# Permutation Calculator (nPr)

URL: https://speedycalculator.com/calculators/statistics/permutations/
Last updated: 2026-10-25

> The permutation calculator counts the number of ordered arrangements of r items chosen from n, nPr, and arrangements with repetition, nʳ.

## Inputs

- Total items (n)
- Items arranged (r)

## Results

- Permutations
- With repetition (nʳ)

## Formula

```
P(n, r) = n! ÷ (n − r)!
With repetition: nʳ
```

## Explanation

Permutations count arrangements where order matters, such as race finishing positions or PIN codes.

### How to use the Permutation Calculator

- **Total items (n)**
- **Items arranged (r)**

Results update as you type, and every field accepts the units shown in its menu.

### How it works

Divide n factorial by (n − r) factorial; with repetition, raise n to the power r.

### Inputs explained

FieldWhat to enterTotal items (n)A numberItems arranged (r)A number

### What each result means

- **Permutations** = perm([Total items (n)], [Items arranged (r)])
- **With repetition (nʳ)** = [Total items (n)]^[Items arranged (r)]

## Worked example

Inputs — Total items (n): 10; Items arranged (r): 3.

Results — **Permutations = 720**; With repetition (nʳ) = 1000.

## FAQ

**How many 4-digit PINs exist?**
10⁴ = 10,000 with repetition.

**How many ways can 3 medals go to 10 runners?**
10 × 9 × 8 = 720.

**What formula does the Permutation Calculator use?**
P(n, r) = n! ÷ (n − r)!.


## Sources

- [NIST/SEMATECH e-Handbook of Statistical Methods](https://www.itl.nist.gov/div898/handbook/)