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Knowledge Base

Square of 9 Gann Fan


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.


The price element of the fan is based on taking the value of the anchor point and calculating the next value 180-degrees (by default, but this can be customised) around the square of nine wheel, with the time element being the square root of the value. The Price and Time intervals are used to project a point in the future and then a line is drawn from the starting point through that projection.


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:


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>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: Creates an alert based on the selected line. Click here for more information on Line Alerts.

Add New Level: Allows new angles to be added or existing angles to be edited. See Gann Levels in the Properties section below for more information.

Add to Toolbar: Click this action to add the selected tool to your custom toolbar.

Apply Settings to All: When multiple Square of 9 Fans 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 changing colours - as this allows all the other Square of 9 Fans in the chart, page or entire workbook to be updated instantly.

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

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

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

Price Flip: Adds an additional Square of 9 Fans using the same settings as the original, however, the tool is flipped vertically. This action does not remove the original Fan.

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 (such as the colour) you can save the adjustments as your new default setting. Each time you subsequently apply the tool to a chart it will display using the new settings.

Time Flip: Adds an additional fan using the same settings as the original, however, the tool is flipped horizontally. This action does not remove the original Fan.

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.

Click on this option to display the different Gann Fan levels. For more information on the Levels Editor, click here.
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.

Un-tick this checkbox to hide the tool from the chart.

 Last updated Sat, Jun 8 2019 1:41am

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