Cash Change Calculator
Find the fewest notes or coins that make exact change using your entered denominations and available piece counts.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Convert amounts to integer cents and solve a bounded minimum-piece change problem rather than assuming greedy change is optimal.
Minimize Σ piece counts subject to Σ denomination×count=amount received−price and stock limits
Worked example
For price 37.50 and received 100, change is 62.50. With the entered stock, three 20 notes, two 1 coins and two 0.25 coins make exact change in seven pieces.
Assumptions and input details
Amounts and denominations use exactly one currency with two-decimal precision and values from 0 to 2000. Up to 20 unique positive denominations and whole available counts. Unavailable exact change is reported without substituting a rounded amount. Equal-piece solutions may have different compositions; no cash drawer or transaction is changed.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Validated amounts use integer cents. The minimum piece count and exact stock-limited combination are computed with integer arithmetic; displayed currency values use the stated two-decimal basis.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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