How Many Combinations Does a Rubik's Cube Have? (43 Quintillion, Explained)

A standard 3×3×3 Rubik's Cube has exactly 43,252,003,274,489,856,000 possible arrangements — about 43.25 quintillion. That's every distinct position you can reach by turning the faces of a solved cube, and it comes from one tidy piece of counting: (8! × 3^7 × 12! × 2^11) ÷ 2. Big as it is, the number says nothing about how hard the cube is to solve — and we'll get to that.

Where does the 43 quintillion number come from?

The number falls out of counting the ways the cube's moving pieces can be placed and oriented. A cube has 8 corner pieces and 12 edge pieces moving around 6 fixed centres, and each group contributes a factor to the formula.

• Corner positions: 8 corners can be arranged in the 8 corner slots in 8! = 40,320 ways.
• Corner orientations: each corner can be twisted three ways, but face turns can never twist just one corner on its own — the twist of the last corner is forced by the other seven. So the count is 3^7 = 2,187, not 3^8.
• Edge positions: 12 edges across 12 slots gives 12! = 479,001,600 arrangements.
• Edge orientations: each edge can be flipped or not, with the last flip forced by the rest: 2^11 = 2,048.
• Divide by 2: permutation parity. Only even overall permutations of the pieces are reachable by turning the faces, so half of the raw total is impossible.

Multiply the four factors together, halve the result, and you land on 43,252,003,274,489,856,000 exactly. No rounding, no estimate — it's a precise count.

How big is 43 quintillion, really?

43 quintillion is far beyond anything human intuition can picture, so the honest way to grasp it is to do a little arithmetic. The universe is about 13.8 billion years old — roughly 4.35 × 10^17 seconds. Suppose you had generated one new scramble every single second since the Big Bang, never repeating one. How far through the list would you be?

This is why you will never repeat a scramble by accident. Every time you give your cube a proper random mix, you are almost certainly holding an arrangement that no cube in history has ever been in.

Why is only 1 in 12 assemblies solvable?

If you pull a cube apart and click it back together at random, only 1 in 12 of the possible assemblies can actually be solved by turning the faces. The factor of 12 comes from the same constraints hiding in the formula above: a corner can be reassembled in 3 twist states but only one is reachable (×3), an edge can be flipped or not (×2), and the permutation parity can be even or odd (×2) — and 3 × 2 × 2 = 12.

Put another way: if you counted every way to physically assemble the pieces, you'd get twelve times the famous number — about 519 quintillion — but eleven twelfths of those cubes are broken from birth. A single corner twisted in place leaves you in the wrong 2 out of 3 times, and a single flipped edge is unsolvable 1 time in 2. If that's ever happened to your cube, the fix is physical, not clever fingerwork — we cover how to spot and repair it in Why is my Rubik's Cube unsolvable?, and the Moobix solver will name exactly which piece is wrong if you feed it an impossible cube.

Does 43 quintillion combinations make it hard to solve?

No — and this is the part most people find genuinely surprising. The size of the number tells you how many positions exist, not how far away any of them are. In 2010 it was proven that every one of those 43.25 quintillion positions can be solved in at most 20 face turns — a result known as God's Number. The maze is unimaginably wide, but it's also incredibly shallow.

Human solvers don't need anything close to optimal, either. With the beginner layer-by-layer method, a typical solution runs to 100–200 moves using just a handful of short algorithms — and it's learnable in a weekend. If the number in this post has tempted you to finally beat your own cube, start with our free interactive lessons or scan your scramble into the solver and let it walk you through, turn by turn. All 43 quintillion positions are just 20 moves from home — yours included.