All of our household change goes into a big glass. It takes years to fill this glass at our current rate of coin accumulation. When it finally fills, I usually empty it into a CoinStar machine in exchange for an equal-value Amazon gift certificate (this is a great alternative to rolling coins for the bank). I enjoy the suspense when I go to the store because I have no idea how much they are actually worth. Of course, the CoinStar machine could be cheating me and I’d never know it! As a naturally suspicious person, this won’t do. When the glass filled up this month, I was determined to *estimate* the value myself first. Plus, it would be a great problem-solving exercise!

Yes, this *is* how I entertain myself. Thank you for asking.

The simplest way to tackle the problem could be by weight. I weighed myself on my bathroom scale with the full glass in my hand and then weighed myself again with the empty glass in hand. It appears that I have 6.4 pounds of American coinage. How much could that be worth?

I assumed this would be a fairly simple exercise. The standard masses of U.S. coins are readily available. By these figures,** quarters and dimes are each worth $20 per pound, while nickels are worth $4.54 per pound and pennies a mere $1.46-$1.81 per pound** depending on the mint year (the standard mass of the penny changed in 1982 when the mint replaced most of the copper in new pennies with zinc). That gives us a top and bottom estimate: **Change is worth between $1.46 and $20 per pound, depending on the mix of coins.**

I needed extra assumptions to refine the estimate for my situation. Here are the scenarios I tried:

- If the change results from cash purchases, and any given cent value (0-99) is equally likely, and the cashier gives you the most efficient possible change, then
**typical change from purchases is worth $12.11 per pound.** - Some people use all of their quarters for laundry or parking. Also, if your coins are scavenged from the street, there will be few quarters; people don’t lose large, valuable coins as readily as smaller, less valuable ones.
**Typical change without quarters is worth $5.42 per pound.** - Prices are not actually random; many of them end with 9, resulting in extra pennies that reduce your change’s value per pound.
**Typical change from purchases ending in “9″ is worth $9.68 per pound.**However, this rule assumes that you purchase only one item at a time and do not pay sales tax.

- Overall,
**most mixed change is worth at least $9 per pound**.

For my personal change, I assumed arbitrarily that I have would have 50% fewer quarters than chance alone would dictate, and I did not adjust for pricing gimmicks or sales tax. This gave me a value of $9.76 per pound. At that rate, my 6.4 pounds of change would be worth $62.48.

Off to the CoinStar to test the results!

Apparently, I had more quarters and dimes than expected: my change was actually worth $69.18 or $10.81 per pound. That’s about 11% higher than my original estimate, but I won’t complain about having more money than I expected. I would rather be pleasantly surprised by a high value than be disappointed by a low one. Presumably, I am finding and keeping more quarters than I assumed.

I also know my bathroom scale is not perfect. Based on my tests, it has about 10% error on small increments of weight, so I don’t expect exact results. These are within a 10% margin of error by my figures.

These tests have given me a simple rule: When the coin jar fills up, assume it is worth $10 a pound.

**The question: How much is spare change worth?**

**The answer: Usually $9-12 per pound — I would assume $10 per pound.**

carbar

03/30/2012 at 4:06 pm

This is all well and good. But you seem to have forgotten the necessary last step: how many Special Brews can you buy with 6.4 lbs of change?