William Gann’s Square of Nine

technical analysis William Gann square of nine

In this article we will explain one of the many technical analysis methods used by William Gann. In his books and studies he revealed some of his methods, to be used by traders who are patient and wise enough to study and understand them fully.

We will present you William Gann’s Square of Nine: idea of conception, special properties and the characteristics for bull and bear market. We will then find some specific and less known geometrical and mathematical proportions between the numbers in the square. We will also look on the charts for the numbers in the square. We will discover that between a High and a Low there is a specific ratio. This ratio has an explanation and we will find its origin and use. Finally we will end with having a powerful tool that gives us clear targets for the trend to reach.

William Gann and his trading methods

William D. Gann was a trader of the early 20th century (his full biography has been published in the July-September edition of FX Trader Magazine).  His abilities to profit from the stock and commodity markets remain unchallenged. Gann’s technical analysis methods of projecting both the price and the time targets are unique. Even today, his methods have yet to be fully duplicated.

Known as “The Master Trader”, Gann netted over 50 million $ from the markets during his trading career, averaging a success rate of more than 90% of his trades.  It has been said that Gann could very well have been right ALL the time and that any losses incurred by him were only by his own design and not because of any errors in his methods.               

His successes are legendary. Gann literally converted small accounts into fortunes, increasing their net balances by several hundred percents. There are numerous examples of his trading successes, among which:

1908 – a $130 account increased  to $12.000 in 30 days.

1923 – a $973 account increased to $30.000 in 60 days.

1933 – 479 trades were made with 422 being profitable. This is an accuracy of 88% and 4000% profit.                       

1946 – A 3-month net profit of $13.000 from a starting capital of $4500 – a 400% profit.

The following paragraph appeared in the December 1909 issue of “Ticket” Magazine. It was written by R.D. Wyckoff, the former owner and editor of the “Ticket”:

“One of the most astonishing calculations made by Mr. Gann was during last summer (1909) when he predicted that September Wheat would sell at $1.20. This meant that it must touch that figure before the end of the month of September. At twelve o’clock, Chicago time, on September 30th (the last day) the option was selling bellow $1.08 and it looked as though his prediction would not be fulfilled. Mr. Gann said, ‘If it does not touch $1.20 by the close of the market, it will prove that there is something wrong with my whole method of calculations. I do not care what the price is now, it must go there’. It is common history that September Wheat surprised the whole country but selling at $1.20 and no high in the very last hour of trading, closing at that figure”.

Gann’s trading methods are based on personal beliefs that a natural order exists for everything in the universe. Gann was part of a family with strong religious beliefs. As a result, Gann would often use Biblical passages as a basis not only for his life, but for his trading methods. A passage often quoted by Gann was this from Ecclesiastes 1:9 - 10:

“What has been, that will be; what has been done, that will be done. Nothing is new under the sun. Even the thing of which we say, ‘See, this is new!’, has already existed in the ages that preceded us.”

Gann determined that this universal order of nature also existed in the stock and commodity markets. Price movements occurred, not in a random manner, but in a manner that can be pre-determined. The predictable movements of prices result from the influence of mathematical points of forces found in nature. And what is the cause of all these points of forces? Right… cosmos… universe... all the planets around us.

These points of force were felt to cause prices to not only move, but to move in a manner that can be anticipated. Future targets for both price and time can be confidently projected by reducing these mathematical points of forces to terms of mathematical equations and relationships.

The mathematical equations of Gann are not complex. They result in lines of support and resistance, which prices will follow invariably.     

Gann held that time is the most important element of trading. Time is the factor that determines the length of a commodity’s price trend.  When time dictates that trending prices should react, prices may stabilize for a short period, or they may fluctuate within a tight range, but eventually they will react by reversing direction. Time is the element that will determine WHEN prices should react.Certain price reactions are found to occur during specific times.  The actual TYPE of price reaction can be anticipated, and pre-determined, by using Gann time rules.

Gann time periods last not only days or weeks, but months and even years. Gann’s trading year is first divided by half, equivalent to 6 months or 26 weeks. The year is then divided by eighths, and then by sixteenths. And then, after you think you understand all of this, you find that Gann’s year is also divided by thirds.

There are also important time periods within the Gann year. For example, since a week is 7 days, and 7 times 7 is 49, Gann’s work found that 49 is a significant number too. Important tops or bottoms may occur between the 49th and

52th day, although an intermediate change in trend may occur between the 42th and 45th day, because 45 days in 1/8 of a year.

Other time periods that were important to Gann, at which a price reaction could be expected, are:

- Anniversary dates of major tops and bottoms

- 7 months after a major top or bottom for a minor reaction.

- 10 to 14 days is the length for a reaction in a normal market. If this period is exceeded, the next reaction should be expected after 28 to 30 days.

If you’re not already confused, understand that Gann’s year may not only be calendar, but “fiscal” as well; starting from major tops or bottoms. Gann’s time rules consider many periods, including seasonality, Biblical references, and astronomical events.

Let’s see a little example. Figure 1 shows an example of astronomical correlations on a Gann chart. One of Gann’s beliefs, stemming from his “natural order” concept, is the influence of planetary movements on earthly events, such as the moon’s perceived effect in tides. This “cosmic perspective” of Gann is unlike conventional astrology, in that planetary influences, like units of price, are unique to each market.

technical analysis William Gann square of nine astronomical correlations

What is Square of Nine and how it is constructed

We will analyze Square of Nine from William Gann’s perspective. See Figure 2.

technical analysis William Gann square of nine Square of Nine

The basic form is a square. The principle of making this square is very ingenious. The numbers are arranged in increasing order, in a specific pattern, starting with number one set in the centre. We can arrange as many numbers we wish. The numbers can be arranged starting from the middle, to the right and up, in a counterclockwise manner, or to the left and up, in a clockwise manner. When setting the Square of Nine we have to consider the trend’s direction. If the trend is ascending we will arrange the numbers clockwise, if it is descending we will arrange the numbers counterclockwise.

After arranging the numbers we can observe some special similarities forming. For example on one diagonal we have the numbers 1, 9, 25, 49, 81, 121, 169 and so on. These numbers are the square of odd numbers 1, 3, 5, 7, 9, 11, 13 etc. On the same diagonal with 4 we have the numbers 16, 36, 64, 100, 144, 196 and so on which are the square of even numbers 2, 4, 6, 8, 10, 12, 14 etc. Is there a coincidence or is it harmony?

The same principle of arranging numbers can be used for other values as well. With the help of the square presented in Figure 2 we will analyze the value for some financial indicators. We can also input instead of numbers some calendar dates to help us calculate the day for the High and the Low (See Figure 3).

technical analysis William Gann square of nine High and the Low

Examples for Financial indicators and explanation

1. Let’s take the February 2007 High for S&P 500. See Figure 4. That month the indicator had a High of 1.460 points. Let’s identify this value on Gann’s Square of Nine. The next month S&P 500 had a Low of 1.360. We will look for this value in the square also.

technical analysis William Gann square of nine High for S&P 500

We can see below the two values on Gann’s Square of Nine. Between the centre of the square and these points there is an angle forming. This angle is about 250 degrees. This is Gann’s mathematical equation:

Square root of High – 1.4 = Square root of Low

Why 1.4? In trigonometry 360 degrees is defined as 2; 180 degrees as 1; 90 degrees as 0.5; and 250 degrees as 1.4.

In conclusion we have:

Square root of 1.460 - 1.4 = Square root of 1.360 (correct!)

Let’s see now why the indicator has fallen 250 degrees. During the period of time we are referring to, on the sky we had two major astrological aspects: Saturn opposition Neptune (this means 180 degrees) and Sun square Pluto (this means 90 degrees). If we add them: 180 + 90 = 270 degrees. This value is very close to the actual fall of the index.

technical analysis William Gann square of nine 250 degrees

The forecast would have been as it follows:

When analyzing the market at the end of February, after the 1.460 High, we would have looked at the astrological aspects coming the next month. The sum of the aspects was 270 degrees. Using Gann’s Square of Nine and the mathematical equation:

Square root of 1.460 - 1.5 = square root of the value of next month’s Low

The result is 1.350. So the forecast would have said that the S&P 500 would have fallen to the value of 1.350 – 1.360 and then rise. See Figure 5.

2. The second example is the abrupt fall in the summer of 2007, more precisely, in August. These are the steps of the forecast: 

Step 1: S&P 500 has a High of 1.550

Step 2: For the months of July and August 2007 we have the following astrological aspects: Mars square Neptune,  Mars square Saturn, Saturn trine Pluto, Sun opposition Neptune. All these aspects have a negative influence. We are expecting a decline in the evolution of the index with 90 + 90 + 120 + 180 = 480 degrees utmost.

Step 3: 480 degrees means 2.6 in trigonometry

Step 4: we apply the equation:

Square root of 1.550 - 2.6 = square root of the value of next month’s Low

Step 5: Next month’s Low is 1.355

Step 6: We would have predicted that in August 2007 the S&P 500 would fall from a High of 1.550 to a Low of 1.355 -1.365

The facts were that S&P 500 had a Low of 1.370 and then started rising again (see figure 6 and 7). Nice, isn’t it?

technical analysis William Gann square of nine S&P 500

technical analysis William Gann square of nine S&P 500

3. The last example is about the forecast for the S&P 500, which had a historic High in October 2007 and a decline in January 2008.

Step 1: The historic high is 1.576

Step 2: in the period October 2007 – January 2008 we have the following astrological aspects:

Saturn opposition North Pole, Sun square Uranus, Sun square North Pole, Sun square Saturn, Sun square Uranus, Sun opposition Mars, Saturn trine Mercury. All these aspects are negative. We will expect a fall with  180 + 90 + 90 + 90 + 90 + 180 + 120 = 840 degrees.

Step 3: 780 degrees is 4.6

Step 4: We apply the equation:

Square root of 1.576 - 4.6 = Square root of the Low’s value

Step 5: The Low equals 1.260

Step 6: The conclusion is: S&P 500 will fall after the historic High to a 1.260 Low in January 2008

The facts were that S&P 500 had a Low of 1.250 and then started rising (see figure 8 and 9). Is this a coincidence or is it harmony?

 technical analysis William Gann square of nine S&P 500

 technical analysis William Gann square of nine S&P 500


a. This method of prediction is incredibly accurate and has a special harmony in it. It offers us correct ways of assessing future Lows and Highs for financial market’s indicators.

b. Although it seems a complex and difficult method to handle, it is a useful tool in our system of analysis. We have come to these conclusions after many years of thorough research. There are a lot of details to consider for a full understanding of the phenomenon but it can be done.  We have understood Gann’s method and we give traders simple and easy-to-apply analysis, which is the result of a hard and meticulous work. 

c. We have also analyzed many past years and the rules apply. You can also verify the correlation if you are attracted to this kind of research.

d. By showing you this study we are not trying to convince you that astrology is perfect. We just want to highlight the fact that there are correct ways of predicting the local High and Low and the reversal points. These kinds of studies helped us along the years build our trading system, the system we base our analysis and forecasts on.

Dharmik Team