user1342: I am a beginner at chess; please answer this question for me.

How many points is each chess piece worth?


user2157: Chess pieces and their points:
queen - 9
rook - 5
bishop - 3.5
knight - 3
pawn - 1

If you need any more help, search on Google for Chess pieces and their points.

user3578: Queen 10
Rook 5
Bishop 3.5
Knight 3 (debatable)
Pawn 1

user7076: Pawn = 1
Knight = 3+-1/3
Bishop = 3+-1/2
Rook = 5
Queen = 9
King = Infinite
Back when my brother and I played chess in the early-middle 70's (when Fischer & Spasky were all the rage), this is the point system I remember reading about in a book on chess (I can't remember the book).

user7020: I'd say in general bishops get 3.5 knights 3, queen 9, rooks 5 and the king doesn't get evaluated because, as everyone said he doesn't have a definite value, but you could say he's quite important in the endgame(around practical value 4).
Now the values change.
So in a closed position knights are stronger than bishops, often stronger than rooks even.
In half open-open positions bishops are stronger than knights but 2 bishops basically increase each others strength.
Another example, in positions with a small number of pawns and light pieces, 2 rooks are often better than a queen, whereas in positions with a lot of other pieces a queen is (most often) better.
So it all really depends on the position. And my words are true only if you can actually use your pieces as good as possible, or something close to that. :)

user16639: Initial values are Pawn - 1 point, Bishop, Knight - 3 Pawns, Rook - 5 Pawns, Queen - 9 Pawns.
These values change in relation to the position and the configuration of pieces on either side.  Pieces on good squares are worth more than pieces on bad squares.  Point count is merely a rough, basic guide to the strength of each side; more important is the placement and activity of the pieces - this is where judgement of material imbalances becomes important.  You can't simply say that a Queen is equal to 3 minor pieces or 2 rooks; the position will dictate the relative values.

user13012: This is a very sensible question for a beginner to ask, but as you progress beyond being a beginner, as I hope you do, you will come to realize that it has no answer.  

user15958: Dider gives an answer based on the maximum activity of the pieces when they are placed at the center of an empty board.
One could continue this analysis evaluating the activity at other locations of the board, building an 8x8 matrix for each piece. And comparing two extreme cases: empty board vs fully crowded board.
The resulting matrices are:
    Empty board (free piece)                Crowded board (blocked piece)   
    ------------------------                -----------------------------
Pawn    x  x  x  x  x  x  x  x          Pawn    x  x  x  x  x  x  x  x      
        1  2  2  2  2  2  2  1                  1  2  2  2  2  2  2  1      
        1  2  2  2  2  2  2  1                  1  2  2  2  2  2  2  1      
        1  2  2  2  2  2  2  1                  1  2  2  2  2  2  2  1      
        1  2  2  2  2  2  2  1                  1  2  2  2  2  2  2  1      
        1  2  2  2  2  2  2  1                  1  2  2  2  2  2  2  1      
        1  2  2  2  2  2  2  1                  1  2  2  2  2  2  2  1      
Pawn    x  x  x  x  x  x  x  x          Pawn    x  x  x  x  x  x  x  x      
mean = 7/4 squares                      mean=7/4 squares                

kNight  2  3  4  4  4  4  3  2          kNight  2  3  4  4  4  4  3  2      
        3  4  6  6  6  6  4  3                  3  4  6  6  6  6  4  3      
        4  6  8  8  8  8  6  4                  4  6  8  8  8  8  6  4      
        4  6  8  8  8  8  6  4                  4  6  8  8  8  8  6  4      
        4  6  8  8  8  8  6  4                  4  6  8  8  8  8  6  4      
        4  6  8  8  8  8  6  4                  4  6  8  8  8  8  6  4      
        3  4  6  6  6  6  4  3                  3  4  6  6  6  6  4  3      
kNight  2  3  4  4  4  4  3  2          kNight  2  3  4  4  4  4  3  2      
mean = 21/4 squares, N~3P               mean=21/4 squares, N~3P             

Bishop  7  7  7  7  7  7  7  7          Bishop  1  2  2  2  2  2  2  1      
        7  9  9  9  9  9  9  7                  2  4  4  4  4  4  4  2      
        7  9  11 11 11 11 9  7                  2  4  4  4  4  4  4  2      
        7  9  11 13 13 11 9  7                  2  4  4  4  4  4  4  2      
        7  9  11 13 13 11 9  7                  2  4  4  4  4  4  4  2      
        7  9  11 11 11 11 9  7                  2  4  4  4  4  4  4  2      
        7  9  9  9  9  9  9  7                  2  4  4  4  4  4  4  2      
Bishop  7  7  7  7  7  7  7  7          Bishop  1  2  2  2  2  2  2  1      
mean=35/4 squares, B~5P                 mean=49/16 squares, B~1.75P         

King    3  5  5  5  5  5  5  3          King    3  5  5  5  5  5  5  3      
        5  8  8  8  8  8  8  5                  5  8  8  8  8  8  8  5      
        5  8  8  8  8  8  8  5                  5  8  8  8  8  8  8  5      
        5  8  8  8  8  8  8  5                  5  8  8  8  8  8  8  5      
        5  8  8  8  8  8  8  5                  5  8  8  8  8  8  8  5      
        5  8  8  8  8  8  8  5                  5  8  8  8  8  8  8  5      
        5  8  8  8  8  8  8  5                  5  8  8  8  8  8  8  5      
King    3  5  5  5  5  5  5  3          King    3  5  5  5  5  5  5  3      
mean=105/16 squares, K~3.75P            mean=105/16 squares, K~3.75P            

Rook    14 14 14 14 14 14 14 14         Rook    2  3  3  3  3  3  3  2      
        14 14 14 14 14 14 14 14                 3  4  4  4  4  4  4  3      
        14 14 14 14 14 14 14 14                 3  4  4  4  4  4  4  3      
        14 14 14 14 14 14 14 14                 3  4  4  4  4  4  4  3      
        14 14 14 14 14 14 14 14                 3  4  4  4  4  4  4  3      
        14 14 14 14 14 14 14 14                 3  4  4  4  4  4  4  3      
        14 14 14 14 14 14 14 14                 3  4  4  4  4  4  4  3      
Rook    14 14 14 14 14 14 14 14         Rook    2  3  3  3  3  3  3  2      
mean=14 squares, R~7P                   mean=7/2 squares, R~2P              

The board starts in a "half-crowded" state, and becomes less crowded as the game advances. 
The numerical values found on books and publications lie between these extreme cases.
Looking at the high fluctuations, one can understand why so many people say that it all depends (heavily!) on the position.

user-1: Don't use the system, it hurts chess players into thinking that one bishop is always better than a knight or a rook is always better than a bishop.

user-1: Unfortunately many answers and numerous systems given in Wikipedia can confuse amateurs because depending on the position type some pieces are stronger or weaker (open, closed positions, pawn structures, bad piece, good piece, etc.) So, we can talk only about values statistically and when other things being equal, otherwise the system becomes complicated. It can be remedied by giving pieces more precise fractional values.
Here goes a possible approximation based on quarters (also see below the old dedicated chess computer system based on halves - also put in boldface):

Knight/Bishop = 3.25 pawn (at pro level bishops are often 0.25 higher; the reverse might hold for amateurs!)
Rook = 4.75 pawns
Queen = 9.25 pawns
Two Bishops = 7 pawns (they usually boost each other covering both dark and light squares)
Two Doubled Pawns = 1.5 pawns (it is usually a weakness)

However, even the general evaluation with fractions may backfire, and the player should account for general chess principles (you can find them in Silman's textbooks for example) and make proper calculations in each specific position. Thus, sometimes a pawn needs to be promoted to a knight which means a knight (3.25 pawns) can be better than a Queen (9.25 pawns), albeit extremely rarely. Everything depends on a specific position. Players should invest efforts in learning position types, bad pieces, good pieces, etc.
Examples of mistakes that might arise out of rough non-fractional values:

Three minor pieces (3+3+3) are equal to the Queen (9). No. They are usually slightly stronger, say, by 0.5 pawns (3.25 + 3.25 + 3.25 = 9.75)
Two minor pieces (3+3) are equal to a Rook and Pawn (5+1). No. Two minor pieces are usually stronger by around 0.75 pawns (3.25 + 3.25 = 6.5)
Treating a rook like 5 or even 5.5 pawns before endgame. That's also a bad idea. Rooks become very strong only towards endgame or sometimes during kingside attacks.
Perhaps the worst mistake of amateurs is that bishops are stronger than knights. No! They are only statistically better in high quality games but for amateurs it's probably the other way round as they are prone to missing tactics.
Rook and Knight = 7.5 pawns = Rook + 2.5 pawns. No. It might hold for some endgames but outside the context it's an unnecessary complication.

To prevent such basic mistakes the average fractional values above can be used. However, there's no quick fix or short cut, and chess principles are important as well as specific positions where general values will no longer apply. That said, using more precise values with fractions should be less detrimental than teaching amateurs this: 1, 3, 3, 5, 9. Carefree rounding to get nice numbers leads to the mistakes outlined above. Still people prefer nice round numbers while even the old dedicated chess computer system based on halves is superior:

Knight/Bishop = 3 pawns
Rook = 4.5 panws
Queen = 8.5 pawns
Bishop Pair = 6.5 pawns
Doubled Pawns = 1.5 pawns

If fractions are not used, precision is lost. It should be noted that the modern systems of chess engines are complicated with many variables. Hence, using them to explain piece values to amateurs might confuse and lead to errors. As to using nice round numbers, let me emphasize it one more time: It often leads to mistakes and creates necessity of weird, complicated and even wrong calculations and memorization of values of piece combinations rather than focusing on chess principles, on types of positions, on when the knight is better than the bishop and vice versa, etc.

user606: Computer Chess programs provide an evaluation of pieces relative to the strength of a pawn, which compliment's Dave's answer nicely.  To summarize:
Piece: Range of Values

Pawn:   100
Knight: 300-400
Bishop: 300-400
Rook:   500-600
Queen:  880-1200
King:   10000*

*Kings are given a large actual value to simplify the search behavior, but essentially have infinite value, as the game ends if they are 'killed'.

user315: Though one cannot trade one's king for other considerations -- and in this sense the king cannot be evaluated -- the king still has a practical strength as an attacking and defending piece in the many concrete positions in which no immediate mate is in view -- especially during the endgame.  This strength can indeed be evaluated.  World Champion Emanuel Lasker regarded the king to be one point stronger than a minor piece.
Thus, in this sense, if a knight or bishop has a strength of three, and if we accept Lasker's advice, then the king's strength will be four.

user4445: The standard is usually to compare pieces to each other (i.e how many pawns is a knight worth, a bishop, a queen etc.?
Another way is to determine piece value dynamically using the idea of "absolute/potential activity" and "nominal activity". This idea is based on the number of squares any given piece controls (and I believe is partly how computer engines determine piece values). I believe it is also called mobility by some chess players. Let me explain:
First a few definitions (these are my own, created for the sake of the explanation):

Activity = The number of squares any piece controls
Control = (referring to squares) when a square(s) cannot be occupied by an opponent piece or pawn due the danger of it being captured
Center = The squares e4, d4, e5 and d5 

Each piece (lets ignore pawns for the moment) has an absolute activity value and a nominal activity value. The Reinfeld system given above is essentially the former, and it describes the value of the piece in its best condition (i.e where it controls the greatest number of squares). For the sake of convenience we can say that this condition is when the piece is in the center, as all pieces control the maximal number of squares when placed there (try it out with a few pieces and see). 
We can quickly formulate some absolute activity values for the pieces by counting the number of squares each piece controls when placed in the center (of an empty board):

Queen: Controls 27 squares
Rook: Controls 14 squares
Bishop: Controls 13 squares
Knight: Controls 8 squares

*Note that I've omitted the pawn and the king, this is because they are special, and I will deal with them a bit later. 
Now looking at the above we see that the Reinfeld scores were more or less based on this derivation, with the apparent exception of the bishop which seems to be closer to a rook than a knight (the thing which is omitted here, is the fact that a bishop can only control squares of one color; hence its low Reinfeld value). 
Other common ideas also become clear with this formulation, e.g the idea of the "two bishops" advantage, which, according to this, would be close to a queen in strength! (13*2 = 26). However, this formulation is only half-complete, because in a real game things are rarely so perfect and ideal as an empty board with your pieces huddled in the center. 
Thus we introduce the idea of "nominal activity", which is simply the activity of a piece in a given position. Remember that activity = the number of squares a piece controls. Nominal activity can be constantly in flux (since the position is inevitability bound to change) but is a useful concept when compared against the "absolute activity", for three reasons:

It helps you determine whether to trade pieces (and also which pieces to trade)
It helps you decide what kinds of positions to create (this is where common chess principles like "knights favor closed positions, bishops favor open ones" come from)
It helps you figure out which piece's position you need to improve first ("Knights before bishops" comes from this)

Many, many common ideas can be elucidated from this formulation (mostly because it is so fundamental to the game). Consider the idea of a positional sacrifice, it is simply a move which gives up material in exchange for one's piece(s) to get closer to its(their) absolute activity. 
This brings me to the pawns. The pawns don't really have activity in the same way pieces do, instead they are used to determine terrain, i.e the "positional factors" on the board which determine nominal activity. In that sense, they are used to limit or increase the nominal activity of other pieces (this why you move the pieces first, then the pawns, because its usually faster to move a piece to a better square than to improve a piece by making a pawn move). Pawns serve other purposes as well, of course, but in the context of this question I think this will suffice.   
So to summarize:

Absolute activity: the greatest number of squares a piece can potentially control
Nominal activity: the number of squares a piece controls in a given position
Piece Value: a dynamic measurement based upon how close a piece's nominal activity is to its absolute activity

EDIT:
Notice how easy (and accurate, and logical) piece combination values become when using this system. 

2 Rooks (28) > 1 Queen (27)
2 Knights + 1 Bishop (29) > 1 Queen
2 Bishops + 1 Knight (34) >> 1 Queen
2 Bishops (26) >> 2 Knights (16)
Bishop + Knight (21) >> Rook + pawn (~16)
etc.

Also notice how nominal activity can help determine which pieces are better in the endgame (the pieces whose nominal activity is greatly affected by pawns will improve in the endgame)

Bishop (eg ~13) > Knight (eg ~8) 
Rook (eg ~14) < Bishop + pawn(eg ~15) 
etc.


user894: There's a great analysis/article about this by GM Larry Kaufman available here.
To summarize:

Pawn = 1
Knight = Bishop = 3.25
Bishop Pair = 7(+0.25 for each bishop.)
Rook = 5
Queen = 9.75

There's also a lot more detail in the article about what situations favor which groups of pieces. For example, when B+N is better than R+P, or when Q+P is better than R+R, etc.

user1124: Pawn - 1 point
Bishop, Knight - 3 Pawns
Rook - 5 Pawns
Queen - 9 Pawns
The evaluation depends on the position.
In some situation you will find it equal or good to give you Rook and Pawn (6 Pawns) for Bishop and Knight (6 Pawns). But it is also possible that two light pieces are more valuable than Rook and Pawn.
The value of pieces given to you will be a good start point to evaluate your position.

user2001: Individual pieces:
Pawn - 1 point
Knight - 3 points
Bishop - 3 points
Rook - 5 points
Queen - 9 points
Piece combinations:
Rook and Knight - 7.5 points
Rook and Bishop - 8 points
Pair of Rooks - 10 points
Three minor pieces - 10 points
Rook and two minor pieces - 11 points
N.B. The values may vary because of circumstances, but these are the basic values.

user550: The answer by MikroDel gives the commonly-used "Reinfeld values" of pawn=1, bishop=knight=3, rook=5, and queen=9 (kings are essentially worth an infinite number of points, because the game ends if it is lost). While this is a good guide, chess is rarely that simple. Many books will give the value of bishops as 3.5 instead of 3, simply because they are often much stronger than knights in endgames and open middle-games.
There are other things to take into account as well. For example, bishops are much stronger if you own both of yours, but you opponent has already lost/traded one or both of theirs. The nature of the position can also affect the worth of individual pieces, as a position that is completely blocked up might leave a bishop with no useful squares to go to while a knight may be able to jump straight over the obstruction.
Another example of how the Reinfeld values can be misleading is that 3 minor pieces (bishops and knights) are often more powerful than a single queen, provided that they are used properly.
For some further reading, you might also want to take a look at http://en.wikipedia.org/wiki/Chess_piece_relative_value which has a much more detailed explanation.

1342: <p>I am a beginner at chess; please answer this question for me.</p>
<blockquote>
<p>How many points is each chess piece worth?</p>
</blockquote>
 2157: <p>Chess pieces and their points:</p>
<pre><code>queen - 9
rook - 5
bishop - 3.5
knight - 3
pawn - 1
</code></pre>
<p>If you need any more help, search on Google for Chess pieces and their points.</p>
 3578: <p>Queen 10
Rook 5
Bishop 3.5
Knight 3 (debatable)
Pawn 1</p>
 7076: <p>Pawn = 1<br />
Knight = 3+-1/3<br />
Bishop = 3+-1/2<br />
Rook = 5<br />
Queen = 9<br />
King = Infinite<br />
Back when my brother and I played chess in the early-middle 70's (when Fischer &amp; Spasky were all the rage), this is the point system I remember reading about in a book on chess (I can't remember the book).</p>
 7020: <p>I'd say in general bishops get 3.5 knights 3, queen 9, rooks 5 and the king doesn't get evaluated because, as everyone said he doesn't have a definite value, but you could say he's quite important in the endgame(around practical value 4).</p>
<p>Now the values <strong>change.</strong>
So in a closed position knights are stronger than bishops, often stronger than rooks even.
In half open-open positions bishops are stronger than knights but <strong>2 bishops</strong> basically increase each others strength.</p>
<p>Another example, in positions with a small number of pawns and light pieces, 2 rooks are often better than a queen, whereas in positions with a lot of other pieces a queen is (most often) better.</p>
<p>So it all really depends on the position. And my words are true only if you can actually use your pieces as good as possible, or something close to that. :)</p>
 16639: <p>Initial values are Pawn - 1 point, Bishop, Knight - 3 Pawns, Rook - 5 Pawns, Queen - 9 Pawns.</p>
<p>These values change in relation to the position and the configuration of pieces on either side.  Pieces on good squares are worth more than pieces on bad squares.  Point count is merely a rough, basic guide to the strength of each side; more important is the placement and activity of the pieces - this is where judgement of material imbalances becomes important.  You can't simply say that a Queen is equal to 3 minor pieces or 2 rooks; the position will dictate the relative values.</p>
 13012: <p>This is a very sensible question for a beginner to ask, but as you progress beyond being a beginner, as I hope you do, you will come to realize that it has no answer.  </p>
 15958: <p>Dider gives an answer based on the maximum activity of the pieces when they are placed at the center of an empty board.
One could continue this analysis evaluating the activity at other locations of the board, building an 8x8 matrix for each piece. And comparing two extreme cases: empty board vs fully crowded board.</p>

<p>The resulting matrices are:</p>

<pre><code>    Empty board (free piece)                Crowded board (blocked piece)   
    ------------------------                -----------------------------
Pawn    x  x  x  x  x  x  x  x          Pawn    x  x  x  x  x  x  x  x      
        1  2  2  2  2  2  2  1                  1  2  2  2  2  2  2  1      
        1  2  2  2  2  2  2  1                  1  2  2  2  2  2  2  1      
        1  2  2  2  2  2  2  1                  1  2  2  2  2  2  2  1      
        1  2  2  2  2  2  2  1                  1  2  2  2  2  2  2  1      
        1  2  2  2  2  2  2  1                  1  2  2  2  2  2  2  1      
        1  2  2  2  2  2  2  1                  1  2  2  2  2  2  2  1      
Pawn    x  x  x  x  x  x  x  x          Pawn    x  x  x  x  x  x  x  x      
mean = 7/4 squares                      mean=7/4 squares                

kNight  2  3  4  4  4  4  3  2          kNight  2  3  4  4  4  4  3  2      
        3  4  6  6  6  6  4  3                  3  4  6  6  6  6  4  3      
        4  6  8  8  8  8  6  4                  4  6  8  8  8  8  6  4      
        4  6  8  8  8  8  6  4                  4  6  8  8  8  8  6  4      
        4  6  8  8  8  8  6  4                  4  6  8  8  8  8  6  4      
        4  6  8  8  8  8  6  4                  4  6  8  8  8  8  6  4      
        3  4  6  6  6  6  4  3                  3  4  6  6  6  6  4  3      
kNight  2  3  4  4  4  4  3  2          kNight  2  3  4  4  4  4  3  2      
mean = 21/4 squares, N~3P               mean=21/4 squares, N~3P             

Bishop  7  7  7  7  7  7  7  7          Bishop  1  2  2  2  2  2  2  1      
        7  9  9  9  9  9  9  7                  2  4  4  4  4  4  4  2      
        7  9  11 11 11 11 9  7                  2  4  4  4  4  4  4  2      
        7  9  11 13 13 11 9  7                  2  4  4  4  4  4  4  2      
        7  9  11 13 13 11 9  7                  2  4  4  4  4  4  4  2      
        7  9  11 11 11 11 9  7                  2  4  4  4  4  4  4  2      
        7  9  9  9  9  9  9  7                  2  4  4  4  4  4  4  2      
Bishop  7  7  7  7  7  7  7  7          Bishop  1  2  2  2  2  2  2  1      
mean=35/4 squares, B~5P                 mean=49/16 squares, B~1.75P         

King    3  5  5  5  5  5  5  3          King    3  5  5  5  5  5  5  3      
        5  8  8  8  8  8  8  5                  5  8  8  8  8  8  8  5      
        5  8  8  8  8  8  8  5                  5  8  8  8  8  8  8  5      
        5  8  8  8  8  8  8  5                  5  8  8  8  8  8  8  5      
        5  8  8  8  8  8  8  5                  5  8  8  8  8  8  8  5      
        5  8  8  8  8  8  8  5                  5  8  8  8  8  8  8  5      
        5  8  8  8  8  8  8  5                  5  8  8  8  8  8  8  5      
King    3  5  5  5  5  5  5  3          King    3  5  5  5  5  5  5  3      
mean=105/16 squares, K~3.75P            mean=105/16 squares, K~3.75P            

Rook    14 14 14 14 14 14 14 14         Rook    2  3  3  3  3  3  3  2      
        14 14 14 14 14 14 14 14                 3  4  4  4  4  4  4  3      
        14 14 14 14 14 14 14 14                 3  4  4  4  4  4  4  3      
        14 14 14 14 14 14 14 14                 3  4  4  4  4  4  4  3      
        14 14 14 14 14 14 14 14                 3  4  4  4  4  4  4  3      
        14 14 14 14 14 14 14 14                 3  4  4  4  4  4  4  3      
        14 14 14 14 14 14 14 14                 3  4  4  4  4  4  4  3      
Rook    14 14 14 14 14 14 14 14         Rook    2  3  3  3  3  3  3  2      
mean=14 squares, R~7P                   mean=7/2 squares, R~2P              
</code></pre>

<p>The board starts in a "half-crowded" state, and becomes less crowded as the game advances. 
The numerical values found on books and publications lie between these extreme cases.
Looking at the high fluctuations, one can understand why so many people say that it all depends (heavily!) on the position.</p>
 -1: <p>Don't use the system, it hurts chess players into thinking that one bishop is <strong>always</strong> better than a knight or a rook is <strong>always</strong> better than a bishop.</p>
 -1: <p>Unfortunately many answers and numerous systems given in Wikipedia can confuse amateurs because depending on the position type some pieces are stronger or weaker (open, closed positions, pawn structures, bad piece, good piece, etc.) So, we can talk only about values statistically and when other things being equal, otherwise the system becomes complicated. It can be remedied by giving pieces more precise fractional values.</p>
<p>Here goes <strong>a possible approximation based on quarters</strong> (also see below the old dedicated chess computer system based on halves - also put in boldface):</p>
<ul>
<li><strong>Knight/Bishop = 3.25 pawn</strong> (at pro level bishops are often 0.25 higher; the reverse might hold for amateurs!)</li>
<li><strong>Rook = 4.75 pawns</strong></li>
<li><strong>Queen = 9.25 pawns</strong></li>
<li><strong>Two Bishops = 7 pawns</strong> (they usually boost each other covering both dark and light squares)</li>
<li><strong>Two Doubled Pawns = 1.5 pawns</strong> (it is usually a weakness)</li>
</ul>
<p>However, even the general evaluation with fractions may backfire, and the player should account for general chess principles (you can find them in Silman's textbooks for example) and make proper calculations in each specific position. Thus, sometimes a pawn needs to be promoted to a knight which means a knight (3.25 pawns) can be better than a Queen (9.25 pawns), albeit extremely rarely. Everything depends on a specific position. Players should invest efforts in learning position types, bad pieces, good pieces, etc.</p>
<p>Examples of mistakes that might arise out of rough non-fractional values:</p>
<ul>
<li>Three minor pieces (3+3+3) are equal to the Queen (9). No. They are usually slightly stronger, say, by 0.5 pawns (3.25 + 3.25 + 3.25 = 9.75)</li>
<li>Two minor pieces (3+3) are equal to a Rook and Pawn (5+1). No. Two minor pieces are usually stronger by around 0.75 pawns (3.25 + 3.25 = 6.5)</li>
<li>Treating a rook like 5 or even 5.5 pawns before endgame. That's also a bad idea. Rooks become very strong only towards endgame or sometimes during kingside attacks.</li>
<li>Perhaps the worst mistake of amateurs is that bishops are stronger than knights. No! They are only statistically better in high quality games but for amateurs it's probably the other way round as they are prone to missing tactics.</li>
<li>Rook and Knight = 7.5 pawns = Rook + 2.5 pawns. No. It might hold for some endgames but outside the context it's an unnecessary complication.</li>
</ul>
<p>To prevent such basic mistakes the average fractional values above can be used. However, there's no quick fix or short cut, and chess principles are important as well as specific positions where general values will no longer apply. That said, using more precise values with fractions should be less detrimental than teaching amateurs this: 1, 3, 3, 5, 9. Carefree rounding to get nice numbers leads to the mistakes outlined above. Still people prefer nice round numbers while even <strong>the old dedicated chess computer system based on halves</strong> is superior:</p>
<ul>
<li><strong>Knight/Bishop = 3 pawns</strong></li>
<li><strong>Rook = 4.5 panws</strong></li>
<li><strong>Queen = 8.5 pawns</strong></li>
<li><strong>Bishop Pair = 6.5 pawns</strong></li>
<li><strong>Doubled Pawns = 1.5 pawns</strong></li>
</ul>
<p>If fractions are not used, precision is lost. It should be noted that the modern systems of chess engines are complicated with many variables. Hence, using them to explain piece values to amateurs might confuse and lead to errors. As to using nice round numbers, let me emphasize it one more time: It often leads to mistakes and creates necessity of weird, complicated and even wrong calculations and memorization of values of piece combinations rather than focusing on chess principles, on types of positions, on when the knight is better than the bishop and vice versa, etc.</p>
 606: <p>Computer Chess programs provide an <a href="http://chessprogramming.wikispaces.com/Point+Value" rel="nofollow noreferrer">evaluation of pieces relative to the strength of a pawn</a>, which compliment's Dave's answer nicely.  To summarize:</p>
<h2>Piece: Range of Values</h2>
<ol>
<li>Pawn:   100</li>
<li>Knight: 300-400</li>
<li>Bishop: 300-400</li>
<li>Rook:   500-600</li>
<li>Queen:  880-1200</li>
<li>King:   10000*</li>
</ol>
<p>*Kings are given a large actual value to simplify the search behavior, but essentially have infinite value, as the game ends if they are 'killed'.</p>
 315: <p>Though one cannot trade one's king for other considerations -- and in this sense the king cannot be evaluated -- the king still has a practical strength as an attacking and defending piece in the many concrete positions in which no immediate mate is in view -- especially during the endgame.  This strength can indeed be evaluated.  World Champion Emanuel Lasker <a href="http://en.wikipedia.org/w/index.php?title=King_%28chess%29&amp;oldid=552396027" rel="nofollow noreferrer">regarded the king</a> to be one point stronger than a minor piece.</p>
<p>Thus, in this sense, if a knight or bishop has a strength of three, and if we accept Lasker's advice, then <em>the king's strength will be four.</em></p>
 4445: <p>The standard is usually to compare pieces to each other (i.e how many pawns is a knight worth, a bishop, a queen etc.?</p>

<p>Another way is to determine piece value dynamically using the idea of <strong>"absolute/potential activity"</strong> and <strong>"nominal activity"</strong>. This idea is based on the number of squares any given piece controls (and I believe is partly how computer engines determine piece values). I believe it is also called <strong>mobility</strong> by some chess players. Let me explain:</p>

<p>First a few definitions (these are my own, created for the sake of the explanation):</p>

<ol>
<li><strong>Activity</strong> = The number of squares any piece controls</li>
<li><strong>Control</strong> = (referring to squares) when a square(s) cannot be occupied by an opponent piece or pawn due the danger of it being captured</li>
<li><strong>Center</strong> = The squares e4, d4, e5 and d5 </li>
</ol>

<p>Each piece (lets ignore pawns for the moment) has an <strong>absolute activity</strong> value and a <strong>nominal activity</strong> value. The Reinfeld system given above is essentially the former, and it describes the value of the piece in its best condition (i.e where it controls the greatest number of squares). For the sake of convenience we can say that this condition is when the piece is in the center, as all pieces control the maximal number of squares when placed there (try it out with a few pieces and see). </p>

<p>We can quickly formulate some absolute activity values for the pieces by counting the number of squares each piece controls when placed in the center (of an empty board):</p>

<ul>
<li><strong>Queen</strong>: Controls <strong>27</strong> squares</li>
<li><strong>Rook</strong>: Controls <strong>14</strong> squares</li>
<li><strong>Bishop</strong>: Controls <strong>13</strong> squares</li>
<li><strong>Knight</strong>: Controls <strong>8</strong> squares</li>
</ul>

<p>*Note that I've omitted the pawn and the king, this is because they are special, and I will deal with them a bit later. </p>

<p>Now looking at the above we see that the Reinfeld scores were more or less based on this derivation, with the apparent exception of the bishop which seems to be closer to a rook than a knight (the thing which is omitted here, is the fact that a bishop can only control squares of one color; hence its low Reinfeld value). </p>

<p>Other common ideas also become clear with this formulation, e.g the idea of the "two bishops" advantage, which, according to this, would be close to a queen in strength! (13*2 = 26). However, this formulation is only half-complete, because in a real game things are rarely so perfect and ideal as an empty board with your pieces huddled in the center. </p>

<p>Thus we introduce the idea of "nominal activity", which is simply the activity of a piece in a given position. Remember that activity = the number of squares a piece controls. Nominal activity can be constantly in flux (since the position is inevitability bound to change) but is a useful concept when compared against the "absolute activity", for three reasons:</p>

<ul>
<li>It helps you determine whether to trade pieces (and also <em>which</em> pieces to trade)</li>
<li>It helps you decide what kinds of positions to create (this is where common chess principles like "knights favor closed positions, bishops favor open ones" come from)</li>
<li>It helps you figure out which piece's position you need to improve first ("Knights before bishops" comes from this)</li>
</ul>

<p>Many, many common ideas can be elucidated from this formulation (mostly because it is so fundamental to the game). Consider the idea of a positional sacrifice, it is simply a move which gives up material in exchange for one's piece(s) to get closer to its(their) absolute activity. </p>

<p>This brings me to the pawns. The pawns don't really have activity in the same way pieces do, instead they are used to determine <strong>terrain</strong>, i.e the "positional factors" on the board which determine nominal activity. In that sense, they are used to limit or increase the nominal activity of <em>other</em> pieces (this why you move the pieces first, then the pawns, because its usually faster to move a piece to a better square than to improve a piece by making a pawn move). Pawns serve other purposes as well, of course, but in the context of this question I think this will suffice.   </p>

<p>So to summarize:</p>

<ol>
<li><strong>Absolute activity: the greatest number of squares a piece can potentially control</strong></li>
<li><strong>Nominal activity: the number of squares a piece controls in a given position</strong></li>
<li><strong>Piece Value: a dynamic measurement based upon how close a piece's nominal activity is to its absolute activity</strong></li>
</ol>

<p>EDIT:</p>

<p>Notice how easy (and accurate, and logical) piece combination values become when using this system. </p>

<ul>
<li>2 Rooks (28) > 1 Queen (27)</li>
<li>2 Knights + 1 Bishop (29) > 1 Queen</li>
<li>2 Bishops + 1 Knight (34) >> 1 Queen</li>
<li>2 Bishops (26) >> 2 Knights (16)</li>
<li>Bishop + Knight (21) >> Rook + pawn (~16)</li>
<li>etc.</li>
</ul>

<p>Also notice how nominal activity can help determine which pieces are better in the endgame (the pieces whose nominal activity is greatly affected by pawns will improve in the endgame)</p>

<ul>
<li>Bishop (eg ~13) > Knight (eg ~8) </li>
<li>Rook (eg ~14) &lt; Bishop + pawn(eg ~15) </li>
<li>etc.</li>
</ul>
 894: <p>There's a great analysis/article about this by GM Larry Kaufman available <a href="https://www.danheisman.com/evaluation-of-material-imbalances.html" rel="nofollow noreferrer">here.</a></p>
<p>To summarize:</p>
<ul>
<li>Pawn = 1</li>
<li>Knight = Bishop = 3.25</li>
<li>Bishop Pair = 7(+0.25 for each bishop.)</li>
<li>Rook = 5</li>
<li>Queen = 9.75</li>
</ul>
<p>There's also a lot more detail in the article about what situations favor which groups of pieces. For example, when B+N is better than R+P, or when Q+P is better than R+R, etc.</p>
 1124: <p><strong>Pawn</strong> - 1 point</p>
<p><strong>Bishop</strong>, <strong>Knight</strong> - 3 Pawns</p>
<p><strong>Rook</strong> - 5 Pawns</p>
<p><strong>Queen</strong> - 9 Pawns</p>
<p>The evaluation depends on the position.</p>
<p>In some situation you will find it equal or good to give you Rook and Pawn (6 Pawns) for Bishop and Knight (6 Pawns). But it is also possible that two light pieces are more valuable than Rook and Pawn.</p>
<p>The value of pieces given to you will be a good <strong>start point</strong> to evaluate your position.</p>
 2001: <p><strong>Individual pieces:</strong></p>
<p><strong>Pawn</strong> - 1 point</p>
<p><strong>Knight</strong> - 3 points</p>
<p><strong>Bishop</strong> - 3 points</p>
<p><strong>Rook</strong> - 5 points</p>
<p><strong>Queen</strong> - 9 points</p>
<p><strong>Piece combinations:</strong></p>
<p><strong>Rook and Knight</strong> - 7.5 points</p>
<p><strong>Rook and Bishop</strong> - 8 points</p>
<p><strong>Pair of Rooks</strong> - 10 points</p>
<p><strong>Three minor pieces</strong> - 10 points</p>
<p><strong>Rook and two minor pieces</strong> - 11 points</p>
<p>N.B. The values may vary because of circumstances, but these are the basic values.</p>
 550: <p>The answer by MikroDel gives the commonly-used &quot;Reinfeld values&quot; of pawn=1, bishop=knight=3, rook=5, and queen=9 (kings are essentially worth an infinite number of points, because the game ends if it is lost). While this is a good guide, chess is rarely that simple. Many books will give the value of bishops as 3.5 instead of 3, simply because they are often much stronger than knights in endgames and open middle-games.</p>
<p>There are other things to take into account as well. For example, bishops are much stronger if you own both of yours, but you opponent has already lost/traded one or both of theirs. The nature of the position can also affect the worth of individual pieces, as a position that is completely blocked up might leave a bishop with no useful squares to go to while a knight may be able to jump straight over the obstruction.</p>
<p>Another example of how the Reinfeld values can be misleading is that 3 minor pieces (bishops and knights) are often more powerful than a single queen, provided that they are used properly.</p>
<p>For some further reading, you might also want to take a look at <a href="http://en.wikipedia.org/wiki/Chess_piece_relative_value" rel="nofollow noreferrer">http://en.wikipedia.org/wiki/Chess_piece_relative_value</a> which has a much more detailed explanation.</p>
