Square of 144

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Square of 144 Calculator

The Square of 144 Calculator generates a Square of 144 Master Calculator (table) and will then automatically display the position of key turning points on the Calculator. Gann's study of Squares covered two primary areas: Overlays and Master Calculators. This tool allows for the study of Master Calculators while Overlays are contained the drawing tools. Once the subject of Squares is fully understood the commonality between the two uses of Squares can be seen, however that is beyond the scope of this help topic.

The Square of 144 created by the calculator has been designed so that the key vibration levels for prices on the calculator are easily identified. The software has linked this tool to the Turning Points Hi-Lite tool which automates the process of locating turning points on the calculator. This calculator is only studying the security in terms of price. The Square Overlay brings in the study of time and price in relation to the number 144.

Setting the Calculator

The calculator analyses the price data of one symbol at a time due to the link to the Turning Points Hi-Lite tool.

Users must first select the symbol in the Square of 144 Calculator dialog box:



Enter the value in points of the price range to be displayed in the table.

The calculator will be drawn with a starting column of price running from 0 to 144. Then depending on the price range entered into the settings, the second column will begin from the nearest whole multiple of 144 just below the ‘From' value.  The calculator will continue to create columns increasing in value, in multiples of 144 up the nearest whole multiple of 144 just above the ‘To' value.

Along the top row of the calculator will be a count that displays how many full Squares of 144 each column represents.  This count will start at 1 but then jump up the appropriate count for the Display Values you have set.

In the above example we are interested in BHP Billiton which is trading in a range between $15.00 and $25.00. It is quoted as one cent to one point. When the Display Values are entered as points they are 1500 and 2500 respectively.

Set the range of values and click OK to begin the computation.

Results Display

The results of the calculations are displayed in a table on the work area:


Series Columns

As mentioned previously, the 144 calculation involves creating a mathematical table or array of numbers in intervals of 144 in price. Gann used these calculators in his day due to necessity, as modern-day hand-held calculators where not available and he needed to compute numbers quickly. Gann could consult his 144 Master Calculators and by locating the number on the table and studying its position, determine whether that price represented a pressure point.

Numbers along the top or bottom of the table are 100% price pressure points of 144. The table also has the prices in the 25%, 50% and 75% regions shaded in bands.

In the example table above you can see where 1584 is at the top of the second column, which has been numbered 11. This is because 11 multiples of 144, equals 1584.  It can be said that 1584 is 11 Squares of 144. The third column in the example table would then start at 1584 and runs up in prices to 1728, which is 12 multiples of 144.  The calculator will continue to be built this way until the numbers cover the Display Values you set.

If the table contains more series than can fit in the work area, a scroll bar will appear in the bottom border. Drag it right or left to view any of the series.

The first series in the first column on the left is displayed for reference purposes only.

Display Points Control


These settings allow users the choice of which Turning Points will be displayed in the calculator grid. The Primary turning points generally represent the Monthly swing tops and bottoms, Secondary are the Weekly swing tops and bottoms, and Tertiary are the Daily swing tops and bottoms. The Display Points settings can be fully customised as described below in the Advanced Settings section.

Enabling the Primary turning points will set the calculator to show only the monthly turning points as shown below. The same applies for the Secondary and Tertiary turning points.


In addition, any combination of Primary, Secondary and Tertiary turning points can be enabled at the same time on the display grid. For example, if users wish to see Monthly and Weekly turning points together, then enable the Primary and Secondary controls as shown below.


When analysing the display results, there will be times when a data grid is split with 2 colours. This signifies that both a Top and Bottom has occurred at that price making it a more significant price level. An example is the price of 132 in the display grid above.

Adjust Decimal Settings


The Adjust Decimal setting allows users to set the correct price per point value for the instrument being analysed.  Three examples will be shown below:

  1. Stock prices are quoted to 2 decimal places. For example, a price of $15.56 would be represented as a value of 1556 on the Square of 144 display grid. Thus a decimal setting of 2 To The Right would be used to align prices correctly on the calculator grid as shown below.


  2. Index Futures prices are generally quoted with 0 decimal places and so prices should be displayed as the full index value. Thus a decimal setting of 0 To The Right would be used to align prices correctly on the calculator grid as shown below. If the Futures instrument being analysed are quoted to 2 decimal places, then adjust the decimal places setting accordingly.


  3. Forex prices are generally quoted to 4 decimal places. For example, the AUD to USD currency pair is quoted as 0.8064 and would be represented as a value of 8064 on the Square of 144 display grid. Thus a decimal setting of 4 To The Right would be used to align prices correctly on the calculator grid as shown below.


The number of decimal places to shift prices will depend on the quote for the particular market being analysed. Using the Adjust Decimal control allows users to set it accordingly.

Data Display Settings

The data in the table can be high-lighted by the user so that important price levels can be emphasized. This would be used in place of the automatic color coding of prices done by the calculator through the link to the Turning Points Hi-Lite tool. This allows the labeling of major turning points in price to be manually marked on the calculator, giving more control over the analysis.

Right mouse click on a data field and the formatting pop-up menu will display. There are a number of different colors and styles for the text and the text box background.


Select Clear Formatting to return to the basic text style.

Formatting affects one text field at a time.

Advanced Settings


Click on the Settings button in the table's function bar to open the Square of 144 Calculator Settings dialog box:


Turning Points Settings

The Turning Points Settings dialog allows users to effectively superimpose turning points data over the Square of 144 Master Calculator table. These settings are identical to the format used for the Turning Points Hi-Lite. Therefore any turning points that would be high-lighted on the actual chart of the security using these settings, will be color coded automatically on our calculator.


The Primary turning points are the one month swing tops and bottoms, Secondary are the weekly swing tops and bottoms, and Tertiary are the daily swing tops and bottoms.

The default setting for each time frame is a one period swing chart.


You can alter the default settings of using the Monthly, Weekly and Daily trends as the determining factors by selecting a new time period from the list obtained by using the drop down arrow.


You can alter the settings for the Monthly, Weekly and Daily trends to be based upon a swing chart of increasing time periods, for example, identify Tertiary Turning Points using a Three Day Swing Chart as opposed to the default of one day. As in swing charts, this setting identifies more significant turning points, as the direction of the trend is allowed time to establish itself and confirm its direction..

High and Low Color

For each of the categories users can select a different color for both the high and the low turning points.

Display Settings

This is the same setting procedure as in the initial dialog box, see Setting the Calculator above.

Changing this setting will alter the number of Series displayed in the columns in the table.

Enter the number of points, not the actual price. For example, enter 1500 if the price is $15.00.

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