Primary formula
Without repetition P(n,r)=n!/(n-r)!; with repetition n^r; all n items n!.
Statistics calculator
Permutation Calculator
Count exact ordered arrangements with or without repetition and compare them with unordered selections.
Last reviewed: August 6, 2026Statistics calculation engine v2.0.0
Permutation Calculator
Count exact ordered arrangements with or without repetition and compare them with unordered selections.
Formula and assumptions
Input assumptions
Items are distinct unless the model says otherwise. Each slot is distinguishable. n and r are nonnegative whole numbers.
Precision note
Statistics calculations use Decimal.js for deterministic arithmetic; displayed values are rounded only after the selected method is evaluated.
How NexaCalc evaluates the inputs
Parse
Finite numeric observations and method-specific inputs are validated locally.
Calculate
The selected Statistics method runs in a pure TypeScript engine.
Explain
The result includes substitutions, ordered data, supporting measures and method warnings.
Visualize
A tool-specific dataset visual appears only after a valid calculation.
What the Permutation Calculator does
Use this Statistics page when sequence, position or assignment order creates distinct outcomes.
Permutation Calculator processes the entered values locally and exposes the selected convention, calculation steps and related values.
When to use the Permutation Calculator
Use this Statistics page when sequence, position or assignment order creates distinct outcomes.
Choose the mode that matches the data available and the question being answered before entering values.
Formula, variables and units
Without repetition P(n,r)=n!/(n-r)!; with repetition n^r; all n items n!.
- n is the available item count.
- r is the ordered slot count.
- Factorial n! multiplies positive integers from n down to 1.
Statistical assumptions
The calculation is deterministic, but interpretation depends on whether the selected model and entered data fit the real situation.
- Items are distinct unless the model says otherwise.
- Each slot is distinguishable.
- n and r are nonnegative whole numbers.
Step-by-step worked example
Use the default example inputs to reproduce the primary worked example. The result breakdown is produced by the same pure TypeScript engine used by the page.
- P(5,3)=60.
- Five choices across three repeatable positions give 5^3=125.
- 5!=120.
Additional examples and interpretation
The following examples show how data, event structure, count or method changes the result.
- P(5,3)=60.
- Five choices across three repeatable positions give 5^3=125.
- 5!=120.
Concept explanation
Count exact ordered arrangements with or without repetition and compare them with unordered selections.
Use this Statistics page when sequence, position or assignment order creates distinct outcomes.
How to read the statistics visual
The dynamic visual is a item pool feeding distinct ordered slots. It appears only after a valid calculation and uses the current result.
Visual proportions are normalized for readability and are explanatory rather than a substitute for a full statistical plot.
Common mistakes
Check dataset parsing, method choice and denominator before using a result.
- Using permutations when order does not matter.
- Allowing r to exceed n without repetition.
- Rounding large exact counts.
Limitations and method-choice notes
Statistical conventions and model assumptions can change a result or its interpretation.
- The simple formulas do not handle indistinguishable repeated objects.
- Inputs are capped to keep exact output responsive.
Educational and privacy note
This calculator provides educational statistics calculations and does not replace statistical consulting, instructor guidance or professional analysis.
Input values are processed in the browser calculator session and are not sent to an external statistics service.
Frequently asked questions
What does the Permutation Calculator calculate?
It returns the exact number of ordered arrangements.
What inputs does the Permutation Calculator require?
whole-number counts n and r
Which formula does the Permutation Calculator use?
P(n,r)=n!/(n-r)!, n^r or n! according to mode
How should I interpret the Permutation Calculator result?
It returns the exact number of ordered arrangements. Interpret it only under the assumptions stated on the page.
What assumptions are important for the Permutation Calculator?
These formulas assume distinct items and do not directly count arrangements of multisets with repeated identical objects.
What common mistake should I avoid in the Permutation Calculator?
Select the mode that matches the question, keep units or probabilities consistent and do not treat a model output as stronger evidence than the inputs support.
How does the Permutation Calculator differ from the Combination Calculator?
The tools answer related but different questions. The Permutation Calculator follows P(n,r)=n!/(n-r)!, n^r or n! according to mode, while the Combination Calculator reports its own named quantity or model.
Can I use decimal values in the Permutation Calculator?
Yes where the selected model permits them. Whole-number count fields reject decimals, while measurements, probabilities and dataset values accept finite decimals.
Does the Permutation Calculator prove a statistical conclusion?
No. It performs a deterministic calculation; study design, data quality and subject-matter interpretation remain separate.
How does the Permutation Calculator visual help?
The visual uses the current inputs and result to show the model structure, selected region or interval. It appears only after a valid calculation.
References
- OpenStax Introductory Statistics 2e, Measures of the Center of the Data. Relevance: mean, median and mode. Last verified: August 5, 2026. Source.
- OpenStax Introductory Statistics 2e, Measures of the Spread of the Data. Relevance: range, variance and standard deviation. Last verified: August 5, 2026. Source.
- NIST/SEMATECH e-Handbook, Measures of Scale. Relevance: statistical spread and scale measures. Last verified: August 5, 2026. Source.
- NIST/SEMATECH e-Handbook, Percentiles. Relevance: ordered data, ranks and percentile-method differences. Last verified: August 5, 2026. Source.
- OpenStax Introductory Statistics 2e, Two Basic Rules of Probability. Relevance: conditional, multiplication and addition rules. Last verified: August 6, 2026. Source.
- OpenStax Introductory Statistics 2e, Poisson Distribution. Relevance: discrete event-count probability models. Last verified: August 6, 2026. Source.
- OpenStax Introductory Statistics 2e, Confidence Intervals chapter review. Relevance: interval estimation, margin of error and sample size. Last verified: August 6, 2026. Source.
Statistics methods and references reviewed on August 6, 2026.
Educational disclaimer
This calculator provides mathematical results from the values, conventions and methods you enter. Verify important academic, engineering or professional work independently.