William Ganns Square of Nine

In this article we will discuss about one of the many methods of analysis William Gann used. He revealed some of his methods to be used by those patient and wise enough to study and understand them.

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 then 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. We will end with having a powerful tool that gives us clear targets for the trend to reach.

How was William Gann?


William D. Gann was a trader of the early 20th century. His abilities for profiting from the stock and commodity markets remain unchallenged. Gann’s methods of technical analysis for projecting both price and time targets are unique. Even today, his methods have yet to be fully duplicated.

Known as “The Master Trader”, W.D. Gann was born in 1878, in Lufkin, Texas. Gann netted over 50 million $ from the markets during his trading career, averaging a success rate for trades of more than 90%. It has been said that Gann could very well have been right ALL the time. Any losses incurred by him were only there by his own design and not because of any faults with his methods.

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

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 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”, and describes Gann’s proficiency for projecting price targets forward in time:

“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 of a natural order existing 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 for not only his life, but 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.”

This universal order of nature also existed, Gann determined, and we have the same opinion now, in the stock and commodity markets. Price movements occurred, not in a random manner, but in a manner that cat 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 for all this points of forces? Right… cosmos..universe.. all planets around us.  This Gann could say at that time.

These points of force were felt to cause prices to not only move, but 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 witch prices invariably will follow.

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 lat not only days or weeks, but months and even years. Gann’s trading year is first divided in 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.

Lets see a little example. This is an examples 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.

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What is Square of Nine and how is it constructed?


We will analyze Square of Nine from William Gann’s perspective. Here is what it’s about:

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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 above 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. This is how such a square looks like:

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Examples for Financial indicators and explanation


We will explain first the February 2007 High for S&P 500. 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. This is the index’s chart:

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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.

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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. These are the opposition and square presented above. 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 than rise.

The second example is about the abrupt fall in the summer of 2007, more exactly, in August. We present 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 declining 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 predict that in august S&P 500 will 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. Nice, isn’t it?

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This is the last conclusive example:

This example present the forecast for 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. Is there a coincidence or is it harmony?

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

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

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

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 are basing our analysis and forecasts on.

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