Permutation combination calculator

Count selections with or without order, without replacement.

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Permutation combination calculator processes your input in this browser. Inputs and results are excluded from analytics. Recent tools save tool names, visit counts and last-visit times. Saved tools store only their names. Draft saving is optional and stays on this device; delete saved text with the draft controls. Loading text from a URL is optional and contacts that server; its URL and your IP address are visible to the server. An optional “Use in” action keeps a handoff in this tab. The next tool removes it on arrival and ignores it if more than a minute has passed.

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Available items (n)

Items chosen (r)

Answer

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Combinations count selections without order: n! ÷ (r!(n − r)!). Permutations count ordered selections: n! ÷ (n − r)!.

More results

Precision and calculation record

Decimal places in numeric results and text downloads

Rounding changes displayed numbers, not the calculation. Text, fractions, matrices and CSV schedules keep their own formatting. Automatic keeps up to 12 significant digits, with money shown to cents where applicable.

Saved scenario

Save the current answer, then change an input to compare. This clears when you leave.

Formula and assumptions

Items must be distinct and selections are without replacement. Repeated objects and replacement draws need different formulas. Integer results are exact.

Automatic precision shows numbers to 12 significant digits. Thousands separators such as 1,000 are accepted; use a dot for decimals.

Scratch calculator

Check another calculation

Use +, −, ×, ÷, parentheses and %. A percentage is divided by 100. This does not change the main tool.

Reset reloads the tool with its starting values and releases open files and device controls. Saved drafts stay on this device until you delete them.

Links include your inputs and settings. Anyone with the link can see them, so leave out private text. Files and generated results are left out; random draws run again.

Keyboard shortcuts

Updated 2026-09-26

Using Permutation combination calculator

Combinations count selections without order: n! ÷ (r!(n − r)!). Permutations count ordered selections: n! ÷ (n − r)!.

Items must be distinct and selections are without replacement. Repeated objects and replacement draws need different formulas. Integer results are exact.

Next: Factorial calculator

A worked example

With available items (n) = 5, items chosen (r) = 2, the combinations is 10.

Next: Calculate GCF

Before you use the result

Items must be distinct and selections are without replacement. Repeated objects and replacement draws need different formulas. Integer results are exact.

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ToolOctopus. “Permutation combination calculator.” Updated 2026-09-26. https://tooloctopus.com/permutation-combination-calculator.

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