30-degree and 90-degree Rules

• 30-degree rule
• 90-degree rule
• ball condition effects
• carom and kiss shot aiming
• Dr. Dave's peace-sign technique
• half-ball hit "gems"
• largest deflected angle
• poetry
• resources
• safety and ball-in-hand examples
• speed effects
• when the 30-degree rule applies
• where the CB goes for different cases

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

30-degree rule

What is the 30-degree rule ?

The 30-degree 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 30º from its original direction after hitting the OB. If you want to be more precise, the angle is a little more (about 34 degrees) closer to a 1/2-ball hit and a little less (about 27 degrees) 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-degree rule. Also, if you want to know how to account for speed effects, see my June '05 article. And if you want to see how numbers change a little with typical pool equipment conditions, see my November '11 Billiards Digest article.

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

and here are some others:

• NV 3.7 – Using the 90º rule to check for and prevent a scratch
• NV 3.10 – Using the 30º rule to check for and prevent a scratch
• NV 5.1 – Using speed and angle-control to pocket a three-ball sequence
• NV 5.2 – Using speed and angle-control to pocket another three-ball sequence
• NV 7.2 – Cue ball billiard shot
• NV 7.3 – Object ball carom shot
• NV 7.4 – 30º rule billiard shot
• NV B.43 – CB position control stun, roll, and draw reference lines
• NV B.46 – CB path scratch avoid, cluster break-out, and carom examples

Here's a convenient 1-page summary resource page summarizing all of the important points of the 30-degree rule.

For more info, see my April '04 article and where the CB goes for different cases.

carom and kiss shot aiming

How do you aim carom and kiss shots?

My March and June, 2004 instructional articles and my February '10 article explain how to use the 90 and 30 degree rules to aim carom and kiss shots. Also, here are some video demonstrations:

• NV 7.2 - Cue ball billiard shot
• NV 7.3 - Object ball carom shot
• NV 7.4 - 30° rule billiard shot

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

If you need to plan a carom or kiss shot that cannot be conveniently set up in the 90 or 30 degree directions, the 90 and 30 degree 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 degree 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 degree 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. Also, as described in my March, 2005 instructional article, shot speed also affects the exact cue ball trajectory. However, the 90 and 30 degree directions are still good to know to have some definite points of reference.

Here's a good challenge drill, from Disc V of the Video Encyclopedia of Pool Practice (VEPP), for practicing carom and kiss shots:

What are the advantages and disadvantages of stun vs. roll caroms?

One advantage of a tangent line (90 degree) 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-degree 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-degree and 30-degree rules?

Diagram 1 in my April '05 instructional article illustrates the effects of inelasticity (i.e., the coefficient of restitution) and ball friction (i.e., throw) on the 90 degree rule. TP A.5 shows the detailed analysis along with example numbers.

Diagram 1 in my May '05 instructional article shows the effects of English. The details for that are in TP A.7.

I illustrate the effects on both the cue ball and object ball for all cases. If you have a specific question that you think is still unresolved, let me know.

Only inelasticity affects the cue ball direction. Friction, from collision-induced throw and/or English, theoretically (and I think practically) has no affect on the cue ball direction for a stun shot (for which the 90 degree rule applies).

Dr. Dave's peace-sign technique

How does the peace-sign technique work?

See the following videos for complete information and demonstrations:

• NV B.43 - Cue ball position control stun, roll, and draw reference lines
• NV B.44 - Dr. Dave 30-degree-rule peace-sign hand calibration

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

FYI, my June '05 article wraps up a series of 12 (a year's worth!) of articles dealing with the 90 and 30 degree rules. In Diagram 2 of this article (see below), I show how you should move your hand to adjust for speed. It is fairly self-explanatory, but you can see the article for more details. I hope some people can find this useful in their games. I use my 30-degree-rule-peace-sign quite often when I want to know where the cue ball will be heading. As I show in my articles, the 30 degree rule applies for a wide range of shots.

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

See NV B.44. Also, I have a set of angle templates in the instructor and student resources section of my website to help with learning how to use the 30-degree rule to predict cue ball motion for various roll shots. The templates can be used to help you train and calibrate your hand peace-sign (see my April '04 and June '05 articles). Here's a direct link to the templates.

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-degree 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-degree-rule peace-sign at the table?

If I have a critical shot close to a scratch, requiring precise caroms, needing ball break-up or avoidance, or with tight "traffic" of balls to negotiate, I most definitely pull out my well-calibrated fingers. When I do, I know with confidence almost exactly where the cue ball will go. I adjust my peace sign slightly for the cut angle, because I have practiced and calibrated my hand for various important angles using the 30-degree rule angle template. I even adjust for speed, as shown in my June '05 article. My well-calibrated fingers are still much more accurate than my intuition-based visualization.

half-ball hit "gems"

Why is a 1/2-ball hit (30 degree 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: www.sfbilliards.com/articles/2000-11.pdf

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-degree rule, which states that for a rolling CB, the deflected angle is very close to 30 degrees for all cut angles between 1/4-ball and 3/4-ball hits (not just a 1/2-ball hit). I think 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. My June '04 BD article also illustrates and discusses the shot in detail, and 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 my January '06 BD article. 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:

• 30-degree rule resource page (containing many additional resources and video demonstrations of how and when the rule is useful).
• January-July '04, February-June'05, and January-February '09 instructional articles.
• 30-degree rule and peace-sign technique one-page summary and the angle template.

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, English is very effective off the cushions with a 1/2-ball hit. For thinner hits, the faster ball speed reduces the effect of the English; 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 degrees) actually occurs at a cut angle of about 28 degrees, which corresponds to a 0.53 ball-hit fraction. These numbers are close to 30 degrees and a 1/2-ball hit, but not exact.

poetry

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

Here's some poetry:

30-degree rule:

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

90-degree rule:

When the ball has stun,
this is something you should not shun:
Point your finger, and the cue ball will follow the thumb.
If you do this, nobody will think you are dumb.

resources

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

My March '05 instructional article illustrates and describes how to use the peace-sign technique for the 30-degree rule. Also, my June '05 article shows how to account for speed effects. These and other issues and effects and principles are summarized in my 30-degree-rule and peace-sign technique document. Also, I have 12 articles that address all of the intricacies of and uses for both the 90-degree and 30-degree rules.

FYI, I have convenient access to all these and other teaching and learning resources in the Instructor and Student Resources section of my website.

when the 30-degree rule applies

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

The 30-degree 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-degree rule applies only for natural roll shots.

- the 30-degree 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 degrees 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 degree 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 Disc I of the Video Encyclopedia of Pool Shots: