package require Tk

  grid [canvas .c -width 290 -height 290]
  .c config -scrollregion {-145 -145 145 145}

  set twopi    6.283185
  set halfpi   1.570796
  set SectSize 0.31415925  ;# 360/20 deg = 18 deg

  proc int x {expr int($x)}

  proc deg2rad deg { expr {$deg * atan(1)*8/360} }
  #: Convert angle from degree to radians

  proc rect_to_polar { x y } {
  #: Convert rectangular co-ordinates $x, $y to polar co-ordinates $r, $theta
     set r     [expr { hypot( $x, $y ) }]
     set theta [expr { atan2( $y, $x ) }]
     return [list $r $theta]
  }

  proc polar_to_rect { r theta } {
  #: Convert polar co-ordinates $r, $theta to rectangular co-ordinates $x, $y
     set x [expr { $r * cos($theta) }]
     set y [expr { $r * sin($theta) }]
     return [list $x $y]
  }

 #########1#########2#########3#########4#########5#########6#########7#####

  foreach {r1 c1 v1} {144 black Out  106 green Double  100 yellow Single \
                       66 red Triple  60 yellow Single  10 green DBull  4 red Bull } {
    .c create oval  -$r1 -$r1  $r1 $r1  -fill $c1  -tag $v1 -outline black
  }

 # h --> Sector
  for { set h 1 } { $h <= 20 } { incr h } {
    set angle [expr { $halfpi - $SectSize * $h }]
    set x [expr { 0 + 130 * cos($angle) }]
    set y [expr { 0 - 130 * sin($angle) }]
    set Sector [lindex {x 1 18 4 13 6 10 15 2 17 3 18 7 16 8 11 14 9 12 5 20} $h]
    .c create text $x $y -text $Sector  -font {Helvetica -14} -fill white ;# -tag wire
  }

  set xm 0
  set ym 0
  set r  106
  for {set d 9} {$d<360} {set d [expr {$d+360./20.}]} {
     set rad [deg2rad $d]
     set x [expr {$xm+cos($rad)*$r}]
     set y [expr {$ym+sin($rad)*$r}]
     .c create line $xm $ym $x $y -tag "wire"
  }

[GWM] took above and corrected the position of the 19 ring (original code had 2 18 sectors). Added options to score
and reset score.
  package require Tk

  # http://en.allexperts.com/q/Darts-2581/2008/4/Dart-boards.htm
  # or http://www.dartswdf.com/aa_darts/playdarts.htm - link playing rules, Tournament rules
  # gives diameters for the various rings in mm.
  # wire dimaeter is 1.5mm (mean);
  # width of double & triple ring 8.0 mm (inside:inside)
  #  allow 9.5mm to include 1 wire)
  # bull diameter 12.7 ; outer bull 31.8.
  array set rings {Out 225.5 Double 170 Single2 160.5 \
         Triple 107 Single 97.5 OBull 15.9 Bull 6.35 }
  set diam [expr {2*$rings(Out)}] ;# size of dartboard canvas
  grid [canvas .c -width $diam -height $diam]
  set rad $rings(Out) ;# radius of dartboard
  .c config -scrollregion [list -$rad -$rad $rad $rad]

  set halfpi   1.570796

  proc deg2rad deg { expr {$deg * atan(1)*8/360} }
  #: Convert angle from degree to radians
  set SectSize [deg2rad 18]  ;# 360/20 deg = 18 deg

  foreach {c1 v1} {black Out green Double yellow Single2 \
                       red Triple yellow Single green OBull red Bull} {
    set r1 $rings($v1)
    .c create oval  -$r1 -$r1  $r1 $r1  -fill $c1  -tag $v1 -outline black
  # gwm add bind to get score.
    .c bind $v1 <ButtonRelease> [list score $v1 %x %y]
  }

 # h --> Sector labels
  for { set h 1 } { $h <= 20 } { incr h } {
    set angle [expr { $halfpi - $SectSize * $h }]
    set x [expr { 0 + 200 * cos($angle) }]
    set y [expr { 0 - 200 * sin($angle) }]
    set Sector [lindex {x 1 18 4 13 6 10 15 2 17 3 19 7 16 8 11 14 9 12 5 20} $h]
    .c create text $x $y -text $Sector  -font {Helvetica -14} -fill white ;# -tag wire
  }

  for {set d 9} {$d<360} {set d [expr {$d+360./20.}]} {
     set rang [deg2rad $d]
     set xm [expr {cos($rang)*$rings(OBull)}]
     set ym [expr {sin($rang)*$rings(OBull)}]
     set x [expr {$xm+cos($rang)*$rings(Double)}]
     set y [expr {$ym+sin($rang)*$rings(Double)}]
     .c create line $xm $ym $x $y -tag "wire"
  }
 #########1#########2#########3#########4#########5#########6#########7#####
  proc score {v1 x y} {
      # gwm score the hit.
      # v1 is the circle hit (Out, Single etc.)
      global rad
      set x [expr {$x-$rad}] 
      set y [expr {$rad-$y}] ;# y in window is opposite convention to mathematical
      # sector atan(1)/2.5 = 1/20 circle
      # add 5.5 would convert to sector in range -5 to 15
      # added 25.5 to make sure >0 (atan2 returns -pi,pi angle)
      # modulo (%) converts to range 0-19.
      set sec [expr {int(25.5-2.5 * atan2 ( $y, $x ) / atan(1))%20 }]
      set score [lindex {20 1 18 4 13 6 10 15 2 17 3 19 7 16 8 11 14 9 12 5 20} $sec]
      switch -- $v1 {
         Out { set score 0}
         Single2 -
         Single { }
         Double { incr score $score}
         Triple { set score [expr {3*$score}]}
         Bull {set score 50}
         OBull {set score 25}
      }
      set cursc [.c.score1 cget -text]
      incr cursc -$score
      if {$cursc>1 || ($cursc==0 && $v1 eq "Double")} {
         # can continue to score but can only end (reach 0) on a double.
         .c.score1 configure -text $cursc
      }

  }
  # restart score
  proc restart {{from 301}} {
    .c.score1 configure -text $from
  }
  # add scoring at left.
  button .c.reset -text "Restart" -command "restart 301"
  .c create window [expr {30-$rings(Out)}] [expr {$rings(Out)-10}] -window .c.reset
  label .c.score1 -text "301" 
  .c create window [expr {30-$rings(Out)}] [expr {10-$rings(Out)}] -window .c.score1