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View Full Version : A quart of quarters = ??? \$\$\$

Si Amigo
03-11-2007, 12:51 PM
I have several mason jars full of change, about half of them are full of nothing but quarters (the new penny?). It's Sunday and I don't feel up to counting out a tablespoon of quarters and extrapolating that into a quart because I'm certain that A) it's been addressed before (and I'm even to lazy to do a search) or B) some doper keeps this type of knowledge at his fingertips (via google). While we are at it, how much would a quart of pennies or nickles or dimes be worth? Mind you, we are talking about a standard quart size mason jar that has been filled to the point where you can just barely get the cap on, just like you would put your change in at night.

Zeldar
03-11-2007, 01:08 PM
First, I have no idea about the actual count you'd get.

It seems to me that due to the spaces you'll have around the coins, you're liable to get different results with different countings. Settling will help to maximize the number of coins, but except for The Maximum, which I have no idea how you'd calculate, the best I'd think you would get would be a ballpark estimate which might vary by several coins at a minimum.

Just some rendom thoughts.

Si Amigo
03-11-2007, 01:13 PM
Just trying to get a general idea of how much money I have with a minimal amount of effort on my part. :D

DanBlather
03-11-2007, 01:16 PM
\$64

Zeldar
03-11-2007, 01:18 PM
Just trying to get a general idea of how much money I have with a minimal amount of effort on my part. :D

If a ballpark estimate would do, I'd get something like a coffee cup and fill it to the brim and count that. Then take an empty jar and see how many cups of water it would take to fill it. Simplest off-the-cuff solution I can think of. :)

03-11-2007, 01:19 PM
1.) Weigh an empty jar, then a jar full of quarters. Subtract to get the difference. That's the net weight.

2.) Put an ounce of quarters on the scale, and count them.

3.) Multiply the net weight of a full jar x the number of quarters in an ounce.

I'm assuming you have a digital kitchen scale, as I do.

Squink
03-11-2007, 01:26 PM
Numericana Trivia: (http://home.att.net/~numericana/answer/trivia.htm) a gallon would contain [at best] roughly 10500 dimes, 4200 quarters or 2100 half-dollars. Any of these translates into \$1050 per gallon.At 4 quarts per gallon, and knocking it down a bit for edge effects, your mason jar holds a couple hundred bucks in quarters.

Fear Itself
03-11-2007, 02:01 PM
1.) Weigh an empty jar, then a jar full of quarters. Subtract to get the difference. That's the net weight.

2.) Put an ounce of quarters on the scale, and count them.

3.) Multiply the net weight of a full jar x the number of quarters in an ounce.
Divide net weight by 5.670 grams (the weight of one quarter).

Si Amigo
03-11-2007, 02:15 PM
I don't have a scale and I am totally lazy on a Sunday. I'm thinking that there is well over \$250 in there.

drewbert
03-11-2007, 03:35 PM
"The new penny?" Clearly you have a washer/dryer within your own home, lucky dog. :p

Si Amigo
03-11-2007, 04:17 PM
"The new penny?" Clearly you have a washer/dryer within your own home, lucky dog. :p

Actually, no I don't. I spend about \$6 a week in quarters on the laundry and still have more quarters left over than anything else. I started just dropping all my change in jars about five years ago and the quarters are without a doubt the biggest single mass in my collection.

mnemosyne
03-11-2007, 04:25 PM

Sage Rat
03-11-2007, 04:46 PM
I can never seem to find a good link to an image, but just get a change pouch. They don't look girly, and it isn't any more of a hastle to take out a pouch of change than it is to grab your wallet when it comes time to pay.

http://www.magellans.com/store/Wallets__Purses___Totes___BillfoldsLB687?Args=

Get one with a zipper though.

Joey P
03-11-2007, 11:17 PM
Off the top of my head, I'm going to say
Pennies - \$15
Nickles - \$50
Dimes \$175
Quarters - \$200

I'm basing this on having carried hundreds of boxes of coins and having a general idea as to how big a box is vs how much comes in a box.

Bootis
03-12-2007, 05:45 AM
Well, I have 10\$ roll of quarters and a 1 liter bottle (1qt 1.8oz) A 3X3 grid of quarters makes a square the bottle pretty much sits on perfectly, a bit of corners exposed, and 3.5 rolls makes it to halfway between the point where the bottle tapers and the base of the cap (its a stubby bottle, not a slender one) So, the space between the quarters is canceled somewhat be the corners of the square, and there's theres an extra 2 ounces maybe canceled by the tapering, in any case, its reasonably close to a quart of quarters, which is 3.5 rolls X 9 = \$315... so \$300 is a good round estimate I'd say

GiantRat
03-13-2007, 01:06 AM
If a ballpark estimate would do, I'd get something like a coffee cup and fill it to the brim and count that. Then take an empty jar and see how many cups of water it would take to fill it. Simplest off-the-cuff solution I can think of. :)

I don't think that water would be a good test here. Too many open spaces between coin edges. Better to see how many cups of quarters will fit in a mason jar. Even that would be only a guesstimate, though.

Bootis
03-13-2007, 03:00 AM
I don't think that water would be a good test here. Too many open spaces between coin edges. Better to see how many cups of quarters will fit in a mason jar. Even that would be only a guesstimate, though.

It'd be a lot closer than my guess, but im willing to wager that both are under 10% margin of error

Zeldar
03-13-2007, 08:13 AM
I don't think that water would be a good test here. Too many open spaces between coin edges. Better to see how many cups of quarters will fit in a mason jar. Even that would be only a guesstimate, though.

Good point. Good improvement.

BobLibDem
03-13-2007, 08:18 AM
That's a very interesting question. Since the efficiency with which you pack them in is so variable, I don't think a computation would be reliable. Many banks or credit unions have coin counting machines, I'd say dump them in and let us know.

FRDE
03-13-2007, 08:30 AM
In the UK, ASDA, which is owned by Wally World, has change counting machines for coins.

I also used to dump shrapnel in jars, drawers, pots and recently gave the lot to my 'Domestic Hygiene Consultant'. She got a bit confused when it spat out old 50p coins (worth about \$1)

wolf_meister
03-13-2007, 11:06 AM
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.

Spoke
03-13-2007, 11:17 AM
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. :)

wolf_meister
03-13-2007, 11:31 AM
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.

Si Amigo
03-13-2007, 01:45 PM
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. :D

Spectre of Pithecanthropus
03-13-2007, 02:15 PM
"The new penny?"

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.

wolf_meister
03-13-2007, 03:04 PM
Si Amigo
Okay. Sorry if I sounded somewhat overbearing, but this is the Straight Dope and inquiring minds want to know.
Thank you.

Spectre of Pithecanthropus
03-13-2007, 03:37 PM
1.) Weigh an empty jar, then a jar full of quarters. Subtract to get the difference. That's the net weight.

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.

2.) Put an ounce of quarters on the scale, and count them.

3.) Multiply the net weight of a full jar x the number of quarters in an ounce.

I'm assuming you have a digital kitchen scale, as I do.

dgrdfd
03-13-2007, 07:13 PM
I can't wait to find out.

King Friday
03-13-2007, 07:48 PM
All I have to add is...I once had 76 pounds of change and it came to \$583

Si Amigo
03-13-2007, 09:45 PM
Counted by hand. It only came out to \$162.50. Bummer! That's a lot of air.

Jurph
03-13-2007, 09:55 PM
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.

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!

postcards
03-13-2007, 10:14 PM
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?

Si Amigo
03-13-2007, 10:34 PM
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 . . .

wolf_meister
03-14-2007, 01:16 AM
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!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.

Bootis
03-14-2007, 02:37 AM
It'd be a lot closer than my guess, but im willing to wager that both are under 10% margin of error

give or take 40%

Si Amigo
03-14-2007, 11:37 AM
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.

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!

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. :cool:

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. :D

wolf_meister
03-15-2007, 01:39 AM
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: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.
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.

Fear Itself
03-15-2007, 10:26 AM
Would the water fill all the air spaces completely?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.

Auntbeast
03-15-2007, 11:17 AM
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....

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