Gann Calculator — Square of 9

What is the Gann Square of 9?

The Gann Square of 9 is a sophisticated mathematical and geometric trading tool developed by William Delbert Gann (1878-1955), one of the most legendary figures in the history of financial trading. Gann believed that financial markets move in predictable geometric patterns based on the relationship between price and time. The Square of 9 — his most famous tool — arranges numbers in a spiral pattern on a square grid, where each number\'s position relative to the center reveals its mathematical relationship to other numbers along geometric angles (45°, 90°, 135°, 180°, etc.).

Gann\'s core insight was that markets move in cycles and that the same geometric laws that govern the natural world — the movement of planets, the growth of plants, the structure of crystals — also govern financial markets. The Square of 9 embodies these laws in a simple numerical format. When price reaches a number on one of these geometric angles, it encounters "resistance" (the tendency to stop or reverse) or "support" (the tendency to bounce upward). By identifying these levels in advance, traders can plan entries, exits, and stop-losses with greater precision.

How to Calculate Gann Square of 9 Levels

The calculation process is surprisingly simple once you understand the principle:

1. Start with the current price (or a significant high/low). For example, price = $100.
2. Find the square root of the price. √100 = 10.
3. Add the angle increment to the square root. For 45° (1/8 circle): 10 + 0.125 = 10.125. For 90° (1/4 circle): 10 + 0.25 = 10.25. For 180° (1/2 circle): 10 + 0.5 = 10.5.
4. Square the result to get the new price level. For 90°: 10.25² = 105.06. For 180°: 10.5² = 110.25.

You can also subtract the increment to get levels below the current price: √100 - 0.25 = 9.75 → 9.75² = 95.06 (90° support level). The same process works for any price level. The calculator does this automatically and shows you all levels for the selected angle.

Gann Angles and Their Significance

Each angle in the Square of 9 represents a specific geometric division of the circle: 45° = 1/8 of a full 360° rotation, 90° = 1/4, 135° = 3/8, 180° = 1/2, 225° = 5/8, 270° = 3/4, 315° = 7/8, and 360° = full cycle. Gann considered the 90° and 180° angles the most powerful for price reversals, followed by 45° and 135° as secondary levels. The increment values that correspond to these angles are: 1/8 = 0.125, 1/4 = 0.25, 3/8 = 0.375, 1/2 = 0.5, 5/8 = 0.625, 3/4 = 0.75, 7/8 = 0.875, 1/1 = 1.0.

When multiple angles converge on the same price level — for example, 90° from a low and 180° from a high both pointing to the same price — that level becomes extraordinarily significant. Gann called this a "square out" — when price and time meet at the same geometric point — and considered it the most powerful reversal signal in his entire system.

Using Gann Levels in Your Trading Strategy

Here is a practical approach to using Gann Square levels: Identify the major recent swing high and swing low on your chart. Calculate Gann levels from both. Draw horizontal lines at these levels. Watch for price to approach a Gann level from both directions. If price approaches a Gann resistance level from below with declining momentum, consider taking profits or entering a short position. If price approaches a Gann support level from above with declining bearish momentum, consider covering shorts or entering a long position. Always confirm with other indicators and never trade Gann levels alone.

For time-based trading, replace price with the number of days (or weeks/months) from a significant high or low. For example, if a major low occurred 100 calendar days ago, the square root is 10. Adding 0.5 (180°) gives 10.5 → 10.5² = 110.25 days — a potential time turning point. Gann\'s famous saying was: "When price squares time, a change in trend is inevitable." His methods remain popular among traders who appreciate the geometric, mathematical approach to market analysis.