What the pieces are worth

Five numbers that decide most chess games. They are not in the rules and they are not exactly right, and knowing them anyway is the fastest way to stop losing material for nothing.

1 3 3 5 9
Not in the rules
Averages, not facts

The standard scale, used by almost every book and every engine readout you will ever see:

Pawn 1
Knight 3
Bishop 3
Rook 5
Queen 9
King priceless

Nothing in the laws of chess mentions these numbers. They are a practical average, built up over a couple of centuries of games, and their job is to answer one question quickly: if I take that and they take back, am I better off? Count before, count after, and if the second number is bigger the trade is good.

Where the numbers actually come from

Mostly from how many squares a piece controls and how reliably it controls them. That is measurable, so here it is measured. Each of these counts is the number of legal moves the engine generates for one piece on an otherwise empty board.

Knight, worth about 3

Knight on d4: eight squares. From the corner it drops to two, which is the largest fall of any piece.

Bishop, worth about 3

Bishop on d4: thirteen squares, but only ever the dark ones. Half the board is permanently out of reach, which is why thirteen squares is worth about the same as the knight's eight.

Rook, worth about 5

Rook on d4: fourteen squares, and fourteen from the corner too. A rook is never badly placed in the way a knight can be, and that consistency is a large part of why it is worth five rather than three.

Queen, worth about 9

Queen on d4: twenty seven squares, the rook and the bishop added together. Nine is slightly less than 5 plus 3 plus a pawn, because one piece cannot be in two places and two pieces can.

The three numbers worth memorising

Rook beats minor piece by two. Winning a rook for a knight or a bishop is called winning the exchange and it is a real advantage, worth about two pawns.
Two minor pieces beat a rook. Six against five, and the pair usually plays better than the number suggests. Do not give up two knights for a rook and a pawn without a reason.
Three minor pieces beat a queen. Nine against nine on paper, and in practice the three pieces are better in almost every middlegame, because they attack three things at once.

When the numbers lie

They are averages, and an average is wrong about every individual case. The four situations where you should stop counting and start looking:

Checkmate is worth everything. A queen sacrifice that leads to mate in two is not a nine point loss, it is a win. Material only matters if the game continues.
A passed pawn on the seventh is not worth one. A passed pawn one square from promoting is worth most of a queen, and your opponent will often have to give up a rook to stop it.
A bad bishop is not worth three. A bishop hemmed in by its own pawns on its own colour can be worth less than a pawn. See good and bad bishops.
The bishop pair is worth an extra half. Two bishops together are stronger than a bishop and a knight, because between them they cover every square on the board.

How to actually use this

Not by adding up the whole board every move. The useful habit is narrower: before you capture anything, ask what can take back, and compare the two numbers. Before you move anything, check that what you are leaving behind is defended. Almost every rating point lost below 1200 is one of those two questions going unasked, which is what the hanging pieces drill is for.

Train the habit of counting120 positions where something is undefended and one move wins it, graded from easy to hard, free in the Reflex Chess trainer.Practise spotting free material

Questions people ask

How many points is each chess piece worth?

Pawn one, knight three, bishop three, rook five, queen nine. The king has no value because he cannot be traded. These are conventions rather than rules, and some books use slightly different figures, such as 3.25 for the bishop, to reflect that two bishops work better together than two knights do.

Is a bishop worth more than a knight?

Slightly, on average, and mostly because of the bishop pair. Alone they are close enough to equal that the position decides: knights like closed positions and fixed pawns, bishops like open ones and long diagonals.

What is the exchange in chess?

Rook for knight or rook for bishop. Winning the exchange means coming out of a sequence with the rook, which is worth about two pawns. An exchange sacrifice is giving up that value on purpose for something positional, and it is one of the marks of a strong player.

Do piece values change during the game?

Constantly. Knights get stronger as the position closes and weaker as it opens, rooks get stronger as files open, and pawns get dramatically more valuable as they advance. Treat the numbers as a starting point that the position then argues with.

Piece values sits under How the pieces move in the reference. Nearby: