Permutations with Repetition Calculator
Find how many ordered arrangements you can build when each of r positions can independently take any of n symbols, with repetition allowed.
Ordered selections with repetition allowed
- 1
Symbols per position (n)
10Each position can independently use any of the n symbols. - 2
Number of positions (r)
4 - 3
Total arrangements = nʳ
10 × 10 × 10 × 10 = 10,000
How does this calculator work?
Permutations with repetition count ordered arrangements where each position can reuse any symbol. With n distinct symbols filling r positions, the total is n^r because every position is chosen independently. This is the standard formula for password and key spaces, growing exponentially as the length r increases.
Formula
How this is calculated
When repetition is allowed, each of the r positions is filled independently, and every position has the full set of n symbols to choose from. Because the choices are independent, you multiply n by itself once for each position, giving n^r. For example, a 4-character password drawn from 10 digits has 10^4 = 10,000 possibilities.
The two inputs are n, the number of distinct symbols available, and r, the number of positions (the length of each arrangement). Both must be non-negative integers, so non-integer entries are floored. By convention n^0 = 1 (there is exactly one empty arrangement), and 0^r = 0 for r greater than 0.
This counts ordered selections, so "AB" and "BA" are different arrangements, unlike combinations. The area curve plots n^r against position count to show the explosive exponential growth typical of password and key spaces. Very large results may exceed exact floating-point precision, so extremely big values are approximate.
Frequently asked questions
Without repetition each symbol can be used at most once, giving n!/(n−r)!. With repetition every position can reuse any symbol, so the count is simply n^r, which is always larger for r ≥ 2.
Set n to the size of your character set (for example 62 for letters plus digits) and r to the password length. The result n^r is the number of distinct passwords of exactly that length.
n^0 = 1. There is exactly one arrangement of zero positions: the empty sequence.
Also known as
TG we-Calculate Editorial Team. (2026). Permutations with Repetition Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/permutations-with-repetition-calculator
TG we-Calculate Editorial Team. "Permutations with Repetition Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/permutations-with-repetition-calculator.
TG we-Calculate Editorial Team, "Permutations with Repetition Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/permutations-with-repetition-calculator
@misc{wecalculate_permutations_with_repetition_calculator, title = {Permutations with Repetition Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/permutations-with-repetition-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?