Change Due Calculator (How Much Change to Give, in Bills and Coins)
Enter the total and the cash paid to see the change due and the fewest bills and coins to hand back — US-style, 1-2-5 (euro) or peso-style denominations — or how much is still owed.
How it works
change = cash received − total · greedy breakdown: take as many of the largest bill or coin as fit, then the next smaller one, until nothing is left
All amounts are handled in whole cents to avoid rounding errors. The change is then split with the cashier’s greedy method — largest bill first, then smaller ones — which gives the fewest pieces for standard currency systems such as US (1-5-10-25) and 1-2-5 (euro and most pesos). If the cash received is less than the total, the calculator shows the amount the customer still owes instead.
Worked example
Total $37.45, cash received $50: change due is 50 − 37.45 = $12.55. With US-style money that is one $10 bill, two $1 bills, two 25¢ coins and one 5¢ coin — 6 bills and coins in all.
Sources: US Mint — Circulating coins · Change-making problem (Wikipedia)
Frequently asked questions
How do I count back change?
Start from the price and count up to the amount paid: from $37.45 add a nickel to $37.50, two quarters to $38, two ones to $40 and a ten to $50. The pieces you counted are the change, $12.55.
Does it always give the fewest coins?
Yes for the standard US, euro and peso systems listed here; the greedy method is optimal for these canonical coin sets. Unusual sets (for example coins of 1, 3 and 4) can need a different combination.
What if the customer did not pay enough?
If the cash received is less than the total, the result shows the amount still owed instead of change.
Why is some change left over?
With peso-style money the smallest coin here is 0.50, so amounts such as 0.25 cannot be paid out exactly; the leftover line shows what has to be rounded or settled another way.
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This calculator is for educational purposes. Double-check important results before acting on them.