# 30° and 90° Rules for Cue Ball Control in Pool and Billiards

## ... how to predict cue ball motion to prevent scratches, aim break out shots, aim caroms, play position, and get through traffic.

for more information, see Sections 3.03, 3.04, 5.05, and 7.02 in The Illustrated Principles of Pool and Billiards
and Vol. I of the Video Encyclopedia of Pool Shots

30° rule

What is the 30° rule ?

The 30° rule states that for a rolling-CB shot, over a wide range of cut angles, between a 1/4-ball and 3/4-ball hit, the CB will deflect by very close to 30° from its original direction after hitting the OB. If you want to be more precise, the angle is a little more (about 34°) closer to a 1/2-ball hit and a little less (about 27°) closer to a 1/4-ball or 3/4-ball hit. The rule is described and illustrated in the following video:

The Dr. Dave peace-sign technique is very useful in applying the 30° rule. The 30°-rule angle templates can be useful to help you calibrate your V-sign. If you want to know how the CB path varies with speed and how to account for this, see speed effects. And if you want to see how numbers change a little with typical pool equipment conditions, see "Rolling Cue Ball Deflection Angle Approximations" (BD, November, 2011).

Here a video demonstrations showing examples of how the 30° rule can be used in different shot situations:

and here are some others:

Here's a convenient 1-page summary resource page summarizing all of the important points of the 30° rule, and here's a useful handout covering advanced topics.

For more info, see "The 30° rule: Part I - the basics" (BD, April, 2004) and where the CB goes for different cases.

carom and kiss shot aiming

How do you aim carom and kiss shots?

The following instructional articles explain how to use the 90 and 30° rules to aim carom and kiss shots.

"The 90° rule: Part III - carom and billiard shots" (BD, March, 2004)
"The 30° rule: Part III - carom vs. cut" (BD, June, 2004)
"VEPS GEMS - Part II: Basic Shot Making and Position" (BD, February, 2010)

Also, here are some video demonstrations:

and here's a good demonstration from Vol. I of the Video Encyclopedia of Pool Shots

And here's another from Vol. II of How to Aim Pool Shots (HAPS):

If you need to plan a carom or kiss shot that cannot be conveniently set up in the 90 or 30° directions, the 90 and 30° rules still give you good points of reference. The amount of cue ball vertical spin (follow, stun, draw) will determine where it goes relative to the 90 and 30° directions. With full stun, the cue ball will head exactly in the tangent line direction. With complete roll, the ball will deflect in the 30° direction. For other shots, it is difficult to reliably know exactly where the cue ball will go, so it is best to not attempt caroms in these cases unless you have no other options. Like many things in pool, all you can do is practice a bunch and develop intuition for how much the cue ball deflects with various amounts of vertical spin. The following video has an example of how to apply this concept to breaking out clusters:

Also, as described in "90° and 30° Rule Follow-up - Part II: speed effects" (BD, March, 2005), shot speed also affects the exact cue ball trajectory. However, the 90 and 30° directions are still good to know to have some definite points of reference.

Here's a good challenge drill called "Loop" ("pool" spelled backwards), from Vol. V of the Video Encyclopedia of Pool Practice (VEPP), for practicing carom and kiss shots:

For more information, see "VEPP - Part XIII: Safety and Carom Challenge Drills," (BD, April, 2013).

PS: Another game called "Loop" is played on an elliptical table and is quite different from the traditional game "Loop."

With clusters, there is a whole world of possible shots available taking advantage of the concepts above and throw and spin-transfer effects. Many good examples can be found here: throw shot examples, spin transfer shot examples, NV I.11 - 9-ball/10-ball Advanced Herd and Cushion-Compression Shots, an excerpt from VENT-V, and Mark Finkelstein's collection of cluster shots.

One advantage of a tangent line (90°) carom or kiss is that the CB path does not depend on the speed of the shot, assuming the CB has stun at impact (which does depend on both speed and tip position). However, most people have a good feel for stun shots (stop shots at an angle) since they are so important in pool and therefore are practiced a lot.

The advantage of a 30° carom or kiss is that the natural angle applies fairly closely over a fairly wide range of cut angles, so your aim doesn't need to be perfect. Also, it is very easy to ensure ball roll, by using slow enough speed, or with shot distance, and/or by hitting the cue ball above center. The disadvantage is the CB's path off the OB curves before heading in the natural angle direction, and the amount of shift down the tangent line depends on shot speed (see cue ball path speed effects for more info). This isn't a significant factor at slow speeds, but at faster speeds, the shift is significant.

ball condition effects

How do ball conditions affect the 90° and 30° rules?

Diagram 1 in "90° and 30° Rule Follow-up - Part III: inelasticity and friction effects" (BD, April, 2005) illustrates the effects of inelasticity (i.e., the coefficient of restitution) and ball friction (i.e., throw) on the 90° rule. TP A.5 shows the detailed technical analysis along with example numbers.

Only inelasticity affects the cue ball direction. Friction, from cut-induced or spin-induced throw, theoretically (and practically) has no affect on the cue ball direction for a stun shot (for which the 90° rule applies). Diagram 1 in "90° and 30° Rule Follow-up - Part IV: sidespin effects" (BD, May, 2005) shows the effects of friction and sidespin on other types of shots. The technical details for that are in TP A.7.

Experimental verification of the theoretical results in the articles above can be found in the following article: Ball Motion Properties in Stun and Follow Shots

For more information on ball elasticity, see the ball elasticity resource page.

Dr. Dave's peace-sign technique

How does the peace-sign technique work?

See the following videos for complete information and demonstrations:

Here's a good overall video with explanation and demonstrations, from Vol. I of the Video Encyclopedia of Pool Shot, of how the peace-sign is used:

FYI, "90° and 30° Rule Follow-up - Part V: the final chapter" (BD, June, 2005) wraps up a series of 12 (a year's worth!) of articles dealing with the 90 and 30° rules. Diagram 2 of this article (see below) shows how you should move your hand to adjust for speed. It is fairly self-explanatory, but you can see the article for more details. The 30° rule applies for a wide range of shots. For more info, see when the 30° rule applies.

For details on how to apply the peace sign technique accurately for a wide range of shots and situations, see how to position the peace sign and "Peace Sign Subtleties" (April, 2017).

The peace-sign technique can also be applied to draw shots using the trisect system.

An alternative way to visualize the natural-angle direction is to imagine the mirrow image of the ghost-ball on the back of the object ball. For more info and illustrations, see: "Back-of-the-Ball Aiming," BD, September, 2016.

How can you tell if your peace-sign is the correct angle?

See NV B.44. Also, here's a template useful for learning how to apply the 30° rule accurately. The template can be used to help you train and calibrate your hand peace-sign (see "The 30° rule: Part I - the basics" - BD, April, 2004 and "90° and 30° Rule Follow-up - Part V: the final chapter" - BD, June, 2005).

One way to calibrate or check your peace sign at the table is to use your opposite hand index finger as a ruler to measure how much the tips of the "V" fingers should be spread. Using the 30° template or a 30-60-90 drafting triangle (available at office and arts and crafts stores), one can form the peace sign of the correct angles and then place the opposite-hand finger over the finger-tip gap, with the fingertip touching the tip of one of the fingers. Note where the second finger is relative to the other opposite-hand finger (e.g., just below the main knuckle, or at a certain wrinkle). Then (e.g., when you are playing), you can check your peace sign spread by recreating the same finger tip positions on your opposite hand.

Do people really use the 30°-rule peace-sign at the table?

If one has a critical shot close to a scratch, requiring precise caroms, needing ball break-up or avoidance, or with tight "traffic" of balls to negotiate, a well-calibrated peace sign can be extremely useful, allowing one to predict with confidence nearly exactly where the cue ball will go. One can adjust the peace sign slightly for the cut angle using the 30° rule angle template for help. One can also adjust for speed, as shown in "90° and 30° Rule Follow-up - Part V: the final chapter" (BD, June, 2005). Well-calibrated fingers can be much more accurate than intuition-based visualization.

english (sidespin) effects

What affect does english (sidespin) have on the tangent line and the 90° and 30° rules?

"90° and 30° Rule Follow-up - Part IV: sidespin effects" (BD, May, 2005) shows the effects of sidespin on both the 90° and 30° rules. Here's Diagram 1 from the article:

For a given contact point on the object ball (OB), the cue ball (CB) tangent line direction does not change with sidespin. Whether the CB has sidespin or not, a stunned CB heads straight down the tangent line (AKA "stun line"). However, the direction and amount of spin on the CB can have a significant effect on OB direction due to throw effects, as shown in the diagram.

In addition to OB throw, spin can also get transferred to the OB. There are many shots where both throw and spin transfer have significant effects, allowing shots that would not be possible otherwise. Numerous examples are illustrated and demonstrated here:

throw-shot examples
spin-transfer-shot examples
CB "hold" shots

The main purpose for sidespin (when not being used for throw or spin transfer) is to change the CB's direction after hitting a cushion. For more info, see english terminology and uses.

Here's Diagram 2 from the sidespin effects article:

Concerning the 30° rule, when english is used, the deflected cue ball angle decreases slightly over short distance and then increases slightly over long distance The effect is slightly greater with outside english compared to inside english, but in both cases the effect is small.

from 3andstop (in AZB post):

While side spin doesn't (in and of itself) affect the tangent line from the point of contact on the OB, side spin can and does affect where you contact the OB in order to pocket it.

Therefore, in a tight spot (very common in straight pool) pocketing a ball that would send the CB down an undesirable tangent line, can be adjusted with side spin.

This, because now you are able to contact the OB in a slightly different spot, either thicker or thinner than the contact point with no side spin (depending on which english is used) to pocket it (turn it into the pocket) and change both the contact point and tangent line.

So, in a sort of indirect way, side spin one way or the other, can change the standard tangent line when speaking relative to the pocketing of an object ball.

It will not change the tangent line when speaking of a carom only, hitting the OB in the same spot regardless of english.

from BeiberLvr (in AZB post):

Where you strike the CB does not determine the tangent line. It's where the CB makes contact with the OB that determines the tangent line.

So on shots with side spin (especially over certain distances), the contact area on the OB will be different when using left or right spin, then it would be with center. Now if you played a short distance shot where the spin might not have time to take effect, then the tangent lines would be the same, because the contact area on the CB wouldn't change.

Same goes with hitting center on the CB, but playing the OB to different parts of the pocket. That will also result in a different tangent line, but it just goes back to the fact that you're simply changing where the CB contacts the OB.

half-ball hit "gems"

Why is a 1/2-ball hit (30° cut angle) so useful?

Here are some excellent videos Mike Page put together on half-ball hit "gems:"

NV B.6 - Mike Page's half-ball hit gems (part 1, part 2)

and here's a good summary article from Bob Jewett (BD, November, 2000).

The "natural angle" effect associated with a half-ball hit is one of the most important principles in pool and billiards. It has always surprised me how little (if any) coverage is dedicated to these subjects in commercially-available pool and billiards books and videos. These effects have been understood at least as early as 1835 (see Coriolis' book). Maybe if we keep writing articles and posting videos on these topics, maybe they will become more "mainstream."

Gem #4 from the videos is the basis of the 30° rule, which states that for a rolling CB, the deflected angle is very close to 30° for all cut angles between 1/4-ball and 3/4-ball hits (not just a 1/2-ball hit). This gem is the single most important and useful principle in pool, especially when used in conjunction with the peace-sign technique.

Gem #4 is an interesting proposition demonstration with the carom shot from the foot rail. NV A.1 shows a similar "sure-thing" proposition. The following article also illustrates and discusses the shot in "The 30° rule: Part III - carom vs. cut" (BD, June, 2004).

TP A.1 and TP A.2 present an error analysis and look at the effects of table size.

Gem #2 is explained and illustrated in detail in "Draw Shot Primer - Part I: physics" (BD, January, 2006). The concept can also extended into the trisect draw-shot aiming system. This is also a very useful "gem."

Many additional resources, with lots of illustrations, examples, and video links related to these principle, can be found here:

Math and physics backing up Gem #'s 2, 3, and 4 can be found in TP 3.3, TP A.4, and TP A.16.

The 1/2-ball hit is a common shot, especially in the game of 9-ball, where you need to move the CB around the table a lot. With a 1/2-ball hit, the CB easily be given enough speed to travel significant distance. The CB's motion can also be killed fairly easily with a 1/2-ball hit. Also, sidespin is very effective off the cushions with a 1/2-ball hit. For thinner hits, the faster ball speed reduces the effect of the sidespin; and for fuller hits and the resulting slower speed of the CB, the spin doesn't grab as well, especially on new cloth.

largest deflected angle

Does the cue ball deflect the most for a half-ball hit?

Close, but not precisely. See the bottom of TP 3.3. The maximum deflected angle (33.75°) actually occurs at a cut angle of about 28°, which corresponds to a 0.53 ball-hit fraction. These numbers are close to 30° and a 1/2-ball hit, but not exact.

poetry

Are there easy ways to remember the 30 and 90° rules?

Here's some poetry:

30° rule:

If you let one finger stay,
The other finger points the way.
Peace.

90° rule:

When the ball has stun,
this is something you should not shun:
If you do this, nobody will think you are dumb.

resources

What resources are available to help me learn how to use the 90° and 30° rules accurately?

"90° and 30° Rule Follow-up - Part II: speed effects" (BD, March, 2005) illustrates and describes how to use the peace-sign technique for the 30° rule. Also, "90° and 30° Rule Follow-up - Part V: the final chapter" (BD, June, 2005) shows how to account for speed effects. These and other issues and effects and principles are summarized in the 30°-rule and peace-sign technique document. Also, a large collection of instructional articles are available that address all of the intricacies of and uses for both the 90° and 30° rules.

All these and other teaching and learning resources can be found here:

Instructor and Student Resources

when the 30° rule applies

For what kinds of shots can the 30° rule be used?

The 30° rule is very useful for:

- scratch avoidance
- carom shot aiming
- cluster busting
- obstacle avoidance
- position play
- etc!

Here are some important things to keep in mind:

- the 30° rule applies only for natural roll shots.

- the 30° rule applies for the entire range of cut angles between 1/4-ball and 3/4-ball hits. This range includes the 1/2-ball hit (which is at the center of the range).

- the cue ball always leaves initially along the tangent line, which is 90° away from (i.e., perpendicular to) the impact line (AKA object ball direction, line-of-centers, target line, etc.). However, for slow to medium speed natural roll shots, the cue ball deflects to the 30° direction almost immediately (i.e., the curve in the trajectory is almost imperceptible). Only at higher speeds does the travel down the tangent line become significant (e.g., see NV 3.8 vs. NV 4.20). For more info, see the following demonstration from Vol. I of the Video Encyclopedia of Pool Shots: