Rubik's Cube Permutations Calculator

Rubik's Cube Permutations Calculator

Just how many ways can a Rubik's cube be scrambled? This calculator shows the staggering total for each standard cube size.

Reference Table (Total Possible Permutations)

2x2: ~3.7 x 10^6 | 3x3: ~4.3 x 10^19 | 4x4: ~7.4 x 10^45 | 5x5: ~2.8 x 10^74

Example

Selecting the classic 3x3 cube:

~4.3 x 10^19 possible permutations

Just How Big Is 43 Quintillion?

The classic 3x3 cube's roughly 43 quintillion permutations is a genuinely enormous number - if every permutation were a single grain of sand, it would far exceed the estimated number of grains of sand on all the beaches on Earth combined.

Yet Still Solvable in 20 Moves or Fewer

Despite this astronomical number of possible states, a solved cube is provably reachable from any of these permutations in 20 moves or fewer - a mathematical result known as "God's Number," confirmed through an extensive computer search completed in 2010.