Gann Square of Nine

W.D Gann square of 9 | Square of nine technique

How to construct the Gann square

The square of nine, or Gann’s square, is a method of balancing price and time. The Gann square gets its name again because if you look at the diagram above again, the number 9 represents the completion of the first square.

Square 9 is a spiral of numbers with an initial value of “1” from the center. Starting at this value, the number increases as you spiral clockwise. According to experts, each cell of the Gann square once again represents a point of vibration.

How does the Gann Square work?

The Gann square of nine helps to identify time and price alignments in order to forecast prices.

In the Gann Square of nine, the key numbers of importance are as follows:

0 or 360 degrees: 2, 11, 28, 53….
45 degrees: 3, 13, 31, 57, 91…
90 degrees: 4, 15, 34, 61, 96…
180 degrees: 6, 19, 40, 69…

Square Of 9 Cardinal Cross and Ordinal Cross

The next sets of important numbers fall within the cardinal cross and the ordinal cross.

The picture below shows the cardinal cross, represented in the blue horizontal and vertical lines. The ordinal cross numbers are represented in the yellow cells.

The numbers that fall in the cells represented by the cardinal and ordinal cross are key support and resistance levels.

While both are important, the ordinal crosses are of less significance and can be breached at times.

WD Gann

Gann Square – Cardinal and Ordinal Cross

Key Point Of W.D Gann Square Of Nine

The Gann Square of Nine defines important levels where price might shoot and retrace.
Numbers in the square are arranged in ascending order starting from 1 as we have already discussed.
The most important numbers in the Gann Square of Nine occur every 45° on nine chart.

31 32 33 34 35 36 37
30 13 14 15 16 17 38
29 12 3 4 5 18 39
28 11 2 1 6 19 40
27 10 9 8 7 20 41
26 25 24 23 22 21 42
49 48 47 46 45 44 43
Square Of Nine

The construction of the Gann Square of Nine

As we know that square is the basic form of the Square of Nine. Numbers in the square are arranged in ascending order starting from 1 as we have already discussed. The trend of the market decides whether to arrange numbers in a clock wise or anti-clock wise manner starting from middle to right and up. Upward trend demands clockwise while a downtrend requires anti-clockwise number arrangement. Moreover, the Square of Nine gives important cardinal and ordinal levels. Numbers falling on both of these levels are always major vibration points because they represent important support or resistance levels. However, it is crucial to remember that all the important numbers in the Gann Square of Nine occur every 45° on nine chart.


The Gann Wheel, what most people probably think of as the Square of Nine, is sometimes called a “Square Root Calculator” or a device that “Squares the Circle.” This simple illustration may explain how and why these terms came about. You probably recognize that the illustration is just the first few rings of a Gann Wheel with the numeral “1” at the center.

In Square of Nine parlance we say things like 19 is 90 degrees from 15. That makes sense only if you can visualize that this rectangular table of numbers is enclosed in a circle (or series of circles) of 360 degrees. In this case, the number 19 is 1/4 the way around the circle from the number 15, or 90 degrees in circumference from 15. The number 34 is directly above the number 15 and positioned one circumference or one ring outside the circle that contains the number 15. In the same sense that we can say that 19 is 90 degrees from 15, we can say that 34 is 360 degrees from 15, or one complete rotation of the circle from 15. That explains where squaring the circle comes from. A more accurate expression would be that we’re circling the square but that never did catch on.


Here’s where it gets fun. The square root of 15 is 3.87. Add two to the square root of 15 and we get 5.87. Square 5.87 and we get 34.49 which rounds to 34. Now we know that adding two to the square root of a number and squaring that sum is the same thing as a 360 degree rotation up on the Gann Wheel. If “2” represents a 360 degree rotation then “1” represents a 180 degree rotation, “0.5” a 90 degree rotation, and so on. W.D. Gann tells us that 90 degrees in very important in the stock market. What Gann is really saying is that adding and subtracting .5 (and exact multiples or proportions of .5) to the square root of a stock price and then squaring the result is very important! We acknowledge that there is is another school of Gann thought that will say that Gann’s reference to 90 degrees relates to the movement of celestial bodies. We’ve looked into that and they may be right, but for our purposes we’ve also learned that these schools of thought can peacefully exist alongside each other without contradiction.

A very few people have been using some variation of the Gann Wheel for about 100 years now. In his now famous interview given to Richard D. Wyckoff in 1909, W.D. Gann attributed market movements to some undefined “law of vibration.” People can disagree about what W.D. Gann meant by that but we, at least, are fairly certain he was talking about the principles underlying the Square of Nine.


The Square of Nine is unique because unlike every other method of technical analysis, the Square of Nine is totally indifferent to whether the input variable is a price, a range of prices, or a number of trading days or calendar days. They are all the same and completely interchangeable.

Say what? That can be a little hard to get your brain around after spending years studying chart patterns, exotic moving averages, and oscillators. That’s the beauty of it. Price and time become interchangeable by converting them to degrees of a circle. Squares and square roots are part of that process. Once price and time are conceptualized in degrees of concentric circles we could care less about their magnitude. At that point we care only about their orbital relationship. Are they in opposition, conjunction or square?


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