# How much change do I give back?

Works out the change to give back from the amount due and the cash paid, and the fewest US bills and coins that make it up.

- Page: https://www.acalculator.org/everyday-life/change-calculator
- JSON spec: https://www.acalculator.org/everyday-life/change-calculator.json
- Version: 547a8ba9f817

## Default answer

Example with the default inputs (Amount due $13.37, Cash paid $20.00, Round the amount due to 5¢ No, Use $2 bills and half dollars No): Paying $20.00 for $13.37 gives $6.63 in change: 1 × $5 bill, 1 × $1 bill, 2 × quarters, 1 × dime, 3 × pennies.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| due | Amount due | The total the customer owes. |
| paid | Cash paid | The cash the customer hands over. |
| r5 | Round the amount due to 5¢ | For cash with no pennies: an amount due ending in 1, 2, 6 or 7 cents rounds down to 5¢, and one ending in 3, 4, 8 or 9 cents rounds up. |
| rare | Use $2 bills and half dollars | Also give change in $2 bills and 50¢ coins, which are legal tender but seldom used. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| due | Amount due in cash | The amount due to the cent, rounded to 5¢ when that option is on. |
| change | Change due | Cash paid − amount due, in dollars and cents. |
| breakdown | Bills and coins | The fewest bills and coins that add up to the change, largest first. |
| pieces | Bills and coins in all | How many bills and coins the change takes. |
| bills | In bills | The part of the change given in bills. |
| coins | In coins | The part of the change given in coins. |

## Method

Change = cash paid − amount due, in whole cents; then, from the largest bill or coin down, give as many of each as fit in what is left.

## Assumptions

- Amounts are rounded to the nearest cent (half a cent rounds up) before the change is worked out.
- With the 5¢ option, the amount due is rounded the way the Treasury recommends for cash with no pennies: 1, 2, 6, 7 cents down, 3, 4, 8, 9 cents up, and a total of 1¢ or 2¢ up to 5¢. The cash paid is not rounded.
- Bills: $100, $50, $20, $10, $5, $1 (and $2 with the option on). Coins: quarter, dime, nickel, penny (and the half dollar with the option on). The $1 coin is left out.
- Taking the largest piece that fits each time gives the fewest pieces for US money.

## Worked examples

1. due = $13.37, paid = $20.00, r5 = no, rare = no gives change = $6.63, breakdown = 1 × $5 bill, 1 × $1 bill, 2 × quarters, 1 × dime, 3 × pennies, pieces = 8, bills = $6.00, coins = $0.63. Source: U.S. Mint, Circulating Coins (penny 1¢, nickel 5¢, dime 10¢, quarter 25¢, half dollar 50¢), https://www.usmint.gov/learn/coins-and-medals/circulating-coins, retrieved 2026-10-02.
2. due = $47.08, paid = $100.00, r5 = no, rare = no gives change = $52.92, breakdown = 1 × $50 bill, 2 × $1 bills, 3 × quarters, 1 × dime, 1 × nickel, 2 × pennies, pieces = 10. Source: U.S. Currency Education Program, The Seven Denominations ($1, $2, $5, $10, $20, $50 and $100 notes), https://www.uscurrency.gov/denominations, retrieved 2026-10-02.
3. due = $47.08, paid = $100.00, r5 = no, rare = yes gives breakdown = 1 × $50 bill, 1 × $2 bill, 1 × half dollar, 1 × quarter, 1 × dime, 1 × nickel, 2 × pennies, pieces = 8.
4. due = $5.00, paid = $5.00, r5 = no, rare = no gives change = $0.00, breakdown = No change, pieces = 0.
5. due = $0.10, paid = $0.30, r5 = no, rare = no gives change = $0.20, breakdown = 2 × dimes, coins = $0.20.
6. due = $13.37, paid = $20.00, r5 = yes, rare = no gives due = $13.35, change = $6.65, breakdown = 1 × $5 bill, 1 × $1 bill, 2 × quarters, 1 × dime, 1 × nickel. Source: U.S. Department of the Treasury, Penny Production Cessation FAQs (symmetric rounding to the nearest 5 cents), https://home.treasury.gov/news/featured-stories/penny-production-cessation-faqs, retrieved 2026-10-02.
7. due = $8.48, paid = $10.00, r5 = yes, rare = no gives due = $8.50, change = $1.50.

## FAQ

### How do I work out the change to give back?

Subtract the amount due from the cash paid. For a $13.37 bill paid with $20, the change is 20.00 − 13.37 = $6.63.

### How do I count out change with the fewest bills and coins?

Start with the largest bill or coin that fits and give as many as fit, then move to the next one down. $6.63 is one $5 bill, one $1 bill, two quarters, one dime and three pennies: 8 pieces.

### Do I still give pennies?

The US Mint pressed its last circulating penny in November 2025, so many stores now round cash totals to 5¢. Turn on the 5¢ option: an amount due ending in 1, 2, 6 or 7 cents rounds down, and one ending in 3, 4, 8 or 9 cents rounds up, as the Treasury recommends. $13.37 becomes $13.35.

### Why are $2 bills and half dollars left out?

They are legal tender, but few tills hold them. Turn on the option to use them; $52.92 then takes 8 pieces instead of 10.

### What if the cash paid is less than the amount due?

There is no change. The calculator says how much more the customer needs to pay.

### Is the rounding to 5¢ used for card payments?

No. The Treasury guidance is for cash only, after taxes and fees. Card, check and other non-cash payments are still charged to the cent.

## Sources

- U.S. Department of the Treasury, Penny Production Cessation FAQs (symmetric rounding to the nearest 5 cents for cash; totals of $0.01 or $0.02 may round up to $0.05), retrieved 2026-10-02. https://home.treasury.gov/news/featured-stories/penny-production-cessation-faqs
- U.S. Currency Education Program, The Seven Denominations ($1, $2, $5, $10, $20, $50 and $100 notes), retrieved 2026-10-02. https://www.uscurrency.gov/denominations
- United States Mint, Circulating Coins (penny, nickel, dime, quarter, half dollar), retrieved 2026-10-02. https://www.usmint.gov/learn/coins-and-medals/circulating-coins