Comprehensive Research Report: The Gann Square of 9 Chart

Report Date: April 29, 2026

Executive Summary

This report presents a comprehensive analysis of the Gann Square of 9 chart, a technical analysis tool attributed to W.D. Gann. The research synthesizes available literature, mathematical definitions, software implementations, and empirical evidence regarding the tool's efficacy. The investigation reveals that while the Gann Square of 9 is a prominent feature in retail trading software and enjoys enduring popularity among practitioners, it exists in a peculiar state of scientific ambiguity. The mathematical foundations, rooted in square root progressions and geometric angles, are clearly defined in practitioner literature but lack standardization in digital implementations. Furthermore, this research uncovered a significant lack of peer-reviewed quantitative validation and open-source algorithmic transparency, contrasting sharply with the tool's widespread availability in commercial trading platforms.

1. Introduction and Historical Context

1.1 The Enigma of W.D. Gann

William Delbert Gann (1878–1955) is a seminal figure in the history of technical analysis, renowned for his complex methodologies involving geometric angles, time cycles, and mathematical formulas. His work, often shrouded in mystery, posits that market movements are not random but follow natural law and geometric principles 66|PDF66|PDF. The "Square of 9" (also known as the Square of Nine) stands as one of his most enduring and enigmatic tools. It is described as a fundamental calculator for determining support and resistance levels and forecasting time cycles 2|PDF.

1.2 Definition of the Square of 9

The Gann Square of 9 is fundamentally a geometrical structure. It is constructed as a spiral of numbers, typically beginning with the number 1 at the center and spiraling outward in a clockwise direction 13|PDF. This two-dimensional array is used to map price and time relationships. The core philosophy dictates that price and time are interchangeable and related; when they "square" or balance, significant market turns are predicted to occur 2|PDF5|PDF7|PDF.

The tool is often referred to by various names in literature and software, including the "Gann Wheel" or simply the "Square of Nine" 13|PDF. Its primary function is to serve as a mathematical and astronomical calculator for market analysis 64|PDF.

2. Mathematical Foundations and Theoretical Framework

The architecture of the Gann Square of 9 is built upon specific mathematical relationships. While no single unified "Gann Equation" exists in the public domain that fully replicates Gann's private methodology, modern practitioners and software developers rely on established interpretations of his principles.

2.1 The Spiral Structure and Numeric Progression

The visual representation of the Square of 9 is a grid, often containing 81 numbers in a standard 9x9 formation, though the spiral theoretically extends infinitely . The numbers increase in a spiral form, creating a matrix where specific angles and "rings" correspond to price levels 13|PDF.

Numeric Progression:
The progression starts at the center (1) and moves outward. While the search results did not yield a specific "numeric progression rule" for distinct "inner and outer rings" , the construction implies a relationship between the numbers on the spiral and their geometric position. The "inner" circles are viewed as shorter-term price levels, while the "outer" rings represent longer-term targets .

Angles and Cardinal Crosses:
Critical to the methodology are the angles formed by numbers on the chart relative to the center. The "Cardinal Cross" refers to the vertical and horizontal axes intersecting the center, while the "Ordinal Cross" refers to the diagonal axes. Key angles cited in the research include 45°, 90°, 180°, 270°, and 360° (or 0°) 13|PDF28|PDF. These angles are used to identify points of "vibration" or key resistance and support levels 13|PDF. For instance, a price located 180 degrees opposite a starting price on the square is considered a significant target for a reversal or pause 32|PDF.

2.2 The Square Root Relationship

The most significant mathematical concept underpinning the Square of 9 is the Square Root Theory. This theory posits that the price levels on the Square of 9 are derived from the square roots of integers 2|PDF32|PDF.

The Formula:
One specific formula referenced in the search results defines the price calculation logic:
$Price = (\sqrt{Anchor} + (Degree / 180) \times Direction)^2$
.

In this equation:

• Anchor: The starting price or significant high/low from which the calculation is derived.
• Degree: The angular increment on the Square of 9 (e.g., 90, 180).
• Direction: The trend direction (positive for increasing prices, negative for decreasing).

This formula highlights that price movement is viewed not as a linear progression but as a function of the square root of the price. For example, moving one full rotation (360 degrees) around the square corresponds to an increment in the square root of the price, which translates to a non-linear increment in the actual price 75|PDF75|PDF.

Calculation Steps:
The practical application involves:

1. Taking the square root of a significant price (e.g., a major low).
2. Adding or subtracting an increment (representing degrees or time).
3. Squaring the result to find a new price target 2|PDF32|PDF.

This methodology allows traders to calculate potential support and resistance levels without necessarily drawing the physical spiral, using "cell prices" derived by multiplying cell numbers by an increment 10|PDF10|PDF.

2.3 Price and Time Interchangeability

A central tenet of Gann theory is the balance of price and time. The Square of 9 is used to determine when these two factors are in equilibrium 2|PDF7|PDF. Gann angles are specifically used to define these balance points 7|PDF. The concept implies that a specific price level may act as support or resistance only when a specific time interval has passed, creating a "squaring" event 5|PDF9|PDF.

3. Software Integration and Digital Implementation

The transition from hand-drawn charts to digital trading platforms has necessitated the standardization of Gann's methods into algorithmic indicators.

3.1 Modern Technical Analysis Software

Modern trading platforms like NinjaTrader and MetaTrader 5 have integrated Gann tools, although the depth of integration varies.

• NinjaTrader: The search results highlight the "BET indicator Gann Square of 9" as a specific implementation 13|PDF13|PDF. This indicator functions as a digital spiral, calculating support and resistance levels. It allows for configurations such as update frequency and look-back periods, automating the manual calculation process 13|PDF13|PDF.
• MetaTrader and Other Platforms: Tools like "GANNZILLA PRO" are used for Square Nine analysis, integrating with Forex platforms 19|PDF. The Gann Square tool is also mentioned in the context of Ensign Windows for drawing Gann Squares on charts 32|PDF.
• Mobile Applications: There are dedicated "Gann Square of 9 Calculator" apps designed for quick calculation of pivot points, support, and resistance . These function more as utility tools than integrated charting systems.

3.2 Algorithmic Challenges and Standardization

The implementation of the Square of 9 in software reveals several challenges and a lack of standardization.

Price Anchor Inputs:
Software implementations must standardize the "starting price variable." The search results indicate that indicators often allow users to select the price type (Close, High, Low, Medium) to anchor the calculation 13|PDF13|PDF13|PDF. However, there is no consensus on a universal standard for different currency pairs; the calculation logic remains dependent on user input rather than an automated, cross-market standard .

Adjustment for Scale and Splits:
Digital versions of the Gann Wheel and Square of 9 face difficulties with price scale changes. The search results note the necessity of converting prices to three significant digits and using multiples of 10 to adjust prices for proportional results 2|PDF. While some software uses "Optimized routines" with volatility adjustments 81|PDF, the search results did not detail a specific, automatic adjustment protocol for stock splits within the spiral calculation . Traders are often required to manually adjust the price scale or use specific conversion factors for different markets 79|PDF.

Pine Script and TradingView:
Interestingly, the search results did not identify specific open-source Pine Script libraries commonly used for the Gann Square of 9 grid in TradingView . While Pine Script is used for creating indicators 73|PDFthe absence of a prominent, cited library in the results suggests that implementations may be proprietary or fragmented within the TradingView community, lacking a standardized "canonical" library.

3.3 Open Source and Calculation Logic

The search for open-source code repositories demonstrating the calculation logic yielded no direct results . This implies that the specific algorithms used in popular commercial tools (like the BET indicator) are proprietary. While the mathematical formula ($Price = (\sqrt{Anchor} + \dots)^2$) is publicly available , the implementation details—particularly regarding dynamic updating and volatility integration—remain largely within commercial or closed-source domains.

4. Empirical Validation and Academic Discourse

A critical component of this research was the evaluation of the Gann Square of 9's standing in the academic and quantitative communities.

4.1 Lack of Peer-Reviewed Quantitative Analysis

The search results reveal a distinct lack of peer-reviewed quantitative analysis validating Gann methods.

• Absence of Journal Articles: While general journals like "The Journal of Finance" and "Review of Financial Studies" exist as venues for financial research 59|PDF63|PDFand articles exist in practitioner journals like "Technical Analysis of Stocks & Commodities" , the search found no evidence of specific quantitative analysis of Gann methods in top-tier peer-reviewed academic journals .
• Validation Studies: There were no search results found for empirical studies evaluating the long-term profitability of the Gann Square of 9 strategy . Furthermore, no third-party independent research verifying the effectiveness of its support and resistance levels was identified .

4.2 Institutional Research and Validation

Proprietary trading algorithms and institutional research firms do not appear to publicly validate or reject Gann trading methods within quantitative research frameworks . The search results mention that Gann's tools are sometimes viewed as "mysterious and unexplored" within technical analysis 69|PDF, and institutional firms typically focus on quantitative frameworks that are more statistically robust and less reliant on geometric interpretation.

4.3 The Divide Between Practitioners and Academia

The research highlights a stark divide.

• Practitioner View: Traders utilize the Square of 9 for its perceived ability to identify "price vibration" and time cycles 13|PDF28|PDF. Books like "Pattern, Price & Time: Using Gann Theory in Technical Analysis" serve as authoritative guides for application 50|PDF50|PDF.
• Academic View: The lack of rigorous backtesting data in accessible databases suggests that the method is largely ignored by mainstream quantitative finance , . While the Market Technicians Association in New York holds collections of material on these methods 57|PDF, they are treated as historical or specialized technical tools rather than subjects of empirical scrutiny.

4.4 Comparison with Original Methodology

The search results indicate a lack of documented comparisons between William Gann's original methodology and modern algorithmic implementations . This gap is significant: modern software relies on precise mathematical formulas , whereas Gann's original work was graphical and interpretive. The "original" methodology's logic is not fully detailed in Gann's works, with some aspects being inferred from studies by others 5|PDF64|PDF65|PDF. Modern tools like "GANNZILLA PRO" or the "BET indicator" represent an interpretation of this logic, often focusing on the square root calculation method 32|PDFbut the fidelity of this translation lacks comprehensive documentation.

5. Advanced Concepts and Modern Interpretations

5.1 Volatility Adjustments

Modern interpretations of the Square of 9 spiral structure face the challenge of integrating market volatility. Traditional Gann theory uses fixed geometric angles. However, the search results hint at "Optimized routines" that allow users to find optimal angles for any market and include volatility adjustments 81|PDF. This suggests that modern software attempts to adapt the rigid geometric structure of the Square of 9 to the dynamic nature of volatility, although the specific algorithms for this adjustment are not detailed in the provided snippets .

5.2 Machine Learning Integration

The integration of Machine Learning (ML) with Gann methods appears to be in a nascent or undeveloped stage. While modern trading systems extensively use ML for predictive analysis and signal generation the search results found no direct link or documented methodology for using ML to improve the signal generation of the Gann Square of 9 . This represents a significant opportunity for future research, specifically in training ML models to recognize patterns within the "squaring" events that human analysis might miss.

5.3 Arithmetic vs. Geometric Progression

A query regarding the consensus on using arithmetic versus geometric progression in modern Square of 9 software yielded no relevant information . The core "Square Root" formula implies a geometric relationship (squares of numbers), but the specific debate regarding software implementation using arithmetic vs. geometric progression remains unaddressed in the provided literature.

6. Conclusion

The Gann Square of 9 chart remains a fascinating artifact of financial analysis theory. It bridges ancient geometric concepts and modern algorithmic trading.

Key Findings:

1. Mathematical Consistency: The tool relies on a defined mathematical formula involving square roots and angular degrees ($Price = (\sqrt{Anchor} + \dots)^2$), providing a calculable basis for support and resistance levels .
2. Software Adoption without Standardization: It is widely integrated into modern software (NinjaTrader, MetaTrader) via indicators and calculators 13|PDF19|PDF. However, standardization regarding price anchors, stock split adjustments, and volatility integration is inconsistent or proprietary 2|PDF79|PDF.
3. Empirical Vacuum: There is a critical lack of peer-reviewed empirical evidence supporting its long-term profitability , . The tool thrives in the realm of practitioner literature and proprietary software rather than academic validation.
4. Proprietary Opacity: Despite the availability of the core formula, modern implementations are largely closed-source, with no open-source libraries or algorithmic repositories prominently cited , .

The Gann Square of 9, therefore, stands as a tool with a robust theoretical construct and significant commercial presence but lacks the rigorous scientific scrutiny found in other areas of quantitative finance. Its continued use suggests a perceived value by practitioners that has not yet been fully captured or validated by the broader scientific community.