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This study calculates and displays Gann's Square of 9 indicator.

If you find that your price graph is getting compressed by the Square of 9 lines, then set the Scale Range Type in the Scale settings for this study to Same As Region.

Let the Inputs Number of Days to Calculate, Anchor Value, Degrees, Level, and Price Multiplier be denotes as \(D\), \(a\), \(\theta\), \(l\), and \(v\), respectively. These Inputs are subject to the following restrictions.

• If the Price Multiplier is set to \(0\), then it is automatically reset to \(1\).
• Suppose there are \(N\) bars in the chart. If the Anchor Value is set to \(0\), then it is automatically reset to \(v \cdot C_{N - 1}\), which is the Price Multiplier times the Close Price at Index \(t = N - 1\).

The Square of 9 study calculates four Subgraphs. We denote their values at Index \(t\) as \(A_t(a,v)\), \(L1^{(+)}_t(a,\theta,l,v)\), \(L1^{(-)}_t(a,\theta,l,v)\), and \(L1_t(a,\theta,v)\). These Subgraphs are displayed as horizontal line segments over the last \(D\) days of the chart, with levels determined by the values of the Subgraphs at the most recent Index \(t\).

If the Auto Adjust Input is set to No, then these Subgraphs are calculated as follows.

For an explanation of the floor function (\(\left\lfloor{\space\space}\right\rfloor\)), refer to our description here.

If the Auto Adjust Input is set to Yes, then these Subgraphs are calculated using a more complicated set of rules, which we describe below.

We begin by defining six functions that are used in intermediate calculations.

• Base Upper: \(BU_t(a,\theta)\)
• Base Lower: \(BL_t(a,\theta)\)
• Upper: \(U_t(a, \theta, l)\)
• Mid: \(M_t(a, \theta, l, v)\)
• Lower: \(L_t(a, \theta, l)\)
• Offset: \(k_t(\theta)\)

These functions are initialized as follows at \(t = 0\).

For \(t > 0\), we begin by setting the values of the six functions as follows.

Once these values are set, the Auto Adjustments are made via a sequence of two while loops, described below.

while\((vC_t > BU_t(a,\theta))\):

• \(k_t(\theta) = k_t(\theta) + \theta\)
• \(BU_t(a,\theta) = \left(\sqrt{a} + (k_t(\theta) + \theta)/180^{\circ}\right)^2\)
• \(BL_t(a,\theta) = \left(\sqrt{a} + (k_t(\theta) - \theta)/180^{\circ}\right)^2\)
• \(U_t(a, \theta, l) = \left(\sqrt{a} + (k_t(\theta) + \lfloor l + 0.5 \rfloor\cdot\theta)/180^{\circ}\right)^2\)
• \(M_t(a, \theta, l, v) = \left(\sqrt{a} + k_t(\theta)/180^{\circ}\right)^2\)
• \(L_t(a, \theta, l) = \left(\sqrt{a} + (k_t(\theta) - \lfloor l + 0.5 \rfloor\cdot\theta)/180^{\circ}\right)^2\)

while\((vC_t < BL_t(a,\theta))\):

• \(k_t(\theta) = k_t(\theta) - \theta\)
• \(BU_t(a,\theta) = \left(\sqrt{a} + (k_t(\theta) + \theta)/180^{\circ}\right)^2\)
• \(BL_t(a,\theta) = \left(\sqrt{a} + (k_t(\theta) - \theta)/180^{\circ}\right)^2\)
• \(U_t(a, \theta, l) = \left(\sqrt{a} + (k_t(\theta) + \lfloor l + 0.5 \rfloor\cdot\theta)/180^{\circ}\right)^2\)
• \(M_t(a, \theta, l, v) = \left(\sqrt{a} + k_t(\theta)/180^{\circ}\right)^2\)
• \(L_t(a, \theta, l) = \left(\sqrt{a} + (k_t(\theta) - \lfloor l + 0.5 \rfloor\cdot\theta)/180^{\circ}\right)^2\)

Upon completion of these two while loops, the four Subgraphs are computed as follows.