Square of 9 Gann Fan

Author: Optuma Team Last updated: Jul 7, 2021 00:04
Included in Gann Edition Included in Astro Edition


The main concept that needs to be understood when using a Gann Fan is the relationship between time and price that Gann proposed. This means that for one unit of time the market will rise (or fall) by one unit of price, resulting in a one-by-one line (1 x 1).

The Square of 9 Gann Fan differs from the standard Gann Fan in that the angles are calculated using the square root principals of the Square of 9, as described in the work of Daniel Ferrera.


To add the tool to your chart, select the tool from the Gann tool group, and left-click on the bar on the chart you wish to calculate the tool from. Next, extend the lines and left-click again where you want it to end. Optuma will then draw the tool using the default settings.

### Example:
If the Square of 9 Fan (with a Price Unit of 1) is placed at a value of $100 the 1x1 would pass through $121 (being 180-degrees away from 100) in 10 calendar days:

Square of 9 Gann Fan 2

*Note: The fan can also be placed on a high so that it is descending. In the above example, the 1x1 would pass through 81 in 10 calendar days, as 81 occurs 180 degrees before 100 on the Square of 9.*

Calculation and Usage

This tool is based on the Sq9 helper function. That is:

EndPrice = ( ?(StartPrice) + Angle/180)²

On the Sq9 chart you can see that if we wanted to find the next rotation (360°) from 16, we would get
(?16 +360/180)²
= (4 + 2)²
= 36


It’s not 100% accurate but it gives us a really close approximation of the square. Note there is a slight drift around 120 and 240 degrees - we’ve spent days trying to find a model which would account for that but have not solved that yet.

The above formula gets complicated when we have a price unit because we have to divide the start price by the price unit and multiply our final result by the price unit. In the example above, imagine that we had a price unit of 0.1 and the price was 16. This means that there are 160 intervals of price to get to a price of 16.

Our formula becomes (?(16/0.1) + 360/180)² x 0.1 which equals 214.6.

You can see that below.


But we need to convert that 214.6 back into the same price range - we do that by multiplying by the price unit giving a final number of 21.5

Something which causes a lot of trouble for people is that the values you see on the chart/tool do not match the Sq9 when a price unit is in play.

With the Sq9 Gann Fan, we also have the time component. That is simply the Square Root of price factoring in the price unit again. So for 16 with a price unit of 0.1 will give us a time interval of 12.6.

So, on the Gann Sq9 Fan on the Jan 3rd, 2019 AAPL low of 1$42 and a price unit of 0.1, we get:

price = (?(142/0.1)+360/180)² x 0.1 = 157.5<br></br>time = ?(142/0.1) = 37.7

You can see those results on this chart when we measure the interval (Tip: Hold down shift and click and drag to measure an interval on a chart). Note that the hint is rounding the 37.7 to 37.


If you have any questions regarding this explanation, please reach out to our support team using the link below:

Actions & Properties


Add Line Alert: Selecting this action will set a Line Alert based on the selected line.

Add to Toolbar: Adds the selected tool to your custom toolbar.

Apply Settings to All: When multiple Square of 9 Gann Fan tools have been applied to a chart, page or workbook, this action can be used to apply the settings of the one selected to other instances of the tool. This is a great time saver if an adjustment is made to the tool - such as line colour - as this allows all the other Square of 9 Gann Fan tools in the chart, page or entire workbook to be updated instantly.

Copy Tool: Allows you to copy the selected tool, which can then be pasted onto a different chart window.

Move to Back: If the tool is displaying in front of other tools or indicators clicking this action will move the tool view to the background.

Move to Front: If the tool is displaying behind other tools or indicators on the chart, clicking this action will bring the tool to the forefront.

Price Flip: Allows you to create a duplicate of the tool along the price axis.

Time Flip: Allows you to create a duplicate of the tool along the time axis.

Restore Default Settings: Click this action if you have adjusted the default settings of the tool, and wish to return to the standard properties originally installed with Optuma.

Save Settings as Default: If you have adjusted any of the tool’s properties (colour, for example) you can save the adjustments as your new default setting. Each time you apply a new Square of 9 Gann Fan to a chart, the tool will display using the new settings.

Delete: Deletes the tool from the chart.



Tool Name: Allows for the name of the tool to be changed, as displayed in the Structure Panel.
Levels: Click on this option to display the different Gann Fan levels.
To add a new level to the chart, left-click on the blue + button and enter the values as needed.

  • Value - Sets the time/price ratio for the angle (e.g. 1 x 2). To change the value amount, click in the field and enter the new value.
  • Line Style - Sets the line type, thickness, colour and transparency of the angle lines.
  • Visible - To hide a level, deselect the check box with the green tick.

Use Chart’s Price Unit: By default, the price unit of the chart is used in the tool calculation. Untick the box to manually adjust the value in the Price Unit property.

Price Unit: This option is available when the Use Chart’s Price Unit box is unticked (see above). Enter a new value to manually determine what one unit of price is equal to in the tool’s calculation (eg 0.1). For more information click here.

Degrees: On the Square of 9 wheel, this in the angle from the anchor value, and used to determine the 1x1 calculation. By default this is 180 degrees, so for example, if the anchor value was 53 the next value would be 69 (half way around the wheel). If set to 360 degrees the value would be 86.

Time Intervals: Sets the time unit used in calculating the Gann Fan Angles. Set to Calendar Days by default.

Extend Lines: Check this box to extend the angle lines.

Show Labels: Check this box to display the angle values (e.g. 2 x 1, 1 x 1). Uncheck the box to hide these values.

Font Size: If Show Labels is selected you can adjust the size of the text displayed for each label. Moving the slider bar to the right increases the font size.

Base Line Style: Allows you to adjust the style, width, colour and visibility of the horizontal and vertical base lines.

Tool Transparency: Use this slider bar to adjust the transparency of the tool. Moving the slider to the left will increase the transparency of the tool.
Visible: Un-tick this checkbox to hide the tool from the chart.