# A quart of quarters = ??? $$$ **URL:** \ **Category:** Factual Questions\ **Created:** [March 11, 2007, 4:51pm UTC](https://boards.straightdope.com/t/a-quart-of-quarters/395495 "2007-03-11T16:51:42Z")\ **Posts on this page:** 19\ **Page:** 2
**Author:** ![wolf\_meister](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/wolf_meister/32/15202_2.png) [@wolf\_meister](https://boards.straightdope.com/u/wolf_meister)\ **Post date:** [March 13, 2007, 3:06pm UTC](https://boards.straightdope.com/t/a-quart-of-quarters/395495/21 "2007-03-13T15:06:29Z")
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. ---
**Author:** ![Spoke](https://avatars.discourse-cdn.com/v4/letter/s/a88e57/32.png) [@Spoke](https://boards.straightdope.com/u/Spoke)\ **Post date:** [March 13, 2007, 3:17pm UTC](https://boards.straightdope.com/t/a-quart-of-quarters/395495/22 "2007-03-13T15:17:33Z")
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. 🙂 ---
**Author:** ![wolf\_meister](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/wolf_meister/32/15202_2.png) [@wolf\_meister](https://boards.straightdope.com/u/wolf_meister)\ **Post date:** [March 13, 2007, 3:31pm UTC](https://boards.straightdope.com/t/a-quart-of-quarters/395495/23 "2007-03-13T15:31:52Z")
**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_. ---
**Author:** ![Si\_Amigo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/si_amigo/32/2877_2.png) [@Si\_Amigo](https://boards.straightdope.com/u/Si_Amigo)\ **Post date:** [March 13, 2007, 5:45pm UTC](https://boards.straightdope.com/t/a-quart-of-quarters/395495/24 "2007-03-13T17:45:18Z")
[QUOTE=wolf\_meister] **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_. [/QUOTE] 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. 😃 ---
**Author:** ![Spectre\_of\_Pithecanthropus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/spectre_of_pithecanthropus/32/12343_2.png) [@Spectre\_of\_Pithecanthropus](https://boards.straightdope.com/u/Spectre_of_Pithecanthropus)\ **Post date:** [March 13, 2007, 6:15pm UTC](https://boards.straightdope.com/t/a-quart-of-quarters/395495/25 "2007-03-13T18:15:49Z")
[QUOTE=drewbert] “The new penny?” [/QUOTE] 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. ---
**Author:** ![wolf\_meister](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/wolf_meister/32/15202_2.png) [@wolf\_meister](https://boards.straightdope.com/u/wolf_meister)\ **Post date:** [March 13, 2007, 7:04pm UTC](https://boards.straightdope.com/t/a-quart-of-quarters/395495/26 "2007-03-13T19:04:44Z")
**Si Amigo** Okay. Sorry if I sounded somewhat overbearing, but this is the Straight Dope and inquiring minds want to know. Thank you. ---
**Author:** ![Spectre\_of\_Pithecanthropus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/spectre_of_pithecanthropus/32/12343_2.png) [@Spectre\_of\_Pithecanthropus](https://boards.straightdope.com/u/Spectre_of_Pithecanthropus)\ **Post date:** [March 13, 2007, 7:37pm UTC](https://boards.straightdope.com/t/a-quart-of-quarters/395495/27 "2007-03-13T19:37:04Z")
[QUOTE=AskNott] 1.) Weigh an empty jar, then a jar full of quarters. Subtract to get the difference. That’s the net weight. [/quote] 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. ---
**Author:** ![dgrdfd](https://avatars.discourse-cdn.com/v4/letter/d/eb8c5e/32.png) [@dgrdfd](https://boards.straightdope.com/u/dgrdfd)\ **Post date:** [March 13, 2007, 11:13pm UTC](https://boards.straightdope.com/t/a-quart-of-quarters/395495/28 "2007-03-13T23:13:45Z")
I can’t wait to find out. ---
**Author:** ![King\_Friday](https://avatars.discourse-cdn.com/v4/letter/k/43a26b/32.png) [@King\_Friday](https://boards.straightdope.com/u/King_Friday)\ **Post date:** [March 13, 2007, 11:48pm UTC](https://boards.straightdope.com/t/a-quart-of-quarters/395495/29 "2007-03-13T23:48:38Z")
All I have to add is…I once had 76 pounds of change and it came to $583 ---
**Author:** ![Si\_Amigo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/si_amigo/32/2877_2.png) [@Si\_Amigo](https://boards.straightdope.com/u/Si_Amigo)\ **Post date:** [March 14, 2007, 1:45am UTC](https://boards.straightdope.com/t/a-quart-of-quarters/395495/30 "2007-03-14T01:45:50Z")
Counted by hand. It only came out to $162.50. Bummer! That’s a lot of air. ---
**Author:** ![Jurph](https://avatars.discourse-cdn.com/v4/letter/j/50afbb/32.png) [@Jurph](https://boards.straightdope.com/u/Jurph)\ **Post date:** [March 14, 2007, 1:55am UTC](https://boards.straightdope.com/t/a-quart-of-quarters/395495/31 "2007-03-14T01:55:26Z")
[QUOTE=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\*\*. [/QUOTE] 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! ---
**Author:** ![postcards](https://avatars.discourse-cdn.com/v4/letter/p/8e8cbc/32.png) [@postcards](https://boards.straightdope.com/u/postcards)\ **Post date:** [March 14, 2007, 2:14am UTC](https://boards.straightdope.com/t/a-quart-of-quarters/395495/32 "2007-03-14T02:14:03Z")
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? ---
**Author:** ![Si\_Amigo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/si_amigo/32/2877_2.png) [@Si\_Amigo](https://boards.straightdope.com/u/Si_Amigo)\ **Post date:** [March 14, 2007, 2:34am UTC](https://boards.straightdope.com/t/a-quart-of-quarters/395495/33 "2007-03-14T02:34:00Z")
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 . . . ---
**Author:** ![wolf\_meister](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/wolf_meister/32/15202_2.png) [@wolf\_meister](https://boards.straightdope.com/u/wolf_meister)\ **Post date:** [March 14, 2007, 5:16am UTC](https://boards.straightdope.com/t/a-quart-of-quarters/395495/34 "2007-03-14T05:16:52Z")
> [@](#): > > 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**. ---
**Author:** ![Bootis](https://avatars.discourse-cdn.com/v4/letter/b/e8c25b/32.png) [@Bootis](https://boards.straightdope.com/u/Bootis)\ **Post date:** [March 14, 2007, 6:37am UTC](https://boards.straightdope.com/t/a-quart-of-quarters/395495/35 "2007-03-14T06:37:29Z")
[QUOTE=Bootis] It’d be a lot closer than my guess, but im willing to wager that both are under 10% margin of error [/QUOTE] give or take 40% ---
**Author:** ![Si\_Amigo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/si_amigo/32/2877_2.png) [@Si\_Amigo](https://boards.straightdope.com/u/Si_Amigo)\ **Post date:** [March 14, 2007, 3:37pm UTC](https://boards.straightdope.com/t/a-quart-of-quarters/395495/36 "2007-03-14T15:37:09Z")
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. [QUOTE=Jurph] 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! [/QUOTE] 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. 😃 ---
**Author:** ![wolf\_meister](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/wolf_meister/32/15202_2.png) [@wolf\_meister](https://boards.straightdope.com/u/wolf_meister)\ **Post date:** [March 15, 2007, 5:39am UTC](https://boards.straightdope.com/t/a-quart-of-quarters/395495/37 "2007-03-15T05:39:05Z")
**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. ---
**Author:** ![Fear\_Itself](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/fear_itself/32/19637_2.png) [@Fear\_Itself](https://boards.straightdope.com/u/Fear_Itself)\ **Post date:** [March 15, 2007, 2:26pm UTC](https://boards.straightdope.com/t/a-quart-of-quarters/395495/38 "2007-03-15T14:26:07Z")
[QUOTE=wolf\_meister] Would the water fill all the air spaces _completely_? [/QUOTE] 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. ---
**Author:** ![Auntbeast](https://avatars.discourse-cdn.com/v4/letter/a/5f9b8f/32.png) [@Auntbeast](https://boards.straightdope.com/u/Auntbeast)\ **Post date:** [March 15, 2007, 3:17pm UTC](https://boards.straightdope.com/t/a-quart-of-quarters/395495/39 "2007-03-15T15:17:54Z")
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… [Previous page](https://boards.straightdope.com/t/a-quart-of-quarters/395495.md?page=1)