Pool Cut Angle Chart: Overlap and Aim Point for Every Angle from 0° to 85°
The short version: seen from behind the cue ball, the part of the object ball the cue ball covers is 1 − sin(cut angle). Remember five reference points:
0° full ball · 14.5° 3/4 ball · 30° 1/2 ball · 48.6° 1/4 ball · 61° 1/8 ball
Below there is a simulator you can drag and the full chart from 0° to 85°.
A cut shot is any shot where the cue ball, the object ball and the pocket are not in a straight line, which is almost every shot in a frame. Most cut angle charts online are drawn by hand, and the proportions are often off. Every diagram and number on this page is calculated, using the same formulas the AimGeometry trainer uses to draw its lines on the table. For the aiming methods themselves (ghost ball, contact point, fractional aiming), see How to Aim in Pool.
Three terms first
- Cut angle: the angle between the direction the cue ball is travelling and the direction the object ball leaves in (towards the pocket). A straight shot is 0°.
- Ghost ball: where the cue ball has to be at the moment of impact. It touches the object ball, on the line from the pocket through the object ball's centre, extended. Aiming means sending the centre of the cue ball to the centre of the ghost ball.
- Overlap (ball fraction): standing behind the cue ball, how much of the object ball the cue ball covers along your line of sight. All of it is a full-ball hit; half of it is a half-ball hit.
The three go together: fix the cut angle and you have fixed the ghost ball position and the overlap.
Cut angle simulator
Left, from above: the white ball is the cue ball, the dashed circle is the ghost ball, the yellow ball is the object ball and the green arrow points to the pocket. The blue dashed line is where a stunned cue ball goes after contact (the tangent line, at 90° to the object ball's path). Right: what you see from behind the cue ball. The red area is the overlap.
Overlap diagrams: 10° to 80°
Each small diagram is the view from behind the cue ball. Yellow is the object ball, the white dashed circle is the cue ball's outline (strictly, the ghost ball as you see it), red is the overlap and the blue line is where the centre of the cue ball is aimed.
Two patterns stand out. Up to 30°, every extra 10° takes away about 16–17% of the overlap, so the change is fairly even. Beyond 50° the overlap collapses: 13% at 60°, 6% at 70°. On thin cuts, a tiny misjudgement of the overlap is a big error in the angle.
The full chart
| Cut angle | Overlap | Aim offset (ball widths) | Pool ball 2¼ in | Snooker ball 52.5 mm | Object ball speed | Stun: cue ball turns by |
|---|---|---|---|---|---|---|
| 0° | 100% · full ball | 0.00 | 0.00 in | 0.0 mm | 100% | 90° |
| 5° | 91% | 0.09 | 0.20 in | 4.6 mm | 100% | 85° |
| 10° | 83% | 0.17 | 0.39 in | 9.1 mm | 98% | 80° |
| 14.5° | 75% · 3/4 ball | 0.25 | 0.56 in | 13.1 mm | 97% | 75.5° |
| 15° | 74% | 0.26 | 0.58 in | 13.6 mm | 97% | 75° |
| 20° | 66% | 0.34 | 0.77 in | 18.0 mm | 94% | 70° |
| 25° | 58% | 0.42 | 0.95 in | 22.2 mm | 91% | 65° |
| 30° | 50% · 1/2 ball | 0.50 | 1.13 in | 26.3 mm | 87% | 60° |
| 35° | 43% | 0.57 | 1.29 in | 30.1 mm | 82% | 55° |
| 40° | 36% | 0.64 | 1.45 in | 33.7 mm | 77% | 50° |
| 45° | 29% | 0.71 | 1.59 in | 37.1 mm | 71% | 45° |
| 48.6° | 25% · 1/4 ball | 0.75 | 1.69 in | 39.4 mm | 66% | 41.4° |
| 50° | 23% | 0.77 | 1.72 in | 40.2 mm | 64% | 40° |
| 55° | 18% | 0.82 | 1.84 in | 43.0 mm | 57% | 35° |
| 60° | 13% | 0.87 | 1.95 in | 45.5 mm | 50% | 30° |
| 61° | 12.5% · 1/8 ball | 0.87 | 1.97 in | 45.9 mm | 48% | 29° |
| 65° | 9% | 0.91 | 2.04 in | 47.6 mm | 42% | 25° |
| 70° | 6% | 0.94 | 2.11 in | 49.3 mm | 34% | 20° |
| 75° | 3% | 0.97 | 2.17 in | 50.7 mm | 26% | 15° |
| 80° | 2% | 0.98 | 2.22 in | 51.7 mm | 17% | 10° |
| 85° | 0% | 1.00 | 2.24 in | 52.3 mm | 9% | 5° |
How to read the columns:
- Aim offset is the distance from the object ball's centre to the line through the centre of the cue ball, in ball widths and then in inches and millimetres. It equals the ball diameter × sin(cut angle). At 30° it is half a ball: the centre of the cue ball points at the edge of the object ball. Pool balls are 2¼ in (57.15 mm) under the WPA equipment specifications; snooker balls are 52.5 mm under the WPBSA rules. The angles and overlaps are the same for both, only the distances shrink.
- Object ball speed = cos(cut angle): the share of the cue ball's speed the object ball gets in an ideal collision. The thinner the cut, the harder you have to hit to get the same pace.
- Stun: cue ball turns by = 90° − cut angle. A cue ball with no spin at contact leaves along the tangent line, at 90° to the object ball, so it turns away from its original line by this much. With natural roll it bends forward instead; near a half-ball hit that is about 30° from its original line (see the 30° rule).
How to use the chart
1. Use the half-ball hit as your reference
The half-ball hit (30°) is the one angle you never have to estimate: aim the centre of the cue ball at the edge of the object ball. When you size up a shot, ask first whether it is fuller or thinner than half-ball, then move towards 3/4 ball (14.5°) or 1/4 ball (48.6°). That is far more reliable than guessing a number of degrees. Ghost ball aiming drills has practice routines for building these reference pictures.
2. On thin cuts, aim a touch thinner
During contact, friction between the balls drags the object ball slightly in the direction the cue ball is moving. This is cut-induced throw, and it sends the object ball off a little fuller than the geometry predicts, most noticeably on slow shots. So on thin cuts, aim slightly thinner than the chart says. (The trainer's physics engine leaves throw out, so on the trainer the chart is exact; on a real table it is not.)
3. The thinner the cut, the smaller the margin
The same aiming error turns into a bigger error in the object ball's direction as the cut gets thinner: by a factor of 1/cos(cut angle). At 60° that is double the error of a straight shot. When you choose between position routes, leave yourself the smaller angle if you can.
4. Pool and snooker use the same angles
Overlap depends only on the angle, so the same picture works on a 9 ft pool table, an English pool table and a snooker table. What changes is the scale: a half-ball offset is 1.13 in on a pool ball and 26 mm on a snooker ball, and the pockets on a snooker table are much less forgiving.
Practise reading angles on the table
The AimGeometry trainer draws the ghost ball, the contact point and the cut angle on the table, and after every shot it tells you whether you hit it thick or thin and by how many degrees. The fractional aiming drill asks you to estimate the angle first, then shows you the real one. It runs in the browser, free, with nothing to install.
Try the fractional aiming drill →FAQ
What angle is a half-ball hit?
30°. With the centre of the cue ball aimed at the edge of the object ball, sin(cut angle) = 1/2, which makes the cut angle exactly 30°.
What is the maximum cut angle in pool?
A 90° cut can't be potted: the cue ball only grazes the object ball, and the object ball gets none of its speed. At 80° the object ball gets about 17% of the speed and at 85° about 9%, so the practical limit is in the 80s.
How do you aim a 40-degree cut?
A 40° cut is a 36% overlap. The line through the centre of the cue ball passes 0.64 of a ball width from the object ball's centre, which is about a seventh of a ball width outside its edge: 0.32 in on a pool ball, 7.5 mm on a snooker ball.
Why isn't a quarter-ball hit a 22.5° cut?
Because overlap follows the sine of the angle, not the angle itself. A quarter-ball overlap means sin(cut angle) = 3/4, which is about 48.6°.
Where do you hit the object ball on a cut shot?
The cue ball touches the object ball at the contact point, the spot on the far side of the object ball from the pocket, on the line from the pocket through the object ball's centre. But you send the centre of the cue ball to the ghost ball's centre, not to the contact point. If you aim the cue ball's centre at the contact point you cover only half the offset you need, and the shot goes in thick.
Why do my cut shots go thick?
Throw (see above) and perception: most players judge thin overlaps conservatively. If you miss thin cuts on the full side again and again, aim thinner than feels right.
Related reading: What Is English in Pool? · How to Aim in Snooker · How to Aim in Pool · Ghost Ball Aiming Drills · The 30° Rule · The Geometry of Pool
All figures assume ideal geometry: overlap = 1 − sin θ, aim offset = ball diameter × sin θ, object ball speed = cos θ (no collision losses or throw). Ball sizes: WPA Recommended Equipment Specifications (2¼ in) and WPBSA Official Rules of the Games of Snooker and English Billiards (52.5 mm). This article contains no sponsored or affiliate links.