One of the mysteries surrounding the legendary W.D. Gann is a financial calculator called the Square of Nine.
It is said that Gann often used this calculator to determine exact price points for market turns with great success.
It is also understood that he did not invent it, but rather, discovered it in India or Egypt (as the story goes).
But this article is not about whether the history of the Square of Nine, but whether it is as special as it is hyped up to be.
The Square of Nine has also been described as the “Gann Wheel”. However, I would consider the “Gann Wheel” to be the actual ‘wheel’ calculator tool that includes the Square of Nine values imprinted on its face. On top of the Square of Nine would be one or more transparent discs with a square, triangle and cardinal cross imprinted on them (and possibly a division of ‘thirds’ as well).
The Square of Nine is sometimes referred to as a “Square Root Calculator”. Yet, its purpose is not to calculate the square root of a number, but rather, it does include getting the square root of a value in route to a result. Apparently the name “Square of Nine” comes from the result of squaring the lowest odd number greater than one (since one would not produce anything greater than itself), which is three. Squaring three produces 9 ‘cells’ within the square. To be more useful, however, you would want to make your square much larger than one with just 9 cells.
To create the Square of Nine, you simply draw a large square (or whatever size you like) and then subdivide that square into cells (like a grid). Preferably, be sure to draw the lines so that there is a cell right in the center of the overall square.
Starting with the number 1 in the center cell, start numbering the rest starting with the cell to the left as “2”, then moving clockwise around the center cell by placing a “3” above the #2 cell, then “4” to the right of #3, then “5” to the right of #4, then “6 below the #5 cell, and so-forth, going round and round.
The Square of Nine is applied to a circle, in that each revolution around the Square is a 360-degree cycle. So if you were to overlay a circle upon the Square of Nine, you could start with any number and quickly determine what the value would be ‘x’ degrees away, where ‘x’ could be 45, 90, 180, 360, or anything in between.
For example, if you had a price of 218 and wanted to know what the price would be 360-degrees higher, you would look for 218 on the Square of Nine and then go up to the next value along the same axis and find 281.
What if you wanted to know what a 45-degree move lower from 371 is? Locate 371 on the Square of Nine and follow the prices as it decrements by one along the cycle until you have moved one-quarter (counter-clockwise) of a circle around the square to arrive at 352.
Drawing a circle to completely enclose the Square of Nine is often done to represent not only one complete year from January to December, but also to represent the 12 divisions of the Zodiac. If you divide the Square of Nine into quarters (cardinal cross “+”), the line that goes from the center “1” through “2” to the left and all the way to the end of the Square (and thus touch the circle drawn around it) would represent 0-degrees and the starting point. Here you would label as March 21st (the first day of Spring, the vernal equinox), representing the beginning of the natural year. As far as the constellation reference, that would be considered the Sun at 0-degrees Aries. A quarter of a year later would be June 21, so that marks the top of the Square which is 45-degrees clockwise. Some also mark the cardinal cross with the compass, with June 21 (top at 90-degrees) being North, March 21 (left at 0-degrees) as East, Sept 21 (right side at 180-degrees) as West, and December 21 (bottom at 270-degrees) as South.
If you simply wanted to calculate degrees from any value, you can simply use an electronic calculator. All you need to know is that a complete 360-degree difference is represented by getting the square root of the value, then add (if you want to go 360-degrees higher) or subtract (to go 360-degrees lower) the number “2” from the result, and then square it.
If you want to calculate a different degree from a starting value, you simply divide the value “2” that represents 360 by the same division of 360. For example, if you want to calculate for 180-degrees which is half if 360, then use half of “2” which is “1”. If you want to calculate for 45-degrees, which is one-eighth of 360, then use one-eighth of “2”, which is “.25”, and so-forth.
For example, say you have a price of 974 and wanted to know what a 90-degree move higher would be. First we would get the square root of 974 which is 31.21. Then since 90 is 360 divided by 4, we would divide “2” by “4” to get “.5”, which we add to 31.21 to get 31.71. Now square 31.71 and the answer is 1006 (rounded). Look on your Square of Nine and you will see this to be true.
Now there is little room in an article like this to go into all the known details of the Square of Nine. What I do wish to address is whether it is a useful calculator or just a bunch of hype.
From my personal experience, the Square of Nine is valuable. The more you understand it, the more insight it will give you in calculating support and resistance, as well as turning points in time. There are several different types of calculations you can do.
For example, you can use the Square of Nine to do date calculations based on major tops and bottoms. In respects to dates, simply keep in mind that the Circle is 360-degrees but a year is 365 days. Thus, a 90-degree move on the Square is about 91 days.
For example, the major top in the SP500 of May 19, 2015 was followed by the major bottom of July 6, 2015. This move was based on 45-degrees in calendar days (which fell on a non-trading day, so July 6 marks the first trading day following).
The major bottom in SP500 of December 16, 2014 out 45-degrees (calendar days) resulted in another major bottom for February 2, 2015, which also was 30-degrees (trading days). “30” is considered an important Gann value as it is one-twelfth of 360 (a year is divided in 12 months).
When dealing with prices, the Square of Nine provides the best results when you convert your starting values into whole numbers of 3 or 4 digits left of the decimal. So if you have a value of 20.45, while you can certainly use that value as it is, also try 204.5 and 2045. Just remember to adjust the decimal point on the result back to where it should be.
While I can certainly attest that the value of the Square of Nine is not hype, nothing replaces personal experience. If you really want to know its value, spend the time to learn and use the Square of Nine along with your price charts.