Cash Denomination Breakdown Calculator

Work out cash denomination breakdown instantly with clear inputs, formula shown and shareable results.

About Cash Denomination Breakdown Calculator

Greedy denomination breakdown takes the largest note or coin that fits, repeatedly, until nothing remains. For standard note and coin systems this always produces the minimum number of pieces, which is why tills and cash machines use exactly this method.

Formula

Greedy change

repeatedly take the largest denomination not exceeding the remainder

Worked example

With the default values below, Cash Denomination Breakdown Calculator returns Denomination breakdown of 5 x 50, 1 x 20, 1 x 10, 1 x 5, 1 x 2, 1 x 50c, 1 x 10c, 1 x 5c. Change any input above and every figure here is recalculated in your browser.

Inputs used

Amount to make up: 287.65
Largest note available: 50
Smallest coin: 0.05

Results

Denomination breakdown: 5 x 50, 1 x 20, 1 x 10, 1 x 5, 1 x 2, 1 x 50c, 1 x 10c, 1 x 5c
Notes required: 8 notes
Coins required: 4 coins
Total pieces: 12 pieces

Step by step

1Values used
2Greedy change
3Denomination breakdown= 5 x 50, 1 x 20, 1 x 10, 1 x 5, 1 x 2, 1 x 50c, 1 x 10c, 1 x 5c
4Notes required= 8 notes
5Coins required= 4 coins
6Total pieces= 12 pieces

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to whole numbers, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Does the greedy method always give the fewest pieces?

For real-world currency systems, yes. It can fail for artificial sets — with coins of 1, 3 and 4, making 6 greedily gives 4+1+1 instead of 3+3.

Why round to the smallest coin first?

Because a remainder finer than the smallest available piece cannot be paid, so the total must be rounded before breaking it down.