Billiards Diamond System Calculator
The corner-5 diamond system solved in either direction, with a table diagram — plus an honest note on where the system stops working.
Position − Departure = Arrival. The three-cushion path is shown in purple.
How the corner-5 system works
Every rail carries numbered diamonds. Your position number is where the cue ball sits, your departure number is the diamond you aim at on the first rail, and the difference is your arrival number on the far rail. The arithmetic is genuinely that simple — subtraction is the entire system, and the tool solves it in either direction.
What the numbers assume: a natural running-english stroke at medium speed. Reality adjusts it — new cloth runs longer, dirty or humid cloth shortens the path, more speed flattens the angle, and reverse english shortens it dramatically. Every serious player calibrates the system to the specific table before trusting it, usually by shooting a few known positions and noting the drift. Treat these numbers as the starting line, not the answer.
Simple bank shots (no english)
For a one-cushion bank, forget the diamond numbers and use the mirror: imagine the pocket reflected through the cushion, then shoot straight at that imaginary point. Angle in equals angle out. The two things that break it are speed (hard shots rebound shallower because the cushion compresses) and english (running english widens the rebound, reverse english shortens it). This is why bank shots are taught with a firm, consistent, center-ball stroke — you are removing the variables.
How to use
- Find your cue ball position number from the diamonds.
- Find the target number where you want the ball to land.
- Subtract target from position to get the aim diamond.
- Adjust for speed, spin and cloth condition.
Frequently asked questions
How does the corner-5 system work?
Each rail position is assigned a number from the diamonds, and you subtract the target number from the cue ball's position number to get the diamond to aim at on the far rail. It is arithmetic applied to geometry, and it works because the angles are consistent enough to be numbered.
What spin does it assume?
Running english, with a specific and consistent amount, and a medium speed. The whole system is calibrated to that delivery — change the spin or the pace and the numbers no longer describe what the ball does. Reproducing the stroke matters as much as doing the arithmetic.
Does it work on every table?
Approximately, and every table needs its own correction. Cushion rubber, cloth condition, humidity and how much the cloth has been played all shift the angles. Serious players test a known shot on arrival and adjust the system by a fraction of a diamond.
Is this used in pool as well as three-cushion?
It comes from three-cushion billiards, where it is fundamental, and it transfers usefully to kicking and banking in pool. Pool players more often use simpler mirror or half-ball systems for one-rail banks, since the full diamond system is more machinery than a single bank requires.
Why do my banks come up short?
Usually speed and spin rather than aim. A harder shot narrows the angle off the cushion and a softer one widens it, so the same aim point produces different results at different pace. Consistent speed is the prerequisite for any bank system to be worth using.
Should I learn the system or just develop feel?
Both, and in that order for most people. The system gives a reliable starting point on unfamiliar shots and a framework for understanding why a bank missed. Feel refines it, and strong players use the numbers as a check on instinct rather than a replacement for it.
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