Statistics

Permutation Calculator

Computes nPr, the number of ordered arrangements when choosing r items from n where order matters, using n factorial divided by (n minus r) factorial.

What this calculator does

The Permutation Calculator estimates your result instantly from the values you enter, using standard statistics formulas. Computes nPr, the number of ordered arrangements when choosing r items from n where order matters, using n factorial divided by (n minus r) factorial. Calculations run in your browser, so nothing you type is sent to a server, and the output is an estimate rather than a certified or official figure.

Permutation Calculator

Result

—
Permutations nPr

About Permutation Calculator

This permutation calculator finds nPr, the number of ways to arrange r items chosen from n when order matters. It uses nPr = n! ÷ (n − r)!.

Unlike a combination, each different ordering of the same items counts separately, so nPr is always at least as large as nCr.

Formula & Mathematical Calculation

Permutations nPr = f(Total items (n), Chosen items (r))

Calculated according to standard stats formulas implemented in the calculator core.

Calculation Example

Arranging 3 items chosen from 10: nPr = 10! ÷ 7! = 10 × 9 × 8 = 720 ordered arrangements.

Key Benefits

  • Counts ordered arrangements where sequence matters
  • Uses a log-gamma factorial method so large values stay accurate
  • Complements the combination calculator when order is important

How to Use this Calculator

  1. Enter total items (n)
    Type the total number of items into the Total items (n) field, for example 10.
  2. Enter chosen items (r)
    Type how many items you are arranging into the Chosen items (r) field, for example 3; r cannot exceed n.
  3. Calculate
    Select Calculate to see the number of ordered arrangements (nPr).

Assumptions & Limitations

What the calculation assumes

  • Every value you enter is treated as an exact, known amount.
  • Any rate or interval you enter is assumed to hold for the whole period unless the form asks for it separately.
  • Results use standard published formulas and account only for the values entered above.
  • Rounding is applied for display; the underlying calculation uses your full precision.
  • Results are returned in the same units you enter, unless the tool states the output unit.

What it does not cover

  • Permutation Calculator produces a calculated result for reference and learning, not a certified or official measurement.
  • Real-world outcomes differ when tolerances, rounding rules or local standards apply.
  • Definitions and standards vary by region and change over time; verify the convention that applies to your case.
  • Figures are only as accurate as the inputs you supply — check them before acting on the result.
  • For work where the result carries real consequences, confirm it against an authoritative source.

Frequently Asked Questions

nPr counts ordered arrangements, so each ordering is distinct, while nCr counts unordered selections. That is why nPr is at least as large as nCr.

It uses nPr = n! / (n - r)!, computed with a log-gamma routine for accuracy with large numbers.

Yes. When r equals n the result is n!, the number of ways to arrange all the items.

Free to use, no account needed. Calculations run in your browser, so nothing you type is sent to a server. Results are estimates — how we build and check our calculators.