to count them and today it is 72 degrees and sunny for the first time this year. Those damn quarters will have to wait until late tonight.

Well, considering that fifty of them will barely get you a couple of combo meals at Carl’s Jr., I’d say it’s pretty apt.

Well, OK, maybe we can call them the new nickel.

Si Amigo
Okay. Sorry if I sounded somewhat overbearing, but this is the Straight Dope and inquiring minds want to know.
Thank you.

Assuming you have more than enough quarters to completely fill the jar, you should fill and weigh the jar several times and take the average to get the loaded weight.

I can’t wait to find out.

All I have to add is…I once had 76 pounds of change and it came to \$583

Counted by hand. It only came out to \$162.50. Bummer! That’s a lot of air.

Great estimate, wolf_meister. Solid logic, just over 10% error in the estimate, and 10% to the right side. You can be on my project planning team any day!

Now that that’s answered, anyone want to take a crack at a five-gallon (plastic) water bottle filled entirely with pennies?

Or should I start my own thread?

If we assume the same ratio of ideal volume to observed volume for the quarters it should be easy enough to calculate for all denominations of coins. A worthy task for our calculating commarades. Myself, I’m still upset over my loss of perceived richs to add anymore or do any calculating. Although I do have quite a but of change and some punt size mason jars in order to settle any conflicts . . .

Thank you Jurph.

Okay, let’s determine the “packing efficiency” of quarters and assume it will be roughly the same for all coins.

The theoretical number of quarters in a quart is 1,170.
Si Amigo has counted out 650 quarters in a “quart of quarters”.
This represents a packing efficiency of 55.55%
That is: (650/1,170) * 100 = 55.55%
(My estimate of 50% from personal experience was a little low).

postcards
Okay, so you have a 5 gallon jar filled with pennies.

A US cent has a 19.05 mm diameter and a thickness of 1.55 mm which is a “cylinder” of 441.79 cubic millimeters.
The volume of five US gallons is 18,927,000 cubic millimeters.
So at 100% packing efficiency, we have 42,842 penny volumes.
Using Si Amigo’s 55.55%, this reduces the number of pennies to 23,799 with a value of \$237.99 or rounded off to \$238.00.

give or take 40%

Quote:
Originally Posted by wolf_meister
So, even though a quart contains 1,170 Quarter Volumes, allowing for air spaces between quarters, this would reduce the figure to 585 quarters or \$146.25.

It was even better than that because I gave the total as the mason jar filled to the rim! If you take away quarters until you get to the liquid quart level I suspect that he is within +/- 2%. That’s pretty much dead on in my book.

I actually came up with another method by using liquid displacement. I could have filled the jar up to the quart level line with quarters and then filled the jar with water. Then I could have poured the water into a measuring cup (which I have) and gotten a very accurate measure of the volume of the air space in the jar. Knowing that and the ideal volume of a quart of quarters I could have figured it all out without having to count.

I like being an engineer, its a field were being lazy can be disguised as being efficient.

Si Amigo
I appreciate the fact that you posted an update to your earlier research (especially when it shows my estimate was even closer than previously believed ).

Also, it’s good you alerted me to this because I was preparing to publish my research paper “Mason Jar Determination of an Empirical to Theoretical Coin Packing Ratio”. Of course proper credit would have been attributed to you. What do you think the ratio should be called?
The Si Amigo factor … coefficient … constant … ???

Okay getting a little more serious here, you mentioned another method you could have tried:

That method has 2 ways in which errors can be introduced:

• Would the water fill all the air spaces completely?
• When you emptied the water to measure it, wouldn’t some of the water stay adhered to the coins? One way around this would be to take note of the volume of water in the measuring cup *before *and *after *it is poured into the jar of quarters, allowing a much more accurate measurement.

Of course this does not solve the problem of having the water completely replacing the air space.

You could reduce this problem by adding a surfactant to the water, like a little dish detergent that reduces surface tension, allowing the water to more fully penetrate air spaces. Then place the jar on a vibrating surface to dislodge any air pockets; the result should render insignificant any error due to air spaces.

How many engineers does it take to count a mason jar full of quarters?

There’s gonna be a huge Rube Goldberg machine made soon…