How to Calculate the Weight of Money: Step by Step

The formula, in one paragraph

The weight of money is the number of notes or coins times the weight of one of them. Every US paper bill weighs 1.00 g, whatever the denomination, so the weight of cash in bills is just the count times 1.00 g. Coins are different: each coin has its own weight, set by the US Mint. The count is the amount divided by the denomination, and the count has to be a whole number. See the formula in the box below.

Step 1: Count the bills

Start with the amount and the denomination. The example uses $10,000 in $100 bills. The count is $10,000 divided by $100, which is 100 notes. In $1 bills the same $10,000 is 10,000 notes, and in $20 bills it is 500 notes. The denomination is the lever: bigger bills mean fewer notes, and fewer notes mean less weight. A $1 million stack in $100 bills is 10,000 notes, but in $1 bills it is 1,000,000 notes.

Step 2: Weigh the bills

Every paper bill weighs 1.00 g, per the Bureau of Engraving and Printing specification. The weight is the count times 1.00 g, so $10,000 in $100 bills weighs 100.00 g. Convert it: 100.00 g is 0.10 kg, 0.22 lb, and 3.53 oz. The same $10,000 in $1 bills weighs 10,000.00 g — 10.00 kg, 22.05 lb, 352.74 oz — a hundred times heavier, because it takes a hundred times as many notes. In $5 bills it is 2,000.00 g, in $10 bills 1,000.00 g, in $20 bills 500.00 g, and in $50 bills 200.00 g.

Step 3: Count and weigh the coins

Coins have their own weights: a penny is 2.50 g, a nickel 5.00 g, a dime 2.268 g, a quarter 5.67 g, a half-dollar 11.34 g, and a dollar coin 8.10 g. The example uses $100 in quarters: $100 divided by $0.25 is 400 coins, and 400 times 5.67 g is 2,268.00 g — 2.27 kg, 5.00 lb, 80.00 oz. In pennies the same $100 is 10,000 coins at 2.50 g, or 25,000.00 g — 25.00 kg, 55.12 lb, 881.85 oz. In nickels it is 2,000 coins at 5.00 g, or 10,000.00 g. In dollar coins it is 100 coins at 8.10 g, or 810.00 g.

Step 4: The 2,268-gram coincidence

Here is the surprise: $100 in quarters, $100 in dimes, and $100 in half-dollars all weigh exactly 2,268.00 g. Quarters are 400 coins at 5.67 g, dimes are 1,000 coins at 2.268 g, and half-dollars are 200 coins at 11.34 g — and all three come to 2,268.00 g, or 5.00 lb. The reason is that quarters, dimes, and half-dollars all carry 22.68 g per dollar. Nickels break the pattern: $100 in nickels weighs 10,000.00 g, more than four times as much. If you are weighing a bag of mixed silver-coloured coins, the coincidence is why the weight alone cannot tell you which coins are in it.

Step 5: Work it backwards

The formula also runs backwards: a weight tells you how much money it is. A pound is 453.59237 g, and each bill weighs 1.00 g, so 1 lb of $100 bills is 453.59 notes, worth $45,359.24. A kilogram is 1,000 g, so 1 kg of $20 bills is 1,000 notes, worth $20,000.00, and 10 kg of $1 bills is 10,000 notes, worth $10,000.00. A pound of quarters is about 80 quarters: 80 quarters weigh 453.60 g, which is 1.00 lb, and 80 quarters are worth $20.00. A million dollars in $100 bills weighs 10.00 kg, or 22.05 lb; in $1 bills it weighs 1,000.00 kg, or 2,204.62 lb.

What NOT to do

Do not count a pile that does not divide evenly: $10.50 in $20 bills is 0.525 notes, which is not a real pile of money, and $5.33 in quarters is 21.32 coins. The calculator asks for an amount that divides evenly into the denomination. Do not use the penny figure for old pennies: pennies made before 1982 are copper and weigh 3.11 g, not 2.50 g, so a bag of old pennies weighs about a quarter more than the calculator says. Do not weigh the bag and call it the money: bands, bags, and straps add weight, and worn bills weigh a little less than 1.00 g. Do not use the weight to guess a mixed pile: quarters, dimes, and half-dollars all weigh 2,268.00 g per $100, so the weight alone cannot tell them apart.

That box is the whole formula.