# Formula for estimating change in a jar?
**URL:** https://boards.straightdope.com/t/formula-for-estimating-change-in-a-jar/671751
**Category:** Factual Questions
**Created:** [October 20, 2013, 9:16pm UTC](https://boards.straightdope.com/t/formula-for-estimating-change-in-a-jar/671751 "2013-10-20T21:16:42Z")
**Posts on this page:** 20
**Page:** 2
### Author:  [@Shagnasty](https://boards.straightdope.com/u/Shagnasty)
#### Post date: [October 21, 2013, 3:19am UTC](https://boards.straightdope.com/t/formula-for-estimating-change-in-a-jar/671751/21 "2013-10-21T03:19:35Z")
The others are right, There are no ways of getting a truly accurate measure other than just counting the coins. The missing factor is someone’s spending patterns. Other people got the ratios of average coins stored correct assuming it is truly random but it hardly ever is. It depends on what you buy and what you put in the jar. I spend quarters freely for example but I throw pennies, nickles and dimes into my coin jar. Quarters are the highest value common coin so how you treat those can greatly influence the total value of the jar.
The best way to approach this problem is through statistical trials of similar circumstances. A given person with the same coin jar will end up with very similar value for a given volume of coins. It will also be extremely similar to other people with the same habits.
I can tell you what the result will be within reason for a pickle jar that size because I have done it before myself. It is between $200 and $300 like other people said. My pick is $283.16. Go to a Coinstar machine and check it and post the results. Pro-tips: Most of them offer gift cards from major retailers so it doesn’t cost you anything if you have a place to spend it. Rolling coins to take to the bank is a fool’s errand. Also, lift the sorting tray up with your fingers so that it is at a downward angle the whole time and then just scrape the coins in with your fingers. Many people don’t do it correctly and it takes 5x longer than necessary.
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### Author:  [@pulykamell](https://boards.straightdope.com/u/pulykamell)
#### Post date: [October 21, 2013, 4:02am UTC](https://boards.straightdope.com/t/formula-for-estimating-change-in-a-jar/671751/22 "2013-10-21T04:02:24Z")
> [@Shagnasty](#):
>
> I can tell you what the result will be within reason for a pickle jar that size because I have done it before myself. It is between $200 and $300 like other people said.
Well, actually, I think our spread is much higher than that. I said $150-$200 for the half-filled gallon jar, based on $300-$400 per gallon of mixed change. **Leo Bloom** ’s site that 39 oz of roast coffee beans would equal .67 gallons and **Hail Ant** ’s reporting that such a filled container returned $350 would put it at $522 per gallon (!), which seems high to me.
[This guy](http://www.youtube.com/watch?v=hrbGPY4KJ2w) got $2212.30 out of a filled-to-the-brim 5 gallon jar, for $442.46 per gallon. Now, my hunch is that is not going to downscale perfectly, and you’re going to get a good bit less per gallon with a one gallon jar, but that should leave you in the $300-$400 per gallon range.
That said, as you said, it depends on your spending habits and what change you save. I tend to pick quarters out of the change pile or my pocket, so that would influence the count. If the OP really does have an equal distribution, I could believe the higher end of the estimate.
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### Author:  [@dtilque](https://boards.straightdope.com/u/dtilque)
#### Post date: [October 21, 2013, 4:42am UTC](https://boards.straightdope.com/t/formula-for-estimating-change-in-a-jar/671751/23 "2013-10-21T04:42:46Z")
As I understand it, most banks no longer want human-rolled coins. Too many people try to use them for fraud. So don’t waste your time rolling your own. Just bring them in loose and let them run them through their machine. My bank, in fact, has a self-serve coin counting machine in the lobby. I just put all my loose change into it and it gives me back a receipt that I take to the teller to deposit. And I don’t have to pay anyone 9% for this service.
However, I rarely use this machine. Nowadays, I usually get rid of my coins by spending them. But then I buy lots fo stuff with cash that most people use credit cards for, such as groceries and gasoline. I try to (and usually succeed in) paying exact change in these transactions.
But I do have a jar of coins, well two of them. But the coins in them don’t come from my change, but rather a different source. I bicycle a lot, and about 10 years ago started noticing a lot of coins on the side of the roads. For reasons I can’t quite explain, I started to pick them up and put them in jars. I only put found coins in these jars, never change from transactions. One jar is full, the other is about 75% full. They’re one-quart mayonaise jars, although the full one is packed to the brim, so it’s closer to a liter of coins.
Some day I’ll probably take them to the bank to have them counted. I expect numerous rejects by the machine, though, especially the pennies. You see, it doesn’t take too many times being run over before pennies lose most of their copper coating. I assume the machines go by the electrical properties of the coins and roadkilled pennies will not have the same properties as ordinary ones.
Well, if I ever do cash them in, I’ll have a guess-the-total contest in the Game Room or somewhere. But I’m in no hurry to do that.
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### Author:  [@Leo\_Bloom](https://boards.straightdope.com/u/Leo_Bloom)
#### Post date: [October 21, 2013, 5:11am UTC](https://boards.straightdope.com/t/formula-for-estimating-change-in-a-jar/671751/24 "2013-10-21T05:11:17Z")
> [@pulykamell](#):
>
> … **Leo Bloom** ’s site that 39 oz of roast coffee beans would equal .67 gallons …
[nitpick]
0.68
[/nitpick]
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### Author:  [@TimeWinder](https://boards.straightdope.com/u/TimeWinder)
#### Post date: [October 21, 2013, 5:14am UTC](https://boards.straightdope.com/t/formula-for-estimating-change-in-a-jar/671751/25 "2013-10-21T05:14:40Z")
> [@chacoguy](#):
>
> What’s a $2 coin?
Welcome to the Internet, now available in countries other than the US of A!
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### Author:  [@septimus](https://boards.straightdope.com/u/septimus)
#### Post date: [October 21, 2013, 8:23am UTC](https://boards.straightdope.com/t/formula-for-estimating-change-in-a-jar/671751/26 "2013-10-21T08:23:27Z")
> [@Leo\_Bloom](#):
>
> There must be a math expression governing the result/problem. Right? Right??!
If each coin is an integral multiple of the smaller coins, it would be easy. For example, if no dimes were used then average change would be 1.5 quarters, 2 nickels and 2 pennies. (These sum to $0.495 as expected.) With K pieces of a quadloon, (K-1)/2 is the expected number of pieces; there are K=4 quarters in a dollar, so (4-1)/2 = 1.5 is expected, and so on.
Multiply these numbers by 100 to get (except for the dimes and nickels) the numbers Chronos posted:
150 : 0 : 200 : 200
Quarters do not have a whole number of dimes, so allowing dimes complicates. Simplest is to just write a table showing how the five equally probable cases of nickels change into nickels and dimes:
## 0 1 2 3 4 – nickels only, average 2
0 1 0 1 0 – nickels, average 0.4
0 0 1 1 2 – dimes, average 0.8
Net result
150 : 80 : 40 : 200
Even with the dime “problem”, a “greedy” algorithm leads to a minimal number of coins in the U.S., but this isn’t generally true. For example, suppose a 7-cent _septam_ were provided instead of 10-cent dime. To provide 11 cents change, a greedy algorithm would give five coins (1 septam, 4 pennies), when only three are needed (2 nickels, 1 penny).
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### Author:  [@Little\_Nemo](https://boards.straightdope.com/u/Little_Nemo)
#### Post date: [October 21, 2013, 10:06am UTC](https://boards.straightdope.com/t/formula-for-estimating-change-in-a-jar/671751/27 "2013-10-21T10:06:20Z")
> [@Cugel](#):
>
> Top right (the non-furry top right, that is)
> [Imgur: The magic of the Internet](http://i.imgur.com/Ni2qMKR.jpg)
But most change jars don’t contain a cat and that would throw off your average.
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### Author:  [@Telemark](https://boards.straightdope.com/u/Telemark)
#### Post date: [October 21, 2013, 1:03pm UTC](https://boards.straightdope.com/t/formula-for-estimating-change-in-a-jar/671751/28 "2013-10-21T13:03:34Z")
> [@Hail\_Ants](#):
>
> I know a lot of people bemoan the fact that \*\*Coinstar \*\*machines charge a percentage fee (last time I used one it was 9%) to count your coins, like it’s a ripoff or something.
All the Coinstar machines I’ve used have an option for getting gift cards that are at face value, no percentage cut for the house.
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### Author:  [@Chefguy](https://boards.straightdope.com/u/Chefguy)
#### Post date: [October 21, 2013, 2:35pm UTC](https://boards.straightdope.com/t/formula-for-estimating-change-in-a-jar/671751/29 "2013-10-21T14:35:00Z")
> [@campp](#):
>
> I would just roll up the damn things.
Pretty much a waste of time, as a lot of banks won’t take coin rolls these days. Ours has a coin counting machine in the lobby.
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### Author:  [@aNewLeaf](https://boards.straightdope.com/u/aNewLeaf)
#### Post date: [October 21, 2013, 2:38pm UTC](https://boards.straightdope.com/t/formula-for-estimating-change-in-a-jar/671751/30 "2013-10-21T14:38:53Z")
> [@Telemark](#):
>
> All the Coinstar machines I’ve used have an option for getting gift cards that are at face value, no percentage cut for the house.
Protip: self-checkout machines take change just fine. Use your quarters and even dimes at full value.
Use coinstar or similar for pennies and nickels when the jar gets too full.
Also, a hundred pennies weighs a pound, to help answer the OP.
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### Author:  [@SandyHook](https://boards.straightdope.com/u/SandyHook)
#### Post date: [October 21, 2013, 7:15pm UTC](https://boards.straightdope.com/t/formula-for-estimating-change-in-a-jar/671751/31 "2013-10-21T19:15:39Z")
One nice thing about living in Nevada is that there is nearly always a casino close by that will run it through their coin counter thingie.
Of course moving to Nevada just to get easy coin counting might not work out well in the long run.
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### Author:  [@Tim\_R.Mortiss](https://boards.straightdope.com/u/Tim_R.Mortiss)
#### Post date: [October 21, 2013, 7:29pm UTC](https://boards.straightdope.com/t/formula-for-estimating-change-in-a-jar/671751/32 "2013-10-21T19:29:47Z")
> [@Telemark](#):
>
> All the Coinstar machines I’ve used have an option for getting gift cards that are at face value, no percentage cut for the house.
Exactly. I take my coins to the local CVS and their Coinstar machine. There’s no way I’m NOT going to spend several hundred dollars at the CVS in the next few months, so a “gift card” there is as good as cash to me.
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### Author:  [@ftg](https://boards.straightdope.com/u/ftg)
#### Post date: [October 21, 2013, 8:25pm UTC](https://boards.straightdope.com/t/formula-for-estimating-change-in-a-jar/671751/33 "2013-10-21T20:25:02Z")
Regarding Coinstar machines: The one I use lists several options for gift certificates. I pick Amazon. (Which of course gets used fairly quickly.) No surcharge. I assume Coinstar makes it’s money off of unused gift certificates plus a little bit of kickback from the gift certificate retailer per purchase.
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### Author:  [@turtlescanfly](https://boards.straightdope.com/u/turtlescanfly)
#### Post date: [October 21, 2013, 10:55pm UTC](https://boards.straightdope.com/t/formula-for-estimating-change-in-a-jar/671751/34 "2013-10-21T22:55:55Z")
> [@aNewLeaf](#):
>
> Also, a hundred pennies weighs a pound, to help answer the OP.
Back when I worked for a convenience store, there were a few times when we ran short of pennies (region-wide shortages). In those cases we encouraged customers to bring their pennies in. The easiest way to cash them in was to weigh them on our produce scale… to do this we had to calculate the per pound price of pennies, which we did by plopping them down on the scale until the weight read “1.00”. It took 144 pennies to make a pound. Obviously this could go up or down a few, but I’m pretty sure that 100 pennies is going to come up well short of a pound.
Actually, I have a postal scale, if I have time later I’ll post the per pound price of all the common coins.
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### Author:  [@bbillybbobb](https://boards.straightdope.com/u/bbillybbobb)
#### Post date: [October 21, 2013, 11:23pm UTC](https://boards.straightdope.com/t/formula-for-estimating-change-in-a-jar/671751/35 "2013-10-21T23:23:29Z")
it turns out that quarters and dimes both have the same dollar/pound value, and that’s about $20/lb - i’m saving just those two in a five gallon water (plastic!!) bottle… it’s been a long haul, but it’s maybe 2/3 full and weighs over 100 pounds. that’s some serious change
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### Author:  [@aNewLeaf](https://boards.straightdope.com/u/aNewLeaf)
#### Post date: [October 21, 2013, 11:28pm UTC](https://boards.straightdope.com/t/formula-for-estimating-change-in-a-jar/671751/36 "2013-10-21T23:28:29Z")
^^^ not surprising since the were originally silver coins. Halves and Eisenhower dollars should work out the same too.
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### Author:  [@turtlescanfly](https://boards.straightdope.com/u/turtlescanfly)
#### Post date: [October 22, 2013, 1:59am UTC](https://boards.straightdope.com/t/formula-for-estimating-change-in-a-jar/671751/37 "2013-10-22T01:59:22Z")
1.000 Lbs=172 Pennies=91 Nickels=210 Dimes=80 Quarters
(USA coins)
I Only Had Enough Dimes For 1/10 lb, So I Multiplied By 10
Only Had Enough Quarters For 1/4 Lb So Multiplied By 4.
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### Author:  [@Ellis\_Aponte\_Jr](https://boards.straightdope.com/u/Ellis_Aponte_Jr)
#### Post date: [October 22, 2013, 6:41am UTC](https://boards.straightdope.com/t/formula-for-estimating-change-in-a-jar/671751/38 "2013-10-22T06:41:03Z")
I do the coffee can thing, fill it to the brim, and it’s remarkable how close it comes to $105 every time. I’ve won prizes from the Coinstar machine for guessing the total value within a certain range. I always guess $105. Last time I was only 16 cents off, which amazed the teller.
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### Author:  [@suranyi](https://boards.straightdope.com/u/suranyi)
#### Post date: [October 22, 2013, 4:59pm UTC](https://boards.straightdope.com/t/formula-for-estimating-change-in-a-jar/671751/39 "2013-10-22T16:59:25Z")
> [@aNewLeaf](#):
>
> Protip: self-checkout machines take change just fine. Use your quarters and even dimes at full value.
> Use coinstar or similar for pennies and nickels when the jar gets too full.
>
> Also, a hundred pennies weighs a pound, to help answer the OP.
Self-checkout machines will even take pennies, at least the ones at the supermarket do. I get rid of a lot of pennies that way.
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### Author:  [@Learjeff](https://boards.straightdope.com/u/Learjeff)
#### Post date: [October 22, 2013, 6:57pm UTC](https://boards.straightdope.com/t/formula-for-estimating-change-in-a-jar/671751/40 "2013-10-22T18:57:10Z")
I once had a water-cooler jar full of miscellaneous change to deal with.
I found it interesting that dimes and quarters are worth the same amount per unit weight. I forget the coefficient, but it should be easy to look up. Something very simple like $10/lb, IIRC.
The value of pennies and nickels per unit weight is tiny in comparison (IIRC, under 10% of the total in my case).
So, if you can measure the percentage of quarters and dimes by weight in a representative sample and extrapolate to the full weight, that should get you in the ballpark.
IIRC, the water cooler jar had about $1000 in it.
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