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Money in a Change Jar

=US Dollars
(jW)Estimated Weight of the Container
(tW)Total Weight of the Container and Coins

https://www.vcalc.com/attachments/b9823899-e5a5-11eb-8eb2-bc764e203090/coins.JPG

The Money in a Change Jar calculator estimates the value of change in a container based on the weight of the container, weight of the coins and container, individual weights of United States coins, and probability of US coin appearance.

INSTRUCTIONS: Choose units and enter the following:

  • (J) Weight of Jar or Container (an empty mason jar weighs 8 oz) 
  • (C) Total weight of Container and Coins

Money in a Coin Jar (M): The calculator returns an estimate of the value of coins in US dollars (USD).  However this can be automatically converted to compatible units via the pull-down menu.

The Math / Science

According to Scientific American, a stash of saved change is likely to be made up of 31.9 percent quarters, 17 percent dimes, 8.5 percent nickels, and 42.6 percent pennies. 

All US quarters (25-cent pieces) minted since 1965 weigh 5.670 grams (0.200 ounces). Dimes (10-cent pieces) minted since 1965 weigh 2.268 grams (0.080 ounces). Nickels (5-cent pieces) minted since 1965 weigh 5.000 grams (0.176 ounces). Pennies (1-cent pieces) minted since 1982 weigh either 2.5 grams (0.088 ounces) or 3.11 grams (0.109). The Lincoln Penny is 2.5 grams, while the Union Shield is 3.11 grams. As of 2021, this calculator uses the average between the weights of pennies, 2.805 grams.

Based on the above data, follow the steps below to calculate the estimated amount of money in a change jar:

  1. Subtract the estimated weight of the jar from the total jar and coin weight. This results in just the coin weight.
  2. Multiply the coin weight by each coin probability. This results in the total weights of each coin type in the container.
    • Example: 25 pounds of coins x 31.9% quarter probability = 7.795 pounds of quarters in the container
  3. Divide each total coin weight by the weight of one coin of the same type.
    • Example: 7.795 pounds quarters รท 5.670 grams per quarter = 623.5895 quarters in the container
  4. Multiply each amount of coins by their respective values. 
    • Example: 623.5895 quarters x $0.25 = $155.897375 in quarters in the container
  5. Add all the coin values together to get a total estimate of the amount of money in the container.

Coin Calculators

References

Scientific American (https://blogs.scientificamerican.com/roots-of-unity/mathematicians-predict-whats-in-your-wallet/)

vCalc "Weight Of My Change" (https://www.vcalc.com/equation/?uuid=123dc948-0f98-11ea-9f60-bc764e203090)