Gann Square of Nine: How the Spiral Is Built, the Square Root Formula and a Worked Example

The Gann Square of Nine is a spiral of numbers attributed to W. D. Gann. It starts with 1 in the center and winds outward one cell at a time, so that the first ring ends at 9, the second at 25 and the fourth at 81, which completes a 9 by 9 square. Traders read the numbers that line up on the crosses through the center as possible support, resistance or turning points, in price and sometimes in time. Gann left no complete manual for it: according to LuxAlgo, what survives are course sheets and calculators, reconstructed by later authors, so versions differ. Modern charting software turns the spiral into a formula based on the square root of a price; Optuma credits that square root principle to the work of Daniel Ferrera. Like the other Gann tools, it is a drawing convention with a long following, not a tested signal.

How the Square of Nine is built

Write 1 in the center cell. Put 2 next to it and keep writing the next number in the next cell, turning around the center. In the diagram above the spiral runs clockwise with 2 to the left of 1; published charts differ on the direction and on where 2 sits, which changes the drawing but not the numbers on each cross. The numbers grow in rings:

• the first ring ends at 9, which is 3 squared;
• the second ends at 25, 5 squared;
• the third ends at 49, 7 squared;
• the fourth ends at 81, 9 squared, which completes the 9 by 9 square that gives the tool its name.

The odd squares 9, 25, 49 and 81 fall on one diagonal of the square. That regularity is what the whole method rests on: moving out by one ring along any line from the center adds about 2 to the square root of the number.

The cardinal cross and the diagonal cross

The lines through the center are labeled in degrees, as on a circle. The horizontal and vertical lines form the cardinal cross; the two diagonals form the diagonal cross. Together they give eight arms, one every 45 degrees. On the diagram above, the arms read as follows.

The Square of Nine formula

Software does not draw the spiral; it uses the square root rule that the spiral follows. Optuma documents it as follows: the end price equals the square of the square root of the start price plus the angle divided by 180.

Adding the angle gives levels above the price, subtracting it gives levels below. A full turn of 360 degrees adds 2 to the square root, a half turn of 180 degrees adds 1, and 45 degrees adds 0.25. Optuma’s own example: the square root of 16 is 4, plus 2 for a full turn gives 6, and 6 squared is 36. From an anchor at 53, it gives 69 at 180 degrees and 86 at 360 degrees.

The last step squares the result: from 51, the square root is about 7.14, one full turn down gives 7.14 minus 2 = 5.14, and 5.14² is about 26.4. Do not take a second square root.

The chart below applies the formula to real prices. The anchor is the lowest swing low of the window on the S&P 500 ETF, the low of April 7, 2025, and the lines are the levels every 45 degrees above it, up to the first one beyond the highest price of the window. The full turn, 360 degrees, is drawn stronger. The chart uses prices adjusted for dividends, so the anchor sits a little below the low quoted in April 2025; drawn from the quoted low, each level would come out a little higher.

The chart shows the problem as much as the method. Twelve levels in a rise of about 29% put a line every 2% or so, so almost any pause in the rally sits near one of them. Choosing the April low as the anchor is also easy only after the fact: on April 7, nobody knew it would be the low of the year.

How traders use the Square of Nine

• Price levels. Pick a major high or low, compute the levels at 45 degree steps above and below, and watch how price behaves when it reaches them. They are then used like any other support and resistance zones or alongside pivot points.
• Time. The same numbers can be read as counts of days or weeks from a major turn, looking for a date when price and time line up. That use needs the same free choices: the anchor, the unit of time and which arms to watch.

The Square of Nine is one of several Gann tools that rest on squaring price and time. The Square of 144 is a 12 by 12 grid, the Gann box splits a move into price and time divisions, and the Gann fan draws angles from a pivot. More about the man and his methods is on the W. D. Gann page.

Does the Square of Nine work?

We found no published study showing that Square of Nine levels are reached or respected more often than levels drawn at random, and we do not test it on our bench, which measures chart patterns. The method has two weaknesses that make old examples look better than they are: there are many levels from each anchor, and the anchor is usually chosen after the fact. A fair test would fix the anchor rule in advance and compare the hits with random levels at the same spacing.

Want to learn more about the square? You can check this Gann Square Trading course on Udemy, “Certification in Gann Square Trading” (affiliate links). See also the other guides in technical analysis.