Billiards Shot Angle Calculator

How this billiards angle calculator works

This tool models a top‑down view of a pool table. You can move the cue ball, object ball, and pocket to match a real shot. The calculator then:

• Draws the object ball → pocket line (intended path of the object ball).
• Places the ghost ball one ball diameter behind the object ball on that line.
• Draws the cue ball → ghost ball line (your aiming line).
• Shows the cut angle in degrees.
• Optionally shows the 90° tangent line (for the 90° rule after contact).

Key definitions

• Cut angle – the angle between the line from the object ball to the pocket and the line from the cue ball to the object ball at impact. 0° is straight in; larger angles are thinner cuts.
• Ghost ball – an imaginary cue ball frozen to the object ball on the line to the pocket. If the real cue ball passes through the center of this ghost ball, the object ball will head toward the pocket.
• Contact point – the point on the object ball where the cue ball touches it at impact.

The geometry behind pool angles

In an ideal, no‑spin shot, the cue ball and object ball behave like equal circles in a 2D plane. The calculator uses basic vector math and trigonometry:

90° rule (tangent line)

For a stun shot (no topspin or draw at impact), the cue ball will leave the collision at roughly 90° to the object ball’s path. If you enable “Show 90° tangent line”, the calculator draws this line through the object ball center, perpendicular to the object‑to‑pocket line. This visualizes the classic 90° rule discussed in many advanced aiming guides.

Practical aiming tips you can learn from the tool

• Relate feel to numbers: Try common shots and note that many “medium” cuts are in the 30–40° range.
• Understand thin vs. thick cuts: Move the cue ball around the object ball and watch how the cut angle changes.
• Practice ghost‑ball visualization: After using the calculator, try to imagine the ghost ball on a real table before looking back at the screen.
• Explore distance effects: Longer cue‑to‑object distances make small aiming errors more costly, even though the cut angle is the same.

Limitations and assumptions

To keep the math clean and educational, this calculator assumes:

• No spin (center‑ball hit).
• No throw or skid between balls.
• No cushions before the object ball (no banks or kicks).
• Perfectly round, equal‑sized balls and a flat table.

Real‑world shots are affected by spin, speed, cloth friction, and ball conditions. Use this tool to understand the pure geometry, then refine with table time and experience.

FAQ

Is there a formula for pool angles or is it just practice?

The underlying physics and geometry are precise and formula‑based, as this calculator shows. However, in real play you rarely compute angles explicitly. Strong players internalize these relationships through practice and use visual systems like ghost‑ball, fractional‑ball aiming, the 90° rule, and the 30° rule.

What is a “30° rule” shot?

For many natural rolling‑cue‑ball shots with moderate cut angles, the cue ball path after contact is about 30° away from its original direction. This calculator does not simulate spin, but you can still use it to understand the base geometry before adding roll and draw in your practice.

Can I use this for banks and kicks?

Not directly. The current version focuses on direct shots (cue → object → pocket). For banks and kicks you would need to reflect the table geometry across rails. You can still approximate some banks by placing the “pocket” at a virtual reflection point, but that is beyond the scope of this simple visualizer.

What table sizes does it support?

You can choose 7 ft, 8 ft, or 9 ft tables. The aspect ratio is kept realistic, and distances are reported in table‑relative units. Ball diameter can also be adjusted if you play on non‑standard equipment.