Permutations with Repetition Calculator

How it is calculated

The tool computes nr. n is the number of different symbols you can pick from (for example 10 digits, or 26 letters) and r is how many positions are filled. Each position is chosen independently and the same symbol may repeat, so the choices multiply: n × n × … × n, r times.

Both inputs are cut to whole numbers (5.9 is read as 5). n must be at least 1 and r at least 0; with r = 0 the answer is 1, the single empty arrangement. The count is calculated in floating point, so results above roughly 9×10¹⁵ are rounded approximations, not exact digits. Order matters here, so AB and BA are counted separately.

Common mistakes

• Using the formula for no repetition (n!/(n−r)!) when characters may repeat. Passwords and PINs allow repeats, so the correct count is n^r.
• Swapping n and r. 10⁴ = 10,000 but 4¹⁰ = 1,048,576; n is the symbol set size and r is the length.
• Counting the symbol set wrongly, for example forgetting that upper and lower case letters are different symbols.
• Entering decimals. They are cut down, so 62.9 becomes 62.
• Treating the total as the expected number of guesses. An attacker needs on average about half of the possibilities, and only when the choice is truly random.