# Tools: Automated 1x1 Gann Angle

Every so often some trader engages in a discussion with me regarding the virtues of plotting 45 degree angles on their chart.  Invariably their infatuation with this idea is based on a shallow understanding of what a 45 degree line really means, or is supposed to indicate.  Their introduction to 45 degree lines is usually from reading something about the works of W. D. Gann and how he plotted 45 degree angles on his charts.

Plotting a line on a computer generated chart physically at a 45 degree angle is worthless.   The truth of this statement can be illustrated by comparing these two charts.

The line is plotted at a downward 45 degree angle in both charts, but as can be seen, the line passes through the chart bars in different places.  The line which looks very useful as an indicator of a trend in the left-hand chart suddenly looks useless in the right-hand chart.  So what happened?   The vertical spacing of the chart scale changed!

Computer generated charts typically use a scale range that covers the highest high and the lowest low of the data set that is being plotted.  This scale is mapped to the physical size of the chart window, which might be a couple inches like the examples, or it might be the full size of your monitor display.   Not only can the scale range be dynamic, but the bar spacing is also dynamic.  The following example uses the same range as the 1st chart, but with a narrower spacing between the bars.  The position of the 45 degree line appears quite different now.

Since 45 degree lines are so arbitrary in their relationship to the bars, what then was W. D. Gann doing in plotting 45 degree angles on his charts?  Gann referred to the 45 degree angles as 1x1 lines (one by one lines).  The line was being plotted on his charts with a mathematical slope of one unit of price per one unit of time.  Gann would manually construct his charts using graph paper with a square grid.  The vertical price grid would be labeled with a price interval such as 2 cents.   Thus, the price unit is the grid interval of 2 cents.   The bars would be plotted on the horizontal grid, such as a daily bar on every grid interval.   Thus, the time unit would be one day.

A graph constructed in this manner would give Gann's 1x1 line the following slope definition:   2 cents per day.   A line with this slope could be easily drawn using a 45 degree triangle because of the way the graph paper was laid out.  So, a 45 degree line and a 1x1 line with a slope of 2 cents per day would be one and the same thing only when a specific graph paper grid was used.

Computer generated charts with their dynamic scale ranges and dynamic bar spacing must draw 1x1 lines according to a slope definition.  The plotted 1x1 line may or may not (usually not) be at a 45 degree angle.  When you see a reference to a 45 degree angle, always observe the price grid interval, and the time interval so you know the 1x1 definition for the slope.  The slope will be one unit of price for one unit of time.  Once the slope is known, the same line can be drawn on a computer generated chart.

In Ensign Windows, the slope of a trend line is shown as one of the parameters for the line.   If you want a line to be drawn with a specific slope, you can edit the slope parameter.  The slope of the line in the following chart is -10 points per bar.   The line will plot in the same position through the bars regardless of changes in the scale range or bar spacing.  As changes are made to the chart grid, the angle the line is plotted at will change.  The line's slope will remain constant and its relationship to the bars will remain constant.

For years, I thought finding a useful slope for the 1x1 Gann line was what Gann analysts meant by the phrase 'squaring time and price.'   However, my new understanding is that it is a literal relationship that can be expressed mathematically as:

Price = Time squared     or     P = t ^ 2

For additional information and treatment of this mathematical relationship, please read my 'Time and Price' article.  This relationship gives us the needed mathematics for automatically calculating the slope for the 1x1 Gann angle.

To calculate the slope of the 1x1 line, two prices are needed, and a time interval.  The first price  P1  will be the price on the chart where the 1x1 line (or Gann Fan) is anchored.   Usually this is the top or bottom price of a significant trend.  The time interval is calculated from P1 by normalizing P1 to fall in the range of 100 to 999.  If P1 is below 100, multiply it by 10 as many times as needed until it is in the range of 100 to 999.  If P1 is at or above 1000, repeatedly divide it by 10 until it is in the range of 100 to 999.   Then the time interval  t  is found by taking the square root of P1.

Gann's Square of Nine is used to determine the 2nd price  P2.   P2 is related to P1 by some degree of rotation around the Square of Nine.  The commonly used degrees of rotation are 360, 180, 90, and 45 degrees.  P2 can be calculated using this formula:

P2 = ( t + degrees of rotation / 180 ) ^ 2

Remember, the time interval  t  was determined by taking the square root of the normalized price P1.  Example:  If the trend top or bottom price is \$144.00, then the time interval is 12 bars.  To find the price that is 180 degrees around the Square of Nine, P2 would be ( 12 + 180/180 ) ^ 2, which equals 13 squared or \$169.00.

The slope of the 1x1 line is calculated using this formula:

slope = ( P2 - P1 ) / t

Continuing the example, slope = (\$169.00 - \$144.00) / 12 bars, which equals \$2.08 per bar.  If the 1x1 line determined in this manner is too steep to be useful on the chart, then it is appropriate to use a smaller degree of rotation around the Square of Nine, such as 90, 45, 22.5, or 11.25 degrees, etc.  If the 1x1 line is too flat to be useful on the chart, then it is appropriate to use a higher degree of rotation such as 360 or 720 degrees.

This technology is built into the Gann Fan tool in Ensign Windows.  The Gann Fan is placed on the chart by selecting the point for the vertex.  The 1x1 line can be located manually by selecting a 2nd point, or let Ensign Windows determine the 1x1 slope automatically using the mathematics developed in this article.  The following charts show the Gann Fan with the slope of the 1x1 line determined automatically from the P1 anchor price at the fan's vertex.

Ensign Windows does an excellent job of selecting which degree of rotation to use in determining the slope of the 1x1 line, but even this parameter can be manually overridden on the tool's properties window.  For the fans on the NQ U1 chart, the Gann Fan Properties Window shows that the degree of rotation used for the slope calculation was 11.25 degrees.  Other fan lines can be shown, but were not included in the illustrations to keep the charts from being cluttered with too many fan lines.