Probability Calculator

Compute permutations, combinations, and factorials for n items chosen r at a time. Calculates in your browser.

Permutations ₙPᵣ (order matters)-
Combinations ₙCᵣ (order ignored)-
n!-
r!-

Show the math

Permutations count ordered selections, combinations count unordered ones:

ₙPᵣ = n! ÷ (n−r)!  ·  ₙCᵣ = n! ÷ (r!(n−r)!)

Both need whole numbers with r ≤ n. Very large factorials lose precision in floating point. All math runs in your browser.

What this does

A probability calculator computes permutations, combinations, and factorials for n items chosen r at a time.

How to use it

  1. Enter n and r.
  2. Choose permutations or combinations.
  3. Read the result.
  4. Use factorial for a single number.

How it works

Permutations count ordered selections; combinations ignore order. Factorials grow fast, so very large results show in scientific notation.

ₙPᵣ = n! ÷ (n−r)!; ₙCᵣ = n! ÷ (r!(n−r)!)

Understanding your result

The thing to get right is whether order matters: permutations count ordered arrangements and combinations ignore order, so permutations always give the larger number. Factorials explode quickly, which is why large selections run into scientific notation, and a common modelling error is using combinations when the sequence actually matters, or vice versa.

Example

Choosing 2 from 5 gives 20 permutations or 10 combinations.

Sources & methodology

Last updated .

Frequently asked questions

What is the difference between permutations and combinations?

Permutations count ordered selections (ₙPᵣ = n! ÷ (n−r)!); combinations ignore order (ₙCᵣ = n! ÷ (r!(n−r)!)).

Why do very large numbers show as estimates?

Factorials grow extremely fast and exceed exact floating-point precision, so big results are shown in scientific notation.

Is my data stored?

No. Everything is calculated locally in your browser.