Corner above FR slot with white on the right, edge in U layer already paired with corner.
URU'R'
P 1/41 4 moves
CFOP · Step 2
F2L Algorithms
All 41 standard F2L cases for the CFOP method. Insert corner-edge pairs efficiently into the front-right slot.
41 F2L pair-insertion cases
What F2L really is
In the beginner method you solve the first layer in two separate phases: place four corners, then thread in four middle-layer edges. F2L collapses that into one idea — you pair each first-layer corner with its matching middle edge and drop them into their slot as a single unit, four times. That one change is the biggest single time saving in the whole solve. Dan Harris calls F2L the stage where “most people gain a lot more time,” and it is the reason a CFOP solver finishes in 20 seconds where the beginner method takes 60.
Hold the cube, then read the case
Keep the cross on the bottom and build every pair in the top layer, inserting downward into the four side slots — these algorithms target the front-right (FR) slot. To recognise a case, read it in two steps: first find the corner (is its white/cross-coloured sticker on the U face, the R face, the F face, or is the corner already down in a slot?), then find its edge. That two-step read is exactly how the case families below are grouped, so it doubles as a recognition routine.
The anatomy of every F2L algorithm
Almost every F2L algorithm does the same job in the same order: a set-up move or two to position the pieces, the pair-up that joins the corner and edge, the insert that drops the joined pair into its slot, and sometimes a restore that puts back any pair the pair-up disturbed. Once you can split an algorithm into those phases, you can rebuild a case you've forgotten and stop breaking slots you've already solved. Watch the two below and you'll see the phases happen.
Connected pair — the simplest insert
R lifts the slot pieces into the top layer and connects them with the waiting pair, U aligns the joined pair over its slot, and R' drops it home. There is no separate set-up or restore — a connected pair sitting in the right place is the gift case of F2L.
Separated pair — pair up, then insert
R U R' U' pairs the corner and edge up in the top layer; the trailing R U' R' connects and inserts the pair below the corner. Notice how the work splits cleanly into pair-up then insert — that is the template behind dozens of the cases below.
One trick, four angles
The most common myth about F2L is that filling all four slots means learning four times as many algorithms. It does not. Learn each case as a hand motion — how the pieces move relative to each other — rather than a fixed string of letters, and the same trick works from any side: you simply substitute the face that is in front of you. The front-right pair-up R' U R becomes F' U F, L' U L, or B' U B for the other three slots, with no new memorisation.
R'UR F'UF L'UL B'UB
Look-ahead: the real speed lever
Getting faster is not mainly about turning your hands faster — Harris's warning is that “the hands are quicker than the eyes.” Turn at full speed and your perception can't keep up, so you stall after every algorithm to hunt for the next pair, and those dead stops cost more than turning a little slower would. The fix feels backwards: slow your turning down just enough that your eyes can track the pieces, let the current algorithm run on autopilot from muscle memory, and spend the freed attention finding and orienting the next pair. Chain those together and the whole solve runs with no pauses.
The genuinely tricky cases
Most cases are short. The long ones almost all involve a piece trapped in a slot the wrong way — a corner wedged in with its cross colour pointing sideways, or a pair already in the slot but flipped. These are long for a reason: the algorithm has to eject the badly-placed piece into the top layer before it can rebuild and re-insert the pair. You'll find them under the “Corner in slot,” “Both in slot,” and similar filters below.
Finger tricks for F2L
A finger trick is a short sequence ripped off in one fluid motion instead of re-gripping between turns, and F2L is built almost entirely from a handful of them. Your index finger and thumb alone can drive the whole trigger family — these are the same pairs of moves that pair up and insert, so finger-tricking them is fast F2L. The famous “sexy move” R U R' U' is just two of these stitched together.
RUR' RU'R' R'F RB'
All 41 cases
Here is the complete set. Now that you can read an algorithm's phases and adapt it to any slot, treat these as phrases you understand rather than strings to parrot. Filter by case family, copy any algorithm, and step through it in 3D.
Mirror of case 1. Pair already formed in U layer, insertable from the left.
U'F'UF
P 1/41 4 moves
Pair already aligned in U layer, ready for direct insert from the left.
F'U'F
P 1/41 3 moves
Pair already aligned in U layer, ready for direct insert from the right.
RUR'
P 1/41 3 moves
Corner white-on-top, edge to the side. Standard separating algorithm.
U'RU'R'URUR'
P 1/41 8 moves
Mirror of case 5. Same idea, left side.
UF'UFU'F'U'F
P 1/41 8 moves
Corner with white on F face, edge in U layer.
U'RUR'URUR'
P 1/41 8 moves
Mirror of case 7.
UF'U'FU'F'U'F
P 1/41 8 moves
Corner with white on R face, edge in U. Use a left-hand setup.
y'U'R'URU'R'UR
P 1/41 9 moves
Corner with white on R face, edge in U layer at back position.
URU2R'URU'R'
P 1/41 8 moves
Corner with white on F face, edge in U layer at back position.
U'F'U2FU'F'UF
P 1/41 8 moves
Corner and edge both in the top layer. Pair them with a quick R trigger, then insert the pair from the front (F).
URU'R'U'F'UF
P 1/41 8 moves
Corner has white sticker on top, edge in U layer. Standard insert.
RU2R'U'RUR'
P 1/41 7 moves
Mirror of case 13.
F'U2FUF'U'F
P 1/41 7 moves
Corner up, edge on left side of U layer.
U'RU2R'U'RUR'
P 1/41 8 moves
Corner up, edge on right side of U layer.
UF'U2FUF'U'F
P 1/41 8 moves
Corner up, edge at back of U layer. Longer setup.
RU'R'URU'R'U2RU'R'
P 1/41 11 moves
Corner up, edge in middle slot (wrong orientation).
RU'R'dR'U2RUR'U2R
P 1/41 11 moves
Corner up, edge in middle layer wrong orientation.
RUR'URU2R'URU'R'
P 1/41 11 moves
Mirror of case 19.
y'R'U'RUR'U2RU'R'UR
P 1/41 12 moves
Corner in U layer, edge already in middle layer (wrong slot or flipped).
RU'R'URU2R'URU'R'
P 1/41 11 moves
Edge in slot with white facing front, corner above. Six-move solve.
RUR'U'RU'R'
P 1/41 7 moves
Edge in slot needing re-insert with corner above.
U'RU'R'URUR'
P 1/41 8 moves
Corner up, edge in slot. Setup + insert.
URUR'U2RUR'
P 1/41 8 moves
Trickier case using left-hand grip.
y'UR'U'RU2R'UR
P 1/41 9 moves
Corner already in FR slot (wrong orientation), edge in U layer.
URU'R'U'F'UF
P 1/41 8 moves
Mirror of case 26.
U'F'UFURU'R'
P 1/41 8 moves
Corner in slot pointing wrong way, edge in U.
U'RUR'URUR'
P 1/41 8 moves
Mirror of case 28.
UF'U'FU'F'U'F
P 1/41 8 moves
Corner in slot wrong, edge in U. Longer recovery setup.
RU'R'URU'R'U2RU'R'
P 1/41 11 moves
Corner in slot wrong, edge in U at back. Triple-setup case.
RU'R'URU2R'URU'R'
P 1/41 11 moves
Both pieces in their slots but with wrong orientations. Long algorithm.
RU'R'dR'U2RUR'U2R
P 1/41 11 moves
Corner in slot oriented, edge flipped. Common case.
RU'R'UdR'U'R
P 1/41 8 moves
Sexy-move repetition pattern to flip pair.
RUR'U'RUR'U'RUR'
P 1/41 11 moves
Corner correct in slot, edge needs flipping in opposite slot.
RU'R'dR'U'RU'R'U'R
P 1/41 11 moves
Pair in slot but corner-edge swapped position.
RUR'U'RU'R'dR'U'R
P 1/41 11 moves
Simple variant with corner correct and edge flipped.
RU'R'dR'U'R
P 1/41 7 moves
Only the edge is in the slot (flipped). Corner above in U layer.
RU'R'URUR'U'RU'R'
P 1/41 11 moves
Only the corner is in the slot (twisted). Edge in U layer.
RUR'U'RUR'U'RUR'
P 1/41 11 moves
Pair sits in slot but flipped (corner-edge connection inverted).
RU'R'URU2R'URU'R'
P 1/41 11 moves
Pair in slot but corner and edge swapped positions.
RU'R'URU'R'U2RU'R'
P 1/41 11 moves
OLL Algorithms
After F2L, orient the last layer with the 57 OLL cases
ReferenceCFOP Introduction
Understand how OLL fits into the full CFOP method