gann squares  



Constance Brown, CMT

An Excerpt from chapter 9, Technical Analysis for the Trading Professional, 2nd Edition

  1. Natural Laws of Vibration
  2. Harmonic Ratios
  3. An example Gann Time Study
  4. Why Cycle Periods Expand and Contract
  5. The mathematical relationship between Gann Fan and Gann Squares
  6. How To Use A Gann Wheel
  7. Create Your Own Gann Wheel in Excel

Book questions? Please send them over to twitter @AeroinvestBrown

Copyright © 2012 by Constance Brown. All rights reserved.

McGraw-Hill Companies.
Printed in the United States of America. Except as permitted under the United States Copyright Ac of 1976t, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without prior written permission of the Publisher.

Library of Congress Cataloging-in-Publication Data:
Brown, Constance M.
Technical Analysis for the Trading Professional:
Strategies and Technigues for Today's Turbulent Global Financial Markets, 2nd Edition

Wilbert Delbert Gann WD

Chapter 9: Gann Analysis: Calculating Price and Time

(numerous book paragraphs removed in all sections so that one example only or brief introductions are posted online)

Natural Laws of Vibration

William Delbert Gann was a master of cycle analysis. He used several different approaches with the aim of finding confluence between price, time, and diagonal analysis. One of Gann's approaches to identifying when a trader has permission to enter or exit a market is to use what are known as the "laws of vibration" or "natural laws." These are two very antiquated terms which refer to celestial motion. Gann's prestige grew in 1909 when Richard D. Wyckoff interviewed him for The Ticker and Investment Digest. Wyckoff further witnessed a trading period with an impressive win-to-loss ratio. Keep in mind that the year of the interview was 1909. If you want to know what makes a trader, study the materials you think brought them into their era of success. I made the mistake of beginning with modern resources, when books written in that era would have been easier to use as the language was the same as that used by Gann.

As an example, books of the late 1800s use the term natural law freely to describe the “stellar vibrations” of our solar system. It is a natural law, which we now call “diurnal motion,” where the Earth’s rotation on its axis has an influence on us to move from a cycle of conscious alertness to a state of sleep and back again every 24 hours. It is the natural law of celestial motion, first recognized by Copernicus, where the Earth’s revolution around the sun has a significant effect on the timing of when life springs back to life, blooms, matures, withers, and decays in a rest phase. These two cycles of celestial motion we accept easily, but the third is more difficult, the precision of the equinox as a timing mechanism within the markets.

But the real value of Gann Time Analysis is that it allows us to see the natural expansion and contraction of beats within a cycle as they abide the natural Laws of Vibration.

Time Cycles: Examples of Gann 's Analysis on the Vertical Axis

A Gann cycle is an astronomical formula mapped vertically on the time-axis. As example, we use a formula that will map every occurrence when the Sun and Neptune appear to be very close to one another as seen from Earth. We refer to the four degrees criteria as the period the planets are in orb. A zero degree alignment is rare. Therefore we accept plus or minus four degrees in orb is close enough to say in this example that the Sun is conjunct with Neptune. Had the Sun been 180 degrees from Neptune (plus or minus four) they would be in opposition to one another. The opposition aspect would have produced a different cycle beat.

Why look at the Sun and Neptune rather than some other planets in combination when you study Corn? An astrologer would answer, "Sun is light and Neptune is water. " But an astronomy wants to study physics and statistical correlation. Sun and Neptune create a meaningful cycle in this market. Well in fact every planet, every angle, every multiple combination, individual speed, acceleration, position, direction, or mathematical orbit measurement has been evaluated. Speed? Did you know the motion of the Sun along the ecliptic is not uniform? The seasons are of different lengths of time because the Sun moves faster in December and January, and more slowly in June and July. It is only the perceptions from Earth when Earth is considered to be the center of our Solar System. This view is called geocentric. The Earth's tilt on its axis creates several mathematical issues that must be considered. In fact there are also small differences in the length of seasons from year to year due to perturbations of our orbit by other planets and our motion relative to the barycenter of the Earth-Moon system.


Gann Natural Laws of Vibration

Figure 9.6 Gann Time Analysis Cycle - Natural Laws of Vibration Applied - Corn Futures - 2-week Bar Chart

Source: Aerodynamic Investments Inc., Software: Market Analyst

Gann gives time cycles in his books, but he does not give you charts to make it easy to see his references visually. It is not until you create the chart that it is clear Gann did not reference the start or end of significant price swings. This is very confusing at first, but Gann was teaching us what cycles he used for specific markets.

Figure 9.6 is a two-week chart of Corn prices.It is a time cycle that marks when a planet enters the ninetieth degree or cusp of Cancer. With the cycle beats marked on the chart you can easily see the expansion and contraction character of the downbeats on the vertical lines on the bottom of the price window. The expansion and contraction phases are also rhythmical.

Alignments with more than two planets will magnify the task rapidly. The asteroid Ceres is important. But you will read in Fibonacci Analysis that Ceres is needed to show how the planets all add up to a mean distance of 1.618 when measured in astronomical units from Mercury as the center. This mathematical relationship becomes more interesting when you know that Mercury had great significance in ancient Egypt. Gann travelled to Egypt to further his studies.

Online is only one astrological cycle Gann used as a demonstration. Other cycles you will want to learn about, other than ingress movement and aspect relationships, are solar and lunar eclipses, moon phases, and retrograde motion to name a few more.

Example of Gann's Analysis on the Diagonal Axis; Gann Planetary Lines

(paragraphs and charts removed)

How do you plot a planet's orbital movement on a chart? It is very easy to do; however, believing the market has any relationship to a channel line derived from a planet is a tougher challenge at first to accept. If you are standing in the middle of the New York Stock Exchange on market close, and take a snapshot to freeze the location of all the planets at that moment, each planet will have a position at a specified degree within a circle. Within the 360 degrees, let's say to view Venus you need to turn 47 degrees. Now add 360 to 47 until the value enters the range of prices on the chart. That works for the DJIA for the moment, but Figure 9.8 is trading in a range where 360 cannot be added to 47 without exceeding the price range of Corn. Therefore, factors are involved.

(the discussion about Gann factors can be found in the book.)

Examples of Gann's Analysis on the Diagonal Axis: Gann Fan Lines and Gann Squares

Squaring price (the horizontal axis) and time (the vertical axis) is often misunderstood. This is simply a box whose sides are equal. I will not be addressing the issue of calendar versus trading day differences here. Just keep it simple to develop the concept. One unit of time is equal to one unit of price. The difficulty follows for people because they do not know or have forgotten the simple math associated with a box.

Gann Squares

Figure 9.9 Gann Squares - Japan Nikkei 225 Index- monthly

Source: Aerodynamic Investments Inc., Market Analyst Software


In Figure 9.9 there is a monthly chart of the Nikkei 225 Index. In the same chart are four boxes. Box number one was created as the square of 90. If I smoothed out the corners and had each point along the box an equal distance from the center, what shape would I have drawn? A circle. A circle has 360 degrees. For the box to have sides of equal length and still be connected as a solid, the four corners must be equal to 90 to be right-angled. Four times 90 equals 360 degrees. All right, try this one. Turn the circle with 360 degrees into a triangle with sides of equal length. How many sides are there in a triangle? Three. How many degrees will be between two sides of the triangle that connect at the corner? The answer is 120 degrees. An equilateral triangle has three sides of equal length. Therefore 360 divided by three equals 120. I do not see the difficulty here, but this causes many people a problem.
Now study box 1 in Figure 9.9. Why does it look less than per- fect? Are the lengths of the sides for height and length really equal? Yes. It will often look less than perfect because of the pixel array of a computer screen. Computers and how we elect to scale our x and y axes will affect how the box looks to us.

Next, if you have one box and multiply it by two, how many boxes will you create across the Nikkei chart? Did you think the answer was two? Most people do. You have forgotten this is a box. If I multiply a box by two, the one side (height) doubles for the dimension of height and the box length will be twice as long also. Therefore I get four boxes. Multiply four boxes by 2 and the screen would display 16.

Box 1 has a cross in it that connects the corners. If my box is truly a box with equal lengths in height and width, when I connect the corners with lines they will cross dead center in the middle of a box. What is angle abc that defines the top left corner of box 1 that lies between lines ab and bc? It has to be an angle of 45 degrees as the line passes from corner to corner. Therefore the right-angled corner is divided equally by two.

Notice a line connecting the corners of box 1 will pass through the corners of box 4. Every line of 45 degrees will connect corners of other outer boxes. It becomes extremely important that you recognize this about the square of 90, or any square of 90 that is a multiple of two. Therefore the square of 45, 90, 180 etc. will contain an exact 45-degree angle.

Here is a new question for you to consider. The range of the Nikkei does not accommodate the use of one unit for the price and time relationships. This chart has an old price high still visible near 21,000. I would need 21,000 days to 21,000 price units and a very, very big wall to create the chart—not practical. So how do you fit such a price scale into a chart and keep the geometric proportions correct? That is one of the big questions that cannot be answered with a sound-bite quick answer. There is a very precise way to determine the correct factor to use. In addition, it is not experimental as a Gann software vendor believes. As soon as you start messing with the proportional relationships between width and length, such as thinking it might be better if a Fibonacci ratio were used, the analysis has turned into an experiment that is no longer Gann analysis. If your sources advise you Gann analysis is only about experimentation, they do not understand how the dimensions interlock between the horizontal, vertical, and diagonal.


Figure 9.10 Gann Fan Angles Relative to Gann Squares - Nikkei 225 Index

Source: Aerodynamic Investments Inc., Market Analyst Software

Consider Figure 9.10 where the monthly Nikkei data is displayed with four Gann Squares as described in Figure 9.9. The difference is the addition of Gann Fan lines that subdivide the right-angle corner on the bottom left. A Gann Fan subdivides a right-angled triangle into very specific angles. If you create a line from the corner with a growth ratio of 1:1, the line will move one unit up and one unit to the right, equally dividing the right-angle corner of 90 degrees. It becomes a 1 × 1 line that is a 45-degree line through the chart.

A Gann Fan is a series of lines subdividing 90 degrees. Each line will dissect the right angle at the following degrees: 3.75, 7.5, 15, 26.25, 45, 63.75, and then 82.5 and 86.26. The thirds created from 3 × 1 and 1 × 3 will be on degrees of 18.75 and 71.25.

The ratios needed to create these lines precisely from price and time are 16 × 1, 8 × 1, 4 × 1, 2 × 1, 1 × 1 (the 45-degree angle line), then 1 × 2, 1 × 4, 1 × 8, and 1 × 16. In each, the first value is how many units along the x axis you move before moving up the y axis scale. So 1 × 16 is over one unit and up 16 units.

We mention the use of 1 × 3 and 3 × 1 separately because these are thirds and they do not multiply by factors of two and do not retain an important relationship about to be demonstrated. If you have software with a tool that looks like Gann Fan lines, they must be these specific angles. If not, they are simply speed lines used to observe acceleration and the slope of data swings.

Figure 9.10 contains circles so you can see more easily the Gann Fan lines that intersect box corners and the diagonal crosses. These relationships between Gann Fan lines and box proportions are important. These relationships also relate to the Gann Wheel that defines the horizontal axis. When a software vendor has an error in any one of these three tools, the Gann Square, Gann Fan, or Gann Wheel, it will be recognized by the advanced Gann practitioner because the factors used will no longer be correct that bind these proportional attributes.

If I multiply my Gann Fans drawn in Figure 9.10 by two, where would the 45-degree line that is in the middle of the chart be drawn next? It would shift and be drawn exactly on top of the line above the 1 × 1 in Figure 9.10 and become the new 1 × 1 line. Why? It is a line and not a box. So the 1 × 2 moves to 1 × 4 and the 1 × 4 moves to 1 × 8, etc. That is why the 1 × 3 and 3 × 1 are mentioned separately. But Gann used to subdivide each box into thirds. How many boxes form inside one box that is divided by three? Nine. The 1 × 3 and 3 × 1 will intersect the corners and intersecting crosses within the nine boxes of a single larger box exactly.

I have not made a comment about the highest and lowest Gann Fan lines that do not connect to any corner or middle intersection in Figure 9.10. They will bisect corners or intersecting crosses when additional boxes of equal size are added to a larger chart in width and height. The line circled in Figure 9.10 that bisects the middle of the top left box is heading toward a corner when you zoom out and find the boxes continue above and to the right. When you read Gann’s courses and he describes how he draws Gann Fan lines, it can be confusing because he calls them moving averages and not trend lines. When you delve more deeply into Gann you will realize you are working with a harmonic cycle that is better named a moving average.

I have just demonstrated some of the attributes of the square of 90. We use other squares. For example, the square of 144 will have a diamond-shaped appearance and will be of interest to soybean traders. How do you find the 45-degree angle in a square of 144? That is a good question which I have to leave with you. I can only touch on the tip of the iceberg to give you a conceptual understanding about Gann analysis.

The key thing to take away from this discussion is the understanding that the relationship between Gann boxes and Gann Fan lines is very precise. There is no room for guessing. But many books do guess.

Some describe the intersecting corners and centers of the boxes to be the time objectives for trend changes. Think about this. The length of each box is equal from one to another. The lines that cross in the middle are always half the length or width of the box when the intersection is extended vertically down to the x-axis. Books and books write about these patterns giving you time, yet all they have done is to create a fixed cycle again. We know fixed cycles are not the best cycles to use in trading applications. More importantly, Gann did not use the boxes in this manner. In Figure 9.10 the intersection of box 4 (bottom right) has a circle showing a diagonal target in the year 2011. This method of just looking for intersecting points from a Gann Square will have inconsistent results and poor performance. I would always favor Astrological cycles over this method for time analysis. But diagonal analysis is never used alone. Therefore there has to be more to it, and there is indeed.

Gann Square of 9 Relationship to Gann Angles

Figure 9.11 Gann Square of Nine Relative to Gann Angles and Squares - Nikkei 225 Index

Source: Aerodynamic Investments Inc., Market Analyst Software


Figure 9.11 is the same monthly Nikkei chart as Figures 9.9 and 9.10. Two gray areas will help your eye stay within the white Gann Fan area under the 45-degree-angled line originating from the bottom left. The circled intersections at A, B, and C are the only signals in this chart of Gann significance. Why? Because they occur when price targets have been realized as derived from a Gann Wheel and they are confirmed by diagonal angles. Point B was not even identified in Figure 9.10 because it falls upon a measurement from thirds. Point A was not in Figure 9.10 either, but could have been as it fits the criteria for that discussion. By adding objectives on the horizontal axis only points A, B, and C are of interest because confluence develops on the horizontal, diagonal, and vertical axes. For example, point B is where the 240-degree price target from a Gann Wheel falls on the horizontal axis. It bisects a descending 45-degree line in the bottom right box. It is also using the Gann Fan line radiating from the bottom left box as resistance. It is also a vertical target in time which developed a confluence target zone from astrological cycles (not shown). Therefore all three cycles in price, time, and diagonal converge at points A, B, and C. This is what Gann analysis can identify for you and offers an introduction to the geometry involved on the most elementary level. The Nikkei price high in 2007 was not discussed. Much has to be overlooked in this introductory discussion.


Gann Price Analysis on the Horizontal Axis; How to Use
The Gann Wheel - The Square of Nine

How do you extract price objectives from a Gann Wheel? Figure 9.12 is a Gann Wheel called the Square of Nine or a harmonic wheel. Gann used other wheels such as the hexagon wheel, which is a honeycomb pattern. The honeycomb pattern is better for calculating in units of thirds such as 30 and 60 degrees. The wheel called the Square of Nine starts at the center with a value of 1 and the first box ends at the number 9.

Gann Wheel the Square of 9

Figure 9.12 Gann Square of Nine - The Gann Wheel

Source: Aerodynamic Investments Inc.,


In Figure 9.12 you can follow the numbers to 9 and then run into the first tricky part where beginners can make an error. The bottom left corner requires you to move outward by one square and then the numbers will continue to increase by one sequential unit again until the next outer square is filled again. The numbers 81 and 82 on the bottom left clearly illustrate this movement. If you do not pay attention you can easily find yourself on the wrong column or row. The numbers will be incremental as you move in a clockwise rotation through the wheel. Here is how the numbers relate to one another and how this pattern becomes a calculator.

The horizontal and vertical cross-sections display a double line so that I can later rotate the cardinal cross and angles of the circle as a fixed unit when ‘zero’ is set over a starting price. Here is how the wheel becomes a calculator to create a price objective. If a stock were trading at a price of $15, what would the price objectives be, using a Square of Nine Gann Wheel? Find the number 15 on the Gann Wheel. The number 15 is perfectly aligned under the zero and 360-degree angle marked on the top of the wheel. Because the number 15 is aligned with zero, we need make no further adjustments; just read the Gann targets straight off the wheel. The 45-degree price objective from 15 is 17. The 45-degree line from the center of the circle travels toward the top right corner. The number 17 is the value where the 45-degree line bisects the path of numbers in rows and columns. We would use the phrase “$17 is 45 degrees up from $15. ” Now skip over to 90 degrees and find $19, then 180 degrees up from $15 is $23. The target of $23 is directly opposite $15. (We would still say, “$23 is 180 degrees up from $15,” even though 180 degrees is directly opposite the place where we began. As long as you are obtaining higher price objectives from the wheel, the results of the angles are always “up” from the starting level.) At 270 degrees, $28 is the price objective. A full 360 degrees up from 15 is 34. (You will have to add two numbers from 32 to fill in the blanks and complete the wheel in this diagram.) That is how a Gann Wheel is used. To make your first example easy I have left out the targets from three other degrees. The angles of greatest interest to us in financial markets are 45, 90, 120, 180, 240, 270, 315, and 360. Are all these angles important? No—not in all markets.

Bonds seem to be attracted to 120 degrees when a counter-trend move develops. Currencies love 90 degrees. Each market has its own personality that is consistent.

How do we calculate the major support levels from a stock pivot of $15 using the wheel? Instead of moving clockwise as we did to find resistance levels, we will move counterclockwise to find support because the numbers decrease as you move counterclockwise. The first target will be on a 45-degree line to the left. It is located at $13 where the 45-degree line crosses the top left diagonal. The $11 level would define 90 degrees down. A full 180 degrees down is at $8. (Do not forget to jump the corner at numbers 10 and 9.) Now skip to the 360 degree target, which is at $4, the number just below $15. If you can follow the wheel to identify these price targets, you will be able to obtain the price objectives for the next example. The first example we covered used a value of $15. But a stock that trades in this range would need targets that did not have such a large spread. Therefore Gann used a wheel with increments of .50 cents. A factor could also have been used.

What if the price low is $87? The start has to be changed. Move the Mylar overlay on the top of the numbered boxes to the left so that the zero line at the top now crosses through the number 87. The first target from 87 will be 92. It is just a matter of reading right off the wheel once the start is set correctly. How do you use a wheel for the Nikkei? How do you use a wheel for a market that trades in fractions? There is indeed more than just these basics.

The Square of Nine is a very cool calculator. A four year project to decode it took me through a Journey back in history and to Cairo, Egypt. It has much more to it than just this brief introduction can offer. But we can look at one of the mathematical properties behind this calculator.

The Gann Wheel is really a square root calculator. The square root of 15 from the first example is 3.873. Now add 2 and it equals 5.873. The square of 5.873 is 34.49. Rounded to 34 it is 360 degrees up from 15. This is a full 360-degree rotation of the circle. But using this method creates issues once you try to extend past 360 degrees. The simple formula above is not the whole story. The logarithmic properties of the wheel will cause errors if you do not understand what you are working with when doing math in harmonic ratios. But stay within the first 360 degrees and you will be able to create your own wheel.

How To Create Your Own Gann Wheel in Excel

To identify levels of resistance from a price low, use the following formulas in Excel for each of the degrees. The formulas are:


Please refer to Technical Analysis for the Trading
Professional - 2nd Edition for further reading ...