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Final Answers
© 2000-2016   Gérard P. Michon, Ph.D.    

      Pool and Billiards

It is impossible to imagine Goethe or
Beethoven being good at billiards or golf.

 Henry Louis Mencken (1880-1956)

Is it, really?  Mozart owned 12 cues and Linus Pauling played bottle pool.

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See also:

Related Links (Outside this Site)

Billiards With a Bottle.  And This Game Is Dying?   by  Harry Hurt III.
Billiards and Snooker from England and the Commonwealth  by  J. Masters
The Physics of Billiard  by  Jim Loy.
IlliPool:  The Math and Physics of Billiards  by  Brian Townsend.
BCA Equipment Specifications  (Warning: Wrong weight for snooker balls)
Physical Properties of Pool Equipment  by  Dave Alciatore & Tom Ross.
Amateur Physics for the Amateur Pool Player  by  Ron Shepard  of Chicago.
The Physics of Pool  by  Franco Normani.
Samm Diep / Vidal  "Cherry Bomb" :   Tip Jar | Samm's Side Pocket | Blog
Improving Your Carom Shot   |   Jim Loy's Billiards/Pool Page
Glossary of cue sports terms (Wikipedia).
In French:   Billard  |  Règles  |  Théorie des effets  |  Vocabulaire  |  Blog

Regulating Bodies & Other Billiard Associations:

 Coat-of-arns of 
 Gaspard Gustave de Coriolis
  • Théorie mathématique des effets du jeu de billard  (1835)
    by  Gaspard Gustave de Coriolis  (1792-1843; X1808).
    English translation (2005) by  David Nadler.
  • Advanced Technique in Pool and Billiards  (1990)   by  Robert Byrne.
  • The Science of Pocket Billiards  (1989, 1995)  by  Jack H. Koehler.
  • The Illustrated Principles of Pool and Billiards  (2004, Sterling Publishing) by  David Alciatore, Ph.D.  (Dr. Dave)  with video illustrations, including:
    • NV B.41:  Coriolis massé shot aiming method, with large curve.

Spotlight on Billiards   |   Le Billard.  Français, Américain, Snooker et Pool

Movies :   The Hustler (1961)  |  Trailer
The Color of Money (1991)  |  Trailer  |  Ending
Poolhall Junkies (2002)  |  1  |  2  |  3  |  4  |  5  |  6  |  7  |  8  |  9
9-Ball, the Movie (2011)  |  Promo  |  Trailer
Science :   Amazing Billiards in Super Slow Motion  by  Colin Colenso.
The Double-Kiss Zone  by  David Alciatore  (DrDaveBilliards)  |  Bob Jewett
Digitally Assisted Billiards  by  Matthew Straub  & Justin Needham.
Deep Green & Augmented Reality Pool (ARPool)  RCVLab  (Sammy Jordan).
Product Demos :   The Pro Shop (UK)  |  Cue Clean  |  Pocket Lathe
Magic Ball Rack  |  Just-A-Bridge by Larry Keller  |  Flexi-Rest  (The Big Idea)
Gravity Cue
Pocket Billiards  (Pool, Snooker, Pyramid, Bumper Pool)
[9-Ball]   3-Foul Rule (Dong)  |  2005 US Open (Ismael Paez vs. Mika Immonen)
[8-ball]  Stripes & Solids (US)  |  Blackball cassé-fermé (runout) by Craig Marsh
Efren Reyes vs. Francisco Bustamante [ 1 | 2 ] (2001 8-Ball Invitational)
[Straight Pool = 14.1]  15 Balls to  Thorsten Hohmann's  Championship (2006)
[One-Pocket]  Efren Reyes vs. Jose Parica (Galveston)  |  Max Eberle
[Bank Pool, Banks]  Derby City Classic 1 | 2 | 3 | 4  (Daulton vs. Gregg)
[Rotation Pool, 61]  Rules | Honduran Pool | rotation runout (playing the ghost)
[Ten-ball]  2009 Women's World Championship Yu-Ram Cha vs. Shin-Mai Liu
[Seven-ball]  Luther "Wimpy" Lassiter vs. Willie Mosconi  (1980)   1 | 2 | 3 | 4
[Cutthroat Pool, 3 players]   Scratch? by Michael Lamendola   |   Bikini Pool
[Three-ball, several players]   Carnie Ball by Michael Lamendola  |  Break Trick
[Snooker]   Line of Aim by Jack Karnehm  |  Showmanship of Steve Davis
First televised 147 maximum break (1982)  |  Epic loss to Dennis Taylor (1985)
Stephen Hendry at the  Crucible Theater  in  1995  and  2009.
Ronnie "The Rocket" O'Sullivan's ninth 147 (2008) and his fastest one (2006).
Snooker Coaching by Steve Davis   1  |  2  |  3  |  4  |  5  |  6  |  7  |  8
Pot of the century by "Big" Bill Werbeniuk  (miscue and  rebound  over a ball).
[Russian pyramid]   Kremlin Tournament  |  Evgeny Stalev  |  Tricks
[Kaisa]   Finnish Billiards  (2 white cue balls, 2 reds & 1 yellow kaisa)  |  Trailer
[Bumper Pool, Thomas Jefferson, 1805]   Shots  by  Snoodges.  |  Joy's Shot
Trick Shots  (performed on  pocket  tables)
Oliver Whitehouse  |  Jeanette Lee  "The Black Widow" sinks 12 balls at once.
Mike Massey "Tennessee Tarzan" :   Trick Shot Collection  |  Finger Pool
Florian "Venom" Kohler of Kingersheim, Alsace (France) with Mike Massey
Pavel Poledno (www.trickshot.ic.cz)  |  Tommy Vancraybeek
Yoshikazu Kimura of Osaka, Japan  |  Yoshikazu Kimura & Mike Massey
Eric "The Preacher" Yow :  Massé Insanity  |  Eric Yow and Andy Segal
Andy "Magic Man" SegalMedley  |  Barthelette, Yow, McPhail, Segal
Willie Mosconi (1987)  |  Steve Mizerak (2000)  |  Tom "Dr. Cue" Rossman
Unbelievable Pool Trickshots & Impossible Pool Trickshots (2012) compilations from  InsidePOOL, Florian "Venom" Kohler & Rick "PrayingMantis" McAvay.
French Billiards  or "three-ball carom" is played on a pocketless table with a red object ball  (bille de but)  and two distinct cue balls  (billes de choc,  yellow or white, spotted or not).  Each shot must be a  carambole  where a cue ball hits the other two balls under the conditions imposed by the rules of the  discipline  (for  artistic billiards  those rules are different for each shot).  The  7  currently practiced disciplines of French billiards are listed below in order of increasing difficulty, starting with the 5 so-called  classic disciplines  (jeux de série)  which involve mostly low-speed action over short distances.  Among those, each of the three modern flavors of  Balkline  (jeu de cadre)  is denoted by a pair of numbers; the first one is the width of the  cadre  (in cm)  and the second one is the maximum number of consecutive shots allowed within the same rectangle  (71 cm is half the width of a full-size table, 47.4 cm is one third).  Unrestricted straight-rail allows  poussette  (nursing)  tactics that can make championships uninteresting  (the so-called serie à l'Américaine was invented in Canada by the brothers Cyrille and Joseph Dion around 1870).  Maurice Vignaux (-1916) still holds the straight-rail record for the run of 1531 points he made in Paris in 1880, on April 10-14, against George F. Slosson.  The precursor of the many variants of modern balkline was the short-lived  Champion's Game  (1879-1883) which merely barred corner play using 18'' by 38'' lines  (Slosson held the record for this, with a run of 398 points achieved in 1882 during a match against Vignaux).
-   Straight rail :   (Partie libre)  taught by  Thierry de Marchi  [1,2]  in French.
-   47/2 :   Georges Bourezg [1,2,3]  by Louis-Emile Galey  |  Laurent Guénet [blog]
-   47/1 :   Arnim Kahofer  |  Xavier Gretillat  |  P. Soumagne vs. W. Gerimoni | 2
-   71/2 :   Marek Faus  |  Esteve Mata vs. Raul Cuenca | 2 | 3 | 4 | ... | 16 | 17
-   Cushion caroms ("One-cushion") Raymond Ceulemans (1984)
-   3-Cushion :   15 ways to start  |  Frédéric Caudron (1996)  |  Run of 15 by Sang Lee vs. Hank Habraken (1999)  |  Daniel Sanchez (2005)  |  Torbjörn Blomdahl (2006)  |  Marco Zanetti (2009)  |  Dick Jaspers (2009)  |  Carom
-   Artistic billiards :   Raymond Ceulemans  |  Semih Sayginer  |  Jean Reverchon Haci Arap Yaman vs. Xavier Fonellosa  |  Florian Kohler  |  Martin van Rhee  |  Thomas Ahrens  |  Sander Jonen  | 
Pentathlon  is a form of international billiard competition combining straight-rail to 200 points, 47/1 and 71/2 to 150 points, cushion-caroms to 100 points and 3-cushion to 30 points.  Biathlon  involves 3-cushion French billiards and 5-pin Italian billiards.
[5-pin Italian billiards & 9-pin goriziana]  Brigitte Nielsen (Bye Bye Baby, 1988)
19 Opening Shots  |  11 Opening Safety Shots  |  Biliardo 5 Birilli  |  Uneven Tricks
[4-ball carom]   Yotsudama  or  Sa Gu (Korean billiards)  |  Czech 10-carom, etc.
Boccette is  digital billiards  (no cues)  on a carom table, with 5 skittles & 9 balls.
Pétanque is played with a 38 mm jack, between 4 players.  Each one has 4 cue balls  (48 mm)  of a specific color and plays bank shots to get nearest to the jack.

Training :   Instructional Videos by  Mike Page  (FargoBilliards)  BCA instructor.  Fargo Billiards & Gastropub, in Fargo, North Dakota.


The Physics of Pool and Billiards

This page  (which is still a work in progress)  will neither teach you the rules of the many extant billiard games, nor is it intended to improve your skills  (I am not qualified to do that, but I recommend exploring some of the many encyclopedic and video links provided here).
One limited aim is to provide a rational introduction to all billiard games by describing their common history and characteristics as well as some basic differences in their implements.
Because  Numericana  is a mathematical site, the main emphasis is to explain  why  billiard balls  (and cues)  move the way they do.  Many people share a fascination for the physics involved and rightly celebrate billiard masters as practitioners of a true form of art.

(2010-12-31)   Size of the  playing area  (playbed)  in a billiard table.
The  nominal  size of a pool table is  8''  more than its  playing length.
(Traditionally, that nominal size was the length of the  slate slab.)

The width of the playbed in a billiard table must be half its length.  The width and the length are measured between the tips of opposing rail cushions.

The  nominal size  of a table  (expressed in feet)  is  8''  more than the length of its playing area.  The  advertised size  (or  quoted size)  of a standard pool table is exactly equal to its nominal size, except in two cases:

  • A standard  7'  table has a true nominal size of  7' 2''  corresponding to a playbed length of  78''  (not  76'' ).
  • An  8½'  table has a nominal size of  8' 4''  corresponding to a playing area  92''  long (not  94'' ).  Tables of that unusual size are also referred to as  oversize 8 foot tables  (or even  8 foot tables, which they're not).

The actual outside length of a pool table is almost always a few inches longer than its nominal size,  but that's irrelevant to the calculation of the clearance space needed around a given table  (which depends only on its cushion-to-cushion dimensions and on the length of the longest cue you wish to use).

The traditional length of the playbed in  carom  tables used to be specified as  8 pieds & 9 pouces  in terms of the royal foot  (pied de roi)  used in France  (and elsewhere, for scientific purposes)  before the metric system.  The legal conversion factor for this obsolete unit is effectively determined by Canada, which still uses an exact multiple of it for surveying purposes  (the  arpent).  The  pied de roi  should thus be considered to be exactly  12.789''  or  0.3248406 m.  With ludicrous precision, this makes the nominal length of a traditional carom playing surface exactly equal to  2.84235525 m.  This piece of trivia is now all but forgotten.  Instead, modern regulators have chosen to round the above number to the nearest centimeter  (2.84 m)  and allow a tolerance of  5 mm.  A manufacturer mindful of tradition could still aim for the above bed length rounded to the nearest millimeter  (2.842 mm)  and enjoy a comfortable manufacturing tolerance of  3 mm.  Following the above pattern, the nominal size of a traditional carom table is  8''  longer than its playing area  (9.984' ).  Such  pocketless  tables are  advertised  as  10 foot tables.  Converting a pool table 
 to a carom table...

The 9-foot tournament pool table has exactly the same playing field  (100''  by  50'' )  as the so-called  small  carom table  (which has no pockets).  The diagonal of a small carom bed is nearly the length of a full-sized one  (111.8'' = 2.84 m).

Some manufacturers provide kits  ("plugs")  to convert a pool table into a small carom table with add-on rails that plug the six pockets  (see picture at right).

Inexplicably, the current regulations for snooker specify a width and a length for the playing area which are not in a  1:2  ratio, although this was clearly not the intend of the regulators.  Nevertheless, the large tolerance of  13 mm  allows the construction of correctly proportioned playbeds, including three that have a whole number of millimeters per diamond unit, namely:

  • Width = 1788 mm.  Length = 3576 mm.  Tolerance = 2.7 mm
  • Width = 1784 mm.  Length = 3568 mm.  Tolerance = 7 mm
  • Width = 1780 mm.  Length = 3560 mm.  Tolerance = 4 mm

If the snooker regulators wanted to fix their mistake, they could choose one of these three specifications, ideally adopting a grandfather clause allowing an extended tolerance for tables built before a certain date  (in order not to rule out equipment that was compliant when it was built).  The last possibility listed has the superficial advantage of dimensions involving a whole number of centimeters (playbed dimensions of 3.56 m by 1.78 m)  but it would entail a fairly large grandfather tolerance  (22 mm in length and 15 mm in width).

To avoid numerical inconsistencies in the present article, I chose the middle specifications  (3568 mm by 1784 mm)  which has the best compatibility with the published  (flawed)  standards.  If adopted  (with a simplified grandfather tolerance of  19 mm in either dimension)  those new specifications would entail manufacturing tolerances  of  7 mm  on  12' tables,  which would be directly comparable to what's currently required for carom tables  (namely, 5 mm  on 10' tables).  Every table made to the new specifications would comply with the former standards.

Physical Dimensions of the Basic Equipment Used in Cue Sports
Length of playbed is indicated between parentheses.  It's exactly twice the width, measured between cushions.
  Mini Pool (UK) Pool (US) Carom Snooker
Full-Size Table 5' 7' (78'' ) 9' (100'' ) 10' (2.84 m) 12' (3.57 m)
Smaller Size(s) 4' 6' (64'' ) 7', 8' (88'' ) 9' (100'' ) 8', 9', 10'
Ball Diameter 44.45 mm 50.8 mm 57.15 mm 61.5 mm 52.4 mm
Cue Length 36-48'' 52-57'' 56-58'' 56-58'' 57-63''
Tip Diameter
[ most common ]
(8 mm)
8-10.5 mm
[ 8.5 mm ]
9-14 mm
[ 12.75 mm ]
(12.25 mm)
[ 12 mm ]
8.5-11 mm
[ 10 mm ]
The unofficial format listed as  mini  is found in folding tables for casual family use.  Smaller tabletop billiard boards are used with marble-like balls  (1¼'' = 31.75 mm or smaller)  barely playable with tiny cuesticks.
At the other end of the spectrum, tournaments of Russian billiards  (Pyramid)  are played on regulation snooker tables using large balls  (68 mm diameter)  which are barely 5 mm smaller than the corner pockets.  Some amateurs play that game with slightly smaller balls  (60.3 mm)  on less massive tables  (e.g., 9', 8' or 7').

The  space  around a pool table must allow shots where the cue ball is against the cushion and the cue stick is perpendicular to the edge.  So, the distance between the wall and the  edge of the playing area  (cushion nose)  must be at least one cue length, plus six inches of draw (backstroke).

So, with  58'' cues,  a minimum distance of  64''  (1.63 m)  is required between the nose of a cushion and the wall behind it.  The wall-to-wall distance required to play a given table with a full cue is thus  128''  (3.25 m)  longer than either dimension of the table's playing surface  (the size of the rails is irrelevant).  For a full-size  (9-ft)  pool table, this works out to be  228''  by  178''  (5.79 m by 4.52 m).  A  7-ft table  (playing length  78'')  fits in a  5.23 m x 4.24 m  room.  A table can be used in an undersized room by playing the aforementioned critical shots with a "shorty" cue  (whose maximum length is  6'' less than the smallest cushion-to-obstacle distance).  According to regulations, a pool cue must be at least  40''  in length but shorter cues  (down to  30''  or so)  are available which can accomodate severe space limitations  (they're also great for younger players).

Carom tables have no pockets.  The other tables listed above have 6 pockets  (at the 4 corners and in the middle of the long sides).  The width of each pocket is such that two balls of the tabulated diameter will barely fit side by side between the slanted rails  (watch:  How to Measure a Pocket).

Diamond Sights  & Diamond Unit :

The conventional unit of length in billiards is called the  diamond  and it's equal to the center-to-center distance between the adjacent diamond marks that all billiard tables have  (or should have)  on their rails.  One  diamond  is equal to one fourth of the width of the playing area  (or one eighth of the length). Pocketless  (carom)  tables thus feature  9  diamond marks on the long rails and  5  diamond marks on the short ones,  including extreme marks  (which are sometimes omitted)  that indicate the positions of the noses of the cushions perpendicular to the rail.  On pool tables, the presence of pockets eliminates the four pairs of corner marks and the two marks in the middle of the long sides.  This only leaves six sets of three actual diamond markers between adjacent pockets.  Nevertheless, the underlying diamond grid is exactly the same for pool tables and pocketless tables.

The value of the diamond unit varies with the size of the table
 Quoted Size   Nominal Size   Playing Length  Diamond Unit 
12' Snooker12'''3.568 m446 mm
10' Carom9' + 30 cm2.84 m355 mm
9'9'100''12.5'' = 317.5 mm
'8' 4'' = 100'' 92''11.5'' = 292.1 mm
8'8'88''11'' = 279.4 mm
7' Bar box / Pub7' 2''78''9.75'' = 247.65 mm
6'6'64''8'' = 203.2 mm
5' Mini 5' 2''54''6.75'' = 171.45 mm
 L + 8''LL / 8

For traditional tables, the actual length of the table would typically be  L+11½''  which is slightly larger than the nominal size.

The nominal size  (L+8'')  is the length of the slate slab around which the table is constructed.  The size of that is thus  L+8''  by   L/2+8''  with a thickness of  1''  (thickness may vary, see below).  The density of solid slate rock is  2.691 g/cc.  Neglecting the pocket cutouts, this makes the slate slab for a 7' table weigh  178 kg.  The slab of a 9-foot table weighs 262 kg and is normally divided into 3 pieces of 92 kg each.  A full-sized snooker table features about 512 kg of rock, divided into 5 pieces of 102 kg each.

Do it yourself:  Pool Table Plans   |   "How it's made" Video :  Pool Tables
Novelty Tables:   Modern (Mars Made)  |  Glass (Nottage Design)  |  Round  |  Gyroscopic  |  3D-Miniature

(2011-04-07)   Slate Slab

The density of slate rock is 2.691 g/cc.  Thickness vary from a minimum of 3/4''  (19 mm)  to  7/8'', 1'' (Pool tournament) 30 mm or even 45 mmm (Carom tournament),

 Come back later, we're
 still working on this one...

Do it yourself or repair:  Billiard Slate for Sale   ( Lakeside Billiard Supply )

(2011-02-24)   Billiard Cloth

 Come back later, we're
 still working on this one...

Championship Fabrics   |   Simonis Cloth

 k66 profile (pool cushion)
(2011-02-24)   Cushions

K66 profile.

 Come back later, we're
 still working on this one...

Championship Cushions   |   Brunswick Superspeed Rubber Rails

(2010-12-31)   Billiard Balls
From wood or clay to ivory, to celluloid, to  Belgian phenolic balls.

Early billiard balls were made out of wood.  They wore out quickly and developed bruises and flat spots...  Clay balls were also used as late as the 1960's.  They were fairly inexpensive but broke too easily.

The exact time when ivory billiard balls  (ivories)  were introduced isn't well documented.  Ivory balls are mentioned in the first edition of  The Compleat Gamester (1674)  by Charles Cotton.  The oldest extant reference to ivory balls is in the 1588 inventory of the 4th Duke of Norfolk  (Thomas Howard, 1536-1572)  who kept at Howard House  "a billyard bord covered with a greene cloth [...] three billyard sticks and 11 balls of yvery".

Legend had it that the best matched three-ball sets were obtained from a single tusk of a female elephant.  In fact, this wasn't so, since balls made from the same tooth could vary considerably.  Instead, the matching was done by selecting from a large number of finished balls.  Only  4%  of those matched sets were considered good enough for tournament play  (according to an interview of one  James Burroughes  published in the New York Times on  December 1, 1889).  Balls were turned by highly-qualified workers so that the central nerve in the tusk appeared on opposite points in the ball.  Like wood, ivory swells across the grain in a damp atmosphere.  So, a spherical shape can only be maintained at constant humidity.

Changes in humidity also promotes cracking, which is what motivated the invention of heated billiard tables.  Such tables remain mandatory today in international carom tournaments, because maintaining the surface a few degrees above ambient temperature prevents dampness of the cloth and ensures the consistency of the playing surface.

Thousands of elephants were slaughtered yearly to provide for the needs of the billiard industry.  Well before the current ecological mindset, there were concerns that the supply of ivory was dwindling too rapidly and that human lives were put at risk in the hunts.  A  $10,000  prize for an artificial substitute to ivory billiard balls. was offered by the  Phelan & Collender billiard manufacturer  (which merged with  Brunswick Billiards  in 1884).

The development of the modern substitutes for ivory started with the first man-made plastic, invented in 1856 by Alexander Parkes (1813-1890) who plasticized nitrocellulose with camphor  (the stuff was dubbed  Parkesine  at first).  In 1868, John Wesley Hyatt (1837-1920)  investigated a high-pressure manufacturing process for that same substance, which he would popularize with his older brother, Isaiah Smith Hyatt, under the name of celluloid  (the name was duly registered in 1873, but it's now genericized).

Celluloid was used to make the so-called  composition balls  which used a denser substance in their cores to achieve the correct density.  Such balls didn't quite play like regular balls, partly because they didn't have the same moment of inertia as homogeneous spheres.  That desirable characteristic would only be achieved with the advent of the synthetic resins that allow an homogeneous mix with dense powders  (like calcium carbonate).

Modern  celluloid  (used for ping-pong balls and guitar picks)  is made with acetic acid instead of nitric acid.  It's much safer than the original flammable celluloid that could reportedly explode during manufacture.

The nominal density of modern billiard balls is  1700 kg/m.  That's close to the mean density of ivory  [1.70(2)]  the former substance of reference.  The maximal density of  1740.40 kg/m,  would give a  2¼''  ball  (57.15 mm)  its maximal regulation mass of  6 oz  (about 170 g).  Incidentally, a ball with a volume of  100 cc  (0.1 L)  would have a diameter of  57.59 mm...

A  2¼''  ball  (57.15 mm)  must weigh between 5½ oz  (156 g)  and 6 oz  (170 g).  At the nominal density of 1700 g/L, a  2¼''  ball would weigh  166.15 g.

The most praised modern billiard balls are made with  phenolic resin,  which is a thermosetting bonding compound obtained by polymerizing  CHOH  (phenol or carbolic acid)  with  HCHO  (formol or methanal).  That synthetic material was invented by the Belgian chemist Leo Baekeland (1863-1944) in 1907.  It became popular in the 1920's under the name of Bakelite®.  Its uses have included telephone casings, electrical insulators, kitchenware, toys and even jewelry...  Due to high manufacturing costs, this material has now been supplanted by other mouldable plastics, except in top-quality billiard balls and a few other critical products.

Inert countertops  (in the lab or at home)  are currently made from phenolic resin, with a filler consisting of up to  70%  of cellulose fibers  (e.g., Richlite®).  Phenolic resin is also  commonly  applied as a thin layer on both faces of a wood product known as  phenolic plywood.

Since pure phenolic resin has a fairly low density of  1215 g/L,  heavier filling materials  (colored or not)  must be used to reach the aforementioned nominal density of modern billiard balls  (1700 g/L).

I don't know what filler is actually employed in phenolic balls, but I am tempted to investigate calcite  (density 2.71)  to mimic the high-calcium content of natural ivory,  in which case  51.7%  of calcite  (by mass)  would be needed  (about  32.44%  by volume).  That works out to be 15 parts of finely powdered calcium carbonate for 14 parts of resin.  Recall that the average density of a mix is a harmonic mean:

15 / 2.71  +  14 / 1.215   =   (15+14) / 1.700113...

Sizes of Billiard Balls Used in Modern Games   (nominal density:  1.7 g/cc)
"Grapefruit" and "rock" are calibers for cueballs in automatic tables that detect and return oversized or heavy balls.
Game FormatDiameter VolumeNominal
Regulation Mass
?72.00 mm195.43 cc  332.23 g  
Pyramid - full68.00 mm164.64 cc  279.88 g  
Carom61.50 mm121.79 cc  207.05 g205.00 g220.00 g
Pyramid - small60.50 mm115.95 cc  197.11 g  
Grapefruit ( 23/8'' )60.33 mm114.95 cc  195.41 g205 g  (measured)
Rock ( 2¼'' )57.15 mm97.73 cc  195.41 gHeavier Density
US Pool - 2¼''57.15 mm97.73 cc  166.15 g155.92 g170.10 g
Bumper ( 21/8'' )53.98 mm82.33 cc  139.97 g  
Snooker ( 21/16'' )52.39 mm75.28 cc  127.98 g  
UK Pool - 2''50.80 mm68.64 cc  116.69 g  
Pétanque - cue48.00 mm57.91 cc   98.44 g  
Pétanque - jack38.00 mm28.73 cc   48.84 g  
Mini - 1¼''31.75 mm16.76 cc   28.49 g  
Half-scale ( 11/8'' )28.58 mm12.22 cc   20.77 g  

The Belgian company Saluc S.A.  (founded in 1923 and owned by  Armand Capital Group  of Chicago)  dominates the manufacture of phenolic billiard balls, which it sells under the  Aramith  brand, in several grades.  From the Belgian village of Callenelle, they supply 80% of the billiard balls worldwide.

The largest billiard company in the World,  Brunswick Billiards, an American manufacturer of pool tables founded in 1845, started making phenolic billiard balls in 1945.  Now, they sell only the  Brunswick Centennial  prestige brand, which is actually  manufactured by Saluc  to the same specifications as the finest Aramith balls  (a 16-ball set of either brand retails for about $250).

Other brands offer more affordable balls,  made from unsaturated polyester resins,  which do not quite match the performance or durability of real "Belgian phenolic balls".  Simpson's decorative  Elephant Beautiful Balls  (about $180 a set)  have based their reputation on good looks, not durability.

The manufacture of "Elephant Balls" is now commissioned by Sterling Gaming, a billiard wholesaler from Matthews (North Carolina)  retailing as CueSight Technologies.  Under the  Sterling  brand, they sell other styles of balls, in different grades, based on the same technology.

Bargain brands like  Action  are offering decent 16-ball sets for $30 or so.

Unbranded cheap  acrylic  billiard balls are apparently off the market...

Videos on sphere-making:   Bowling Balls   |   Marbles   |   Ball Bearings

(2010-12-31)   Cue Sticks, Butts & Shafts  (Queues, Talons & Flèches)

A pool stick should have  about  3 times the mass of the ball it's intended for.  Snooker cues have longer and thinner shafts with shorter butts featuring a flat section which can accomodate a plate.  Some snooker cues can be fitted with butt extensions which may or may not be associated with the use of a mechanical bridge  or  rest  (the latter term used to be a slang term).

Because of the large size of snooker tables, rests are more commonly used in snooker than in other forms of billiards.  They come in many shapes and designs:  rake, cross, spider, swan (swan-neck spider) and extended rest.  Lately, the versatile "Flexi-Rest" has been supplementing the traditional assortment and seems to be slowly replacing part of it.

Nowadays, the finest cues are meant to travel with their owner and come in two pieces which are screwed together at play time:

  • An ornate rear thick part, called  butt  (talon  in French).
  • A plain thin part  (½'' in diameter)  called  shaft  (flèche  in French).

For pool and carom billiards, two-piece cues always feature a  center joint  (i.e., the two pieces are roughly of the same length).  On the other hand, snooker cues are almost always "3/4 jointed", which is to say that the buttpiece is about  16''  and the shaft is  42''  (a foot longer than in center-joint design).  The traditional design for a one-piece snooker cue calls for a butt of ebony to be spliced into a shaft of ash up to a distance of about  22''  from the rear.  That distance is typically respected in jointed cues but the splicing is limited to the front part of the cue; the rear part being solid ebony.

The joint between the two parts is mechanically critical.  A superior solution, introduced by the Canadian cuemaker  Thierry Layani,  is the conical joint.

Selecting a snooker cue   |   "How it's made" Video :  Pool Sticks
Thread :  Are We All Using Low-Deflection Shafts, Now?   (Pool.bz)   |   OB Cue Shafts
Novelties :  Demo  by Jason Lynch of Pneu-Power Cues (2010) $199  |  Laser Cue  by CueSight (1999) $149

(2011-03-29)   Cue Case  (French: étui de billard)
 Brown Sonoran (Layani Cue)

Only once in my adult life did I travel to a remote location for the sole purpose of having fun:  In the Summer of 1976,  I spent several weeks on the  Island of Mauritius  at the  Club Méditerranée  resort, where I learned to water-ski and was initiated to a billiard game that I would only know as  billard sud-africain  until I learned its correct name, much later, from a British TV broadcast:  Unwittingly, I had learned  snooker !

Although snooker was invented around 1875  (possibly by Colonel Sir Neville Chamberlain of the British Army garrisons of India)  its modern popularity is due to the advent of British color TV broadcasts  (1969).
 Layani Conical Joint

Today, on my 55-th birthday, I finally got my own state-of-the-art billiard gear...  As an engineer, I could only go for the conical joint of  Thierry Layani.  Once you know about it, no other cue joint makes sense.

Here is what's in  my  case, now:

  • The  29½''  (420 g)  no-point Layani  Brown Sonoran  buttpiece pictured at left  (nutmeg-stained curly maple with bloodwood, Brazilian wood and ebony inlays and rings)  sporting a velvet grip of 32.5 cm  (Renzline  manchon  weighing 15 g). 
  • Predator  3142 shaft  (no logo, 0.6'' ferrule, 114 g).  Conical joint by  Thierry Layani  (thanks to  Philippe Singer  of  Kozoom).
  • Layani pool shaft  (12.75 mm tip / 29 inches = 73.66 cm / 123 g).
  • Layani 3-cushion shaft  (12 mm tip / 69 cm / 105 g).
  • Layani 5-layer medium-hard cue tips  (13.5 mm in diameter).
  • A  25 cm  Layani extension tube  (28.5 cm with joint)  112 g.
  • A weight kit (balancing bolts & key) 56 g, 36 g, 26 g, 16 g, 10 g.
  • 4  female Layani joint protectors  (for shafts).
  • 2  male Layani joint protectors  (for buttpieces).
  • Just-A-Bridge.  Moosehead Bridge Head.
  • Willard's Tip Shapers (nickel and dime).
  • Blue Diamond chalk (blue).  Silvercup chalk (green).
  • Aramith micro-fiber cloth, with backing.
  • Etc.

The Layani extension normally goes between butt and shaft.  Happily, it doubles as an  11½''  buttpiece  (with a joint protector in the rear)  which is just long enough to form a legal  jump cue,  using any  29'' shaft.

The minimum length allowed for a pool cue is  40''  and the maximum weight is  25 oz.  There's no set maximum length or minimum weight.  The diameter of the tip must be between 9 and 14 mm.

What's in the pool cue case of...
Efren "Bata" Reyes  |  Johnny Archer (The Scorpion)  |  Ralf Souquet (The Kaiser)  |  Eric Frost
Earl Strickland (The Pearl)  |  Eric "Fatboy" Peterson  |  Max Eberle (Mad Max)  |  Eric Yow (The Preacher)
Ladies:  Jasmin Ouschan  |  Samm Diep  |  Sarah Rousey  |  Kelly Fisher  |  Laetitia Dos Santos (in French)
Carom Players:  Pierre Soumagne (in French)  |  Peter De Backer  |  Frédéric Caudron

(2010-12-31)   Cue Tip  (French: procédé)

Captain François Mingaud (1771-1847) was one of the most famous billiard player of his day, in his native France and elsewhere.  He had designed a very popular cue in 1790 which he perfected in 1807 by inventing rounded leather tips  (while imprisoned in the Bastille).  Captain Mingaud also inspired the first complete analysis of the game by the physicist Gaspard Coriolis, in 1835.

Modern leather tips come in several grades, according to their mechanical properties:  soft  (or  slowmedium  and  hard.  They may be layered or include additives to achieve the desired grade.  The hardest tips forgo leather entirely, in favor of the type of hard resin used in modern billiard balls; they are commonly known as  phenolic tips  and are exceptionally durable  (they hardly ever require shaping or replacement for many years).  The misguided current trend is to ban phenolic tips on break cues  (such tips will probably always remain legal on jump cues, where they are all but indispensable, and on playing cues, where there are all but useless).  The advertised motivation of regulators is to increase the life expectancy of cueballs...

Curiously enough, the use of leather tips can be objectionable to some players for religious reasons, since  "leather" is often  pigskin  (according to many manufacturer specifications).

The front end of a tip should have a spherical shape.  Poolplayers can choose between only two sizes  (named after the ten-cent and five-cent US coins)  because only two gauges of shaping tools are available:

  • Dime:  Nominal radius of 0.3532''  (8.9535 mm).  About 9 mm.
  • Nickel:  Nominal radius of 0.4175''  (10.6035 mm).  About 10½ mm.

The most popular shaping tools  (single or dual gauge)  include:

Video Guide to Pool Cue Tips  |  Fitting a Snooker Cue Tip

(2011-03-14)   The two kinds of billiard chalk...
One  reduces  hand friction, the other  increases  tip friction.

Modern billiard cue chalk is different from common chalk  (limestone, composed of calcium carbonate)  which billiard players were using on their leather cue tips before 1897.  It's also entirely unrelated to what's variously called blackboard chalk, artist's chalk  or sidewalk chalk  which consists mostly  of compressed  calcium sulfate  powder, obtained from gypsum.

The term  billiard chalk  denotes ambiguously two different things which are better called, respectively,  billiard powder  and  cue chalk :

Billiard Powder Decreases Friction :

 Cone Chalk   To most chemists,  billiard chalk  means  magnesium carbonate  (MgCO3).  This stuff is the powdery substance that gymnasts and other athletes put on their hands, or other body parts, to reduce friction with various sport implements, including barbell and high bar.  (The effect is  opposite  to that of rosin, which is used to  improve  grip on a shot put, baseball or bowling ball.)
In pool halls, this type of "chalk"  (improperly known as  talc )  is called  cone chalk  as it's usually available in the form of solid cones mounted on walls or furniture.  Some billiard players apply that on their  bridge hand  to reduce shaft friction.

Other players choose to bring their own powder to the scene, which is usually some form of  real  talc  in the finely powdered form otherwise known as  baby powder  or, more precisely,  talcum powder.  The solid form is known as  taylor's chalkSoapstone  (steatite)  consists mostly of pure talc  or  magnesium silicate hydroxide  Mg3Si4O10(OH)2  [not  MgSiO].

Above a certain level of humidity, all billiard players need to use such stuff, unless they wear a  billiard glove.  Nowadays,  corn starch  is often substituted for  talc  in actual baby powder  (watch the labels).  Both work fine for billiard use but corn starch will not cause the respiratory problems associated with the repeated inhalation of talc by babies.

Because of its smoothness and ease of carving, soapstone  (steatite)  was chosen by the French sculptor Paul Landowski for the outer layer of the famous statue of  O Cristo Redentor  (Christ, the Redeemer)  710 m  over  Rio de Janeiro, Brazil.
The statue has a  30 m  span.  Its concrete core was designed by the local engineer  Heitor da Silva Costa.  It was built between 1922 and 1931 on top of the prominent Corcovado granite peak  (whose name means  hunchback in Portuguese).
  Christ the Redeemer,  over Rio de Janeiro.
 Cristo Redentor, Corcovado Peak 
 Rio de Janeiro, Brazil
  Martyn Poliakoff's means SiO3 (not 4) and granite (not marble).  Slips of the tongue...

Cue Chalk Increases Friction :

The rest of this article deals with something else entirely, which is what almost all billiard players  (who aren't chemists)  think of as  chalk,  namely the stuff unambiguously known as  billiard-cue chalk  or  cue chalk.  It is applied to cue tips to  increase  friction with the  cue ball  during collision.  With too little friction, some skidding between tip and ball might occur; an undesirable phenomenon known as a  miscue.

The use of  cue chalk  to prevent miscues predates the invention by Mingaud of the leather tip (in 1807).  At first, players were simply scratching the tip of their wooden sticks directly on the plaster finish of surrounding walls (plaster is  calcium sulfate).  Pieces of chalk for specific use in billiards had already been in use for some time when one Jack Carr had the idea of marketing them as "twisting chalk" to stress the idea that his own "brand" of chalk could help players mimic his own skill at imparting spin.

The dominant (cheap) type of cue chalk is still based on the recipe devised in 1896 by the American chemist William Hoskins  (1862-1934, also remembered for invented the nichrome alloy used in electric heating)  and the professional billiard player William A. Spinks (1865-1933), who was more commonly known as  Billy Spinks.  They were jointly issued US pat. 578514, dated March 9, 1897  [ 1, 2 ]  which covers:

substitute for billiard-chalk  composed of [normally white] pulverized silica, corundum, a binding agent and a coloring agent such as chrome-green, the whole being compacted into cakes or blocks.

The stuff was marketed by  Wm. A. Spinks & Co.  early in the 20th century.  The original cakes of  Spinks  chalk were cylinders.  Now, virtually all cakes of  cue chalk  are manufactured as cubes with a small spherical indentation that grows with actual use.

Most brands of chalk are now discontinued  (see table below for today's dominant brands).  Former favorites became collectibles, including:

  • Spinks.
  • Manhattan Club  (by the Brunswick-Callender-Blake Company).
  • Clik  (by the Brunswick-Callender-Blake Company).
  • Etc.

Some Current Brands of Cue Chalk
Pack size is smallest number of pieces available at retail.  Cost is from Internet offers  (without tax & shipping).
Owned byBrand$ / packPieceColorsRecipe
(est. 1945, Italy)
manufactured by Tweeten
for the Norditalia Company
$6.10 / 2 $3.05Blue(c. 1980)
NIR Super
$7.75 / 3$2.58
Blue (c. 2000)
  Brunswick $5.52 / 12$0.46B,G  
Silver Cup Chalk
(est. 1990)
Macon, GA
$3.25 / 12 $0.27
red wrap
US patent
Silver Cup $2.75 / 12$0.23 24
Tweeten Fibre Co.
Chicago, IL
Master [thick] $2.75 / 12$0.23 10
Triangle [thin] $2.75 / 12$0.23 B,G,R

The density of billiard chalk is typically  1.62 g/cc.  A standard cube of chalk is  22 mm  on a side  (with a shallow spherical indentation  12 mm  in diameter)  and weighs about  17.2 g.

Billiard Chalk  |  Best type of chalk?  |  What chalk is the best? (Snooker)
Why I pay $3.50 instead of 25 cents for chalk  by  Michael McCafferty  "FastMikie" (Diary of a Pool Shooter)

 CRC Heavy-Duty Silicone
(2011-04-01)   The Controversial Use of Silicone Spray
A magic lubricant used by some trickshot artists.

To perform critical trickshots, friction with the cloth can be drastically reduced by spraying a ball with heavy-duty silicone.

Another possibility is to apply silicone sparingly to the cloth itself.  To do so, one simple method is to mist the product over the table.  For a more contolled application, the cloth is wiped with a towel sprayed with silicone  (the cloth can be humidified first).

This use of silicone is messy.  Ball treatment is only reliable for a single shot  (after each use, either cleaning or re-coating is required).

The "secret" of Eric Yow (at 5:40)
Silicone Spray Effects  [ Massé-draw  |  Coriolis massé aiming principle ]  by  Dave Alciatore

HTCburton17  (Yahoo! 2011-02-08)   Colliding Carroms
A puck collides with an identical one at rest.  They emerge at angles of  33°  and  46°  from the incoming line.  Was the collision elastic?

Let's call the  oriented  angles of emergence a  and  -b.  They must be of opposite signs  (or else the zero momentum perpendicular to the incoming direction couldn't possibly be conserved).  So,  WLG, we may assume that  a  and  b  are both positive.  Let's call M the mass of each puck and u the speed of the incoming puck.  Let v and w be the outgoing speeds.  We express the conservation of linear momentum in Cartesian coordinates:

M u [  1
 ]   =   M v [  cos a
sin a
 ]  +  M w [  cos b
sin b

This is a system of two simultaneous linear equations in two unknowns  (v & w)  of determinant  sin(a+b).  The solution is:

v   =   u  sin b / sin(a+b)         and         w   =   u  sin a / sin(a+b)

 Come back later, we're
 still working on this one...

Video :  Lecture 16 MIT 8.01  (Physics 1)  by  Walter Lewin (Fall 1999)
How to Play Carroms   |   Carrom Fever   |  
Carrom White Slam by Steeve Collard (France)   |   Carrom White Slam by Karnal Abdin (UK)

 Johann-Albert Euler 
 (1734-1800) (2011-01-30)   The theorem of Johann-Albert Euler  (1758)
The trajectory of a ball is a parabola followed by a straight line.

The eldest son of  Leonhard Euler was a prominent geometer in his own right.  In 1758, Johann-Albert Euler (1734-1800)  published a study of the motion of a sphere on an horizontal plane in the presence of Newtonian friction.  His main result would be rediscovered independently by  Gaspard Coriolis  as part of his authoritative theoretical work on the topic:  Théorie mathématique des effets du jeu de billard  (1835).

A billiard ball in contact with the cloth has  5  degrees of freedom  (2  for position and  3  for spin).

 Come back later, we're
 still working on this one...

Crazy Spin Shots (1984)  by  Jimmy "Whirlwind" White.

(2011-03-19)   The Stop Shot   (Stun Shot)
Making the cue ball stop after hitting the object ball.

In an elastic collision with an object ball of the same mass, the cue ball will stop only when it is aimed  dead center  (i.e., directly toward the center of the object ball)  and has no spin  at the time of impact.

This is achieved by giving the cue ball just enough initial backspin so that the spin can wear off with distance and vanish precisely at the time of impact with the object ball.

 Come back later, we're
 still working on this one...

Video Instruction:  Cue Ball Control 

(2011-04-27)   Draw Shots   (Screw Shots)
Backspin is imparted by hitting the cue ball  below center.

 Come back later, we're
 still working on this one...

Sense & Nonsense of Cue Ball Draw  by Mike Page  (FargoBilliards)   |   Snooker power draw (screw) shot 
Draw shot   by Joe Nichols (Breaktime Billiards, Wilmington, NC).   |   Extreme Draw by Mike Massey

(2011-04-27)   Force Follow Shots
Some forward spin  (topspin)  is needed to achieve  natural roll.

What billiard players call  natural roll  is normally dubbed  pure roll  by physicists...  Either term denotes a rolling motion where the point of contact has zero speed  (solling without sliding).

 Come back later, we're
 still working on this one...

Is Maximum Topspin Overspin?  by Mike Page  (FargoBilliards)
APA Instruction by "Dr. Cue" (Tom Rossman):  Force Follow Shots!  Lesson 44  &  Lesson 45 
Draw shot   by Joe Nichols (Breaktime Billiards, Wilmington, NC).

(2011-02-23)   The Stun Path of the Cue Ball (no sidespin)
Starts at a right angle from the line of the object ball.

Draw or follow spin will pull or push the cue ball away from the stun path.

 Come back later, we're
 still working on this one...

Video Clip by  Jeanette Lee  ("The Black Widow")

(2011-03-26)   Leftover Spin
The cue ball may spin for a long time after stopping.

 Come back later, we're
 still working on this one...

Claimed Records:  Jason Lynch "The Michigan Kid" (2006, 26.2 s)  |  Dave (2007, 26.54 s)
Timothy White "The Australian Oyster" (2008, 26.7 s)  |  Colin Mazaika (2008, 28 s)
Drew Conner, 2009: 27.9 s & 38.5 s

(2011-02-23)   The Stun Path of the Cue Ball (no sidespin)
Starts at a right angle from the line of the object ball.

Draw or follow spin will pull or push the cue ball away from the stun path.

 Come back later, we're
 still working on this one...

Video Clip by  Jeanette Lee  ("The Black Widow")

(2011-01-30)   The not-so-impossible  90°  shot.

In outer space, when a spinless ball collides with an object ball at rest, the latter is ejected at an angle which is at most  90° from the direction of the striking ball.  The limiting angle of  90°  corresponds to a  grazing  collision  (where the object ball is imparted vanishing speed).

On a pool table, extreme english on the cue ball can result in some extra deflection which allows the angle to reach or exceed  90°.

 Come back later, we're
 still working on this one...

Video :  90-degree 'impossible' pool cut-shot by Bob Jewett  to the tune of "Take Five" by Dave Brubeck.
Actual shot is at 2:02; at Shoreline Billiards, on Tuesday September 16, 2008  (using a Balabushka cue).
Video :  Vernon Elliott's Impossible Bank Shot  by Bob Jewett   |   >90° shots by Dave Alciatore

Ray Higley, PE  (2011-01-30.  NE, Georgia)   Squirt Effect
When a level cue induces a pure side-spin  (about a vertical axis)  how is the cue ball deflected away from the cue's central axis?

Squirt  is the modern term for the tendency of the cue ball to be deflected away from the striking axis when it's imparted with lateral english  (side spin).  Pool gurus who have adopted that name include:  Robert ByrneBob JewettRon Shepard, Mike Page, Joe Tucker, etc.

 Come back later, we're
 still working on this one...

Everything You Always Wanted to Know About Cue Ball Squirt, but Were Afraid to Ask
by  Ron Shepard  (2001)
Videos:  Using Left or Right English:  What is Squirt in Pool?
Understanding Cue Ball Deflection  by  Dominic Esposito  (predatorfan314)
Sidespin, squirt & swerve revisited  by Mike Page (FargoBilliards).
3 lessons on  "Cue Ball Side-Spin & Squirt"   [  1  |  2  |  3  ]   by  Joe Tucker (jt10ball)

(2011-03-24)   Jump Shots  (with full cues or shorties)
Legal and illegal ways to send the cue ball up in the air.

 Come back later, we're
 still working on this one...

Using a jump cue  or  Jumping a ball with a full cue   by Joe Nichols (Breaktime Billiards, Wilmington, NC).
Jerico's Stinger Cues :  "Learn to Jump Balls"  [ 1 | 2 ] by BCA Master Billiards Instructor Tom Simpson.
Overhanded Method   |   Bank Jump Shot   |   Close Jump Shot   |   Rocky Lane   |   Joonas Ohtonen

(2016-02-16)   Rules and Vocabulary of Snooker
Regulation snooker is significantly different from other cue sports.

White cue-ball.  15 red balls (1 point) and 6 "color" balls:  Yellow (2 points, top-left spot), Green (3 points, top-right spot), Brown (4 points, top-center), Blue (5 point, middle), Pink (6 points) and black (7 points, bottom).

Reds and colors are alternatively "on" to be potted until the last red is potted.  Once a color has been potted after the last red, the colors must be potted in ascending order of their point values.

The most common foul consists of hitting first a ball which isn't "on".  When that happens, the other player is awarded 4 points

Black cushion, yellow pocket, green pocket.

Respotted black (tie-breaker).

4-point snooker.

 Come back later, we're
 still working on this one...

Each time a player pots a ball, the announcer calls how many points the player has scored  on that particular visit,  not the overall total which will be used to decide the frame  (that total is obtained by adding all the balls potted on successive visits to the penalty points due to the opponent's fouls, if any).

The mythical  maximum break  of 147 is obtained when a player pots 15 times a red followed by the black and then all balls in ascending order:

147   =   15 (1+7) + 2 + 3 + 4 + 5 + 6 + 7

In the final of the UK Snooker Championship 2015Neil Robertson  achieved that maximum break of 147 after a foul from his opponent  (LIANG Wembo)  for a total score of 151.

Theoretically, the opponent could make an unlimited number of fouls, so there's no hard maximum to the total score a snooker player can achieve.

Video :  The Rules of Snooker  by  Ninh Ly.

visits since Jan. 1, 2011
 (c) Copyright 2000-2016, Gerard P. Michon, Ph.D.