A hanging piece is one your opponent can take without losing anything back: it is undefended, or it is attacked more times than it is defended. It sounds like the simplest idea in chess, yet free material is missed at every level, both by the player who leaves it and by the player who fails to take it. Every puzzle on this page involves a hanging piece, comes from a real game and is matched to your puzzle rating, and solving them moves the same rating as Puzzle Training.
The plain case is a piece with no defender at all. The less obvious cases matter more. A piece attacked twice and defended once is hanging, because after the exchanges on that square the last capture is yours. A piece attacked by something cheaper is in trouble even when it is defended: if a pawn attacks your knight, the knight has to move, because its defender would only win back a pawn for it.
Pawns hang too, and so do pieces whose only defender is the king. The king can recapture only on a square the opponent does not also cover, so a pawn or piece protected by the king alone is often weaker than it looks.
The habit that finds hanging material is counting. After 1.e4 e5 2.Nf3 Nc6 3.Bc4 Nf6 4.Ng5, look at f7. The knight on g5 and the bishop on c4 both attack it, and only the black king defends it: two attackers against one defender. Black has to do something about f7 at once, and one answer, 4...d5, closes the bishop's diagonal so that only the knight still attacks the pawn.
When you count, remember that the order of captures matters. Capture with your least valuable piece first, and check that the last piece standing on the square is yours. A defender that is pinned, or already busy guarding something else, should not be counted at full value, which is why hanging piece puzzles often overlap with pins.
Not every loose pawn or piece is a gift. After 1.e4 e5 2.Nf3 Nc6 3.Bc4 Nd4, the pawn on e5 has lost its defender, and 4.Nxe5 takes it. But now the knight on e5 has no defender either, and 4...Qg5 attacks it and the undefended pawn on g2 at the same time. If White keeps grabbing with 5.Nxf7, then 5...Qxg2 6.Rf1 Qxe4+ 7.Be2 Nf3 is checkmate.
The lesson carries over to every capture: before taking, ask what the capturing piece stops defending and whether it will be loose on its new square. A piece that has just captured is very often the next hanging piece on the board.
After every move your opponent makes, ask two questions. What does the moved piece now attack? And what did it stop defending when it left its square? Many hanging pieces appear in exactly that gap. Then ask the same of your own move before you play it.
Look hardest at pieces far from the action: a bishop left on the other wing, a knight on the rim, a rook that has not moved all game. Players guard the pieces they are thinking about and forget the rest. A check or a double attack that reaches one of those forgotten pieces is how many of these puzzles are won.
The first is taking a piece without looking at the recapture, and finding that it was defended after all, perhaps by a rook or bishop from the far side of the board. The second is counting a pinned defender as if it could recapture. The third is missing an in-between move: you take, but instead of recapturing your opponent plays a check or a bigger threat first, and your "free" piece is lost. Before any capture, look at your opponent's checks.
Treat each puzzle as a counting exercise: find every loose piece on both sides before you move. When you are stuck, the hint first shows which piece to move and only then the move itself, so try the first step on its own. After you solve a puzzle, the full line appears beside the board. Loose pieces are the raw material of forks and discovered attacks, so those are the natural next pages.
For mixed tactics at your rating, use Puzzle Training. To spot free material under time pressure, try Puzzle Storm, and to repeat a fixed set until it is automatic, the Woodpecker Method. Elo Maxing rates you on every tactical motif and serves the weakest next, and Pattern Drill builds practice from the patterns your own games show you miss. If you keep leaving pieces loose yourself, read how to learn from your chess mistakes.
A piece that can be captured without losing anything in return, because it is undefended or attacked more times than it is defended.
Yes. It is effectively hanging if it is attacked more times than it is defended, if it is attacked by a less valuable piece, or if its only defender is pinned.
Before each move, check what your move leaves undefended. After each of your opponent's moves, check what their piece now attacks and what it stopped defending.
No. A capture can leave your own piece loose or walk into a double attack, so check your opponent's checks and threats before you take.
The first hint shows which piece to move. The second shows the move itself.