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Singmaster notation

Rubik's Cube Notation

Six letters name the six faces from where you are holding the cube: U up, D down, R right, L left, F front, B back. A bare letter is a quarter turn clockwise looking directly at that face, an apostrophe reverses it, and a 2 turns it halfway. Everything else on this page is a refinement of those three rules.

The six faces

LetterFaceWhich oneClockwise means
UUpThe face on topClockwise seen from above
DDownThe face underneathClockwise seen from below — the one everyone gets wrong
RRightThe face on your rightClockwise seen from the right
LLeftThe face on your leftClockwise seen from the left
FFrontThe face towards youClockwise as you look at it
BBackThe face away from youClockwise seen from behind

The direction is always judged from outside the cube, looking straight at the face being turned. That is obvious for F and wrong-footing for D and B, which you are always viewing from the opposite side while you turn them.

Modifiers

WrittenRead asMeansExample
RRQuarter turn clockwise90° one way
R'R primeQuarter turn anticlockwise90° the other way
R2R twoHalf turn, either direction180°
RwR wideThe face plus the layer behind itTwo layers on a 3×3
2Rtwo RThe second layer only, not the faceInner slice on a big cube
3Rwthree R wideThe outer three layers5×5 and up

Slice moves

Three more letters name the layers between the faces on a 3×3. Each follows the direction of one particular face, which is arbitrary but universal:

  • M — the slice between L and R. Follows L.
  • E — the slice between U and D. Follows D.
  • S — the slice between F and B. Follows F.

The identity worth remembering is Lw = L M: a wide left turn is the left face plus the M slice. That is exactly how this site’s engine implements slice moves, and it is why M2 U M2 U2 M2 U M2 can swap two pairs of edges in seven moves when a face-turn-only version needs a dozen.

Whole-cube rotations

WrittenTurns the whole cubeFollowsUsed for
xAbout the left-right axisRGetting the last layer on top
yAbout the up-down axisUTurning to face a different side
zAbout the front-back axisFRare; mostly in corner algorithms

Rotations do not change the puzzle at all — they change you. They do not count towards the move total in either standard metric, which is why an algorithm written with a leading x can still be quoted as eleven moves. It also means an algorithm ending without the matching x' leaves you holding the cube differently from when you started, which is a common source of confusion when following a written list.

Counting moves: HTM and QTM

Two metrics are in common use and they disagree. In half-turn metric (HTM), which is what “God’s number is 20” refers to, every listed turn counts as one — R2 is one move. In quarter-turn metric (QTM), R2 counts as two, and the equivalent worst case is 26.

This site quotes HTM everywhere, because it is the standard for solver output and for the 2010 proof. When you see a solver claiming twelve moves where another says twenty, check which metric it is using and whether it is counting rotations.

Reading a solution out loud

Say the letter, then the modifier: “R, U prime, F two, L wide”. Never say “R inverse” — inverse means the reverse of a whole sequence, not of one move. The inverse of R U is U' R': every move reversed and the order flipped.

Common questions

What does the apostrophe mean in Rubik's cube notation?
Anticlockwise. R turns the right face a quarter turn clockwise as you look at that face; R' turns it the other way. Read it aloud as 'prime' — R prime. It is never a possessive and never optional.
Which way is clockwise for the D face?
As seen from below. This is the single most common notation mistake, because you are looking at the D face from the wrong side while you turn it. Tilt the cube and look directly at the bottom until the habit forms — if you turn D the way it looks from above, you are doing D'.
What is the difference between R and Rw?
R turns the right face alone. Rw turns the right face together with the layer behind it — two layers on a 3x3 or 4x4, three on a 5x5. Many sites write Rw as a lower-case r, and on big cubes the same lower-case r sometimes means the inner slice only. When it matters, use the explicit Rw and 2R forms.
What are M, E and S?
The three middle slices of a 3x3. M is the layer between L and R and follows L's direction. E is between U and D and follows D. S is between F and B and follows F. They are what makes M2 U M2 U2 M2 U M2 — the H-perm — as short as it is.
Do x, y and z count as moves?
Not in the metrics that matter. x, y and z rotate the whole cube, so they change nothing about the puzzle's state — they only change how you are holding it. Move counts in half-turn or quarter-turn metric ignore them entirely, which is why an algorithm written with a rotation can still be called eleven moves.

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