# Gann Square of 9 A Trend concept (Channels, lines & geometry) in the LuxAlgo Library, with 1 indicator implementation. ## What is the Gann Square of 9? The Gann Square of 9 is W.D. Gann's number spiral: integers wind outward from 1 at the center, and numbers falling on the same angle of the spiral are treated as harmonically related prices. The geometry reduces to square-root arithmetic. Moving one full 360-degree rotation out along the spiral adds 2 to a number's square root, so a 180-degree step adds 1, 90 degrees adds 0.5, and 45 degrees adds 0.25. Practitioners take the square root of an anchor price (a significant high or low), add or subtract these increments, and re-square to generate candidate levels, sometimes called vibration levels, at each angle. The wheel is attributed to William Delbert Gann (1878-1955), the American commodities and stock trader whose courses and master charts circulated among paying students in the first half of the twentieth century. Gann published no complete rulebook for it; what survives are course sheets, the calculators he sold, and decades of reconstruction by later authors, which is why modern treatments disagree on details such as scaling and anchor selection. Stories about Gann's own trading results are largely promotional and contested, so the tool is best judged on what it demonstrably does: generate a reproducible ladder of prices from a single anchor. Gann tied the wheel to both price and time, looking for dates when a market had traveled a square relationship from its anchor. There is no accepted market mechanism behind any of this, and the wheel generates many levels, so hits are easy to find after the fact. The workable reading treats Square-of-9 outputs like any other derived level: candidate prices that earn attention only when the tape actually reacts there, a rejection that develops into a [reversal](https://www.luxalgo.com/library/concept/reversal/) or a decisive close through the level that reads as a [breakout](https://www.luxalgo.com/library/concept/breakout/), ideally in confluence with independent evidence. It also occupies a different niche from the tools most platforms lead with. A moving average such as an [SMA](https://www.luxalgo.com/library/concept/sma/) or [EMA](https://www.luxalgo.com/library/concept/ema/) follows price and updates every bar, and a trailing system such as [Supertrend](https://www.luxalgo.com/library/concept/supertrend/) reacts to what has already happened. The Square of 9 instead fixes static targets in advance from one number, which is precisely why it attracts both devotion and skepticism: the levels are known ahead of time and therefore falsifiable, and nothing about the market is obliged to respect them. ## How to calculate Gann Square of 9 levels The spiral itself is rarely drawn; the square-root shortcut produces the same levels directly. 1. Choose an anchor, a significant swing high or swing low, and take the square root of that price. 2. Add (for levels above) or subtract (for levels below) the rotation increments: 0.25 for 45 degrees, 0.5 for 90, 1 for 180, and 2 for a full 360-degree rotation. 3. Square each result to convert back to price; the outputs are the Square-of-9 levels for that anchor, and further rotations extend the ladder. 4. Rescale first if the arithmetic degenerates: very low-priced or very high-priced instruments are commonly multiplied or divided by a power of ten before taking roots. 5. Audit the output against history: keep the ladder only if past swings show repeated, unprompted reactions near its rungs, and discard anchors that produce a grid the market has ignored. ## How it's calculated Projects support and resistance levels by rotating a price around a square-root spiral of numbers. ``` 1. Write 1 in the center cell of a grid and spiral the integers 2, 3, 4, ... outward one cell at a time, so each completed ring is one full 360-degree turn. 2. Mark the cardinal cross (0, 90, 180, 270 degrees) and the diagonal cross (45, 135, 225, 315 degrees) through the center; numbers on these rays, including the odd squares 9, 25, 49 on one diagonal, act as natural levels. 3. Pick an anchor price P, a significant swing high or low, and shift its decimal point to a workable magnitude (for example into the range 1 to 1000). 4. Convert to the square-root scale: r = sqrt(P). 5. Rotate up for resistance: r' = r + A / 180 (a full 360-degree turn adds 2 to the square root). 6. Rotate down for support: r' = r - A / 180. 7. Square back to price and undo the decimal shift: Level = r'^2. 8. Repeat for the standard angles A = 45, 90, 135, 180, 270, 360 to build the ladder of levels. P: anchor price, a significant swing high or low r: square root of the scaled anchor price A: rotation angle in degrees (commonly 45, 90, 180, 360) r': rotated square-root value Level: projected support or resistance price sqrt(): square root ``` Moving one ring outward along the same ray adds about 2 to the square root of the cell value, which is where the +2 per 360 degrees comes from. Anchor choice and decimal scaling are discretionary, so published levels differ between practitioners. The same wheel is also read against calendar dates and cardinal angles for time analysis. ## How traders use it - As a level map: anchor on a major pivot and mark the 90, 180 and 360-degree prices as candidate support and resistance, watching for actual reactions before trusting them. - For confluence: a Square-of-9 level landing near independent evidence, a prior high, a fib, or a round number, is taken more seriously than one standing alone. - In time work: counting calendar or bar spans that square price and time from the anchor; this is the most speculative part of the method and is best treated as a watch window, not a forecast. - As trade framing around a level: reactions at a watched rotation are traded like any level test, with entry on the rejection and invalidation beyond the level, rather than as a standalone signal from the wheel itself. - With a trend filter: an [MA slope filter](https://www.luxalgo.com/library/concept/ma-slope-filter/) or [trend regime label](https://www.luxalgo.com/library/concept/trend-regime-label/) decides which side of the ladder is tradable, so in an uptrend the lower rotations are watched for buyable reactions instead of shorting into strength at the upper ones. ## Gann Square of 9 vs other ways of projecting levels - **Trendline** (https://www.luxalgo.com/library/concept/trendline/): A trendline is drawn from two or more actual pivots and evolves with the swing structure; the Square of 9 needs one anchor and a formula. Both depend heavily on the operator's choice of starting points. - **Dynamic S/R Via MA** (https://www.luxalgo.com/library/concept/dynamic-s-r-via-ma/): Moving averages supply support and resistance that drifts with price and recalculates every bar. Square-of-9 levels are static once projected, which makes them testable in advance but blind to new information. - **Supertrend** (https://www.luxalgo.com/library/concept/supertrend/): Supertrend is a trailing state line for riding trends, not a forecast: it tells you where the current trend flips. The Square of 9 tries to say where price might turn before it gets there; the two answer different questions. ## FAQ ### How do you calculate Gann Square of 9 levels? Take the square root of an anchor price, add or subtract 0.25, 0.5, 1 or 2 (for 45, 90, 180 and 360 degrees on the wheel), then square the result. Repeat for further rotations. Low or high-priced instruments are usually rescaled by a power of ten first so the increments are meaningful. The output is a ladder of candidate levels above and below the anchor. ### Do Gann Square of 9 levels actually work? There is no verified mechanism, and no honest way to claim they work in general. The wheel produces many levels across every rotation, so price will inevitably touch some, which makes anecdotal confirmation cheap. If you use them, mark levels in advance and log the reactions, demand confluence with independent analysis, and size as if any level can fail, because many do. ### Who created the Gann Square of 9? W.D. Gann (1878-1955), an American trader who sold courses and analytical tools during the first half of the twentieth century. The wheel appears among his master charts and calculators, but he left no definitive published manual for it, so modern usage is a reconstruction assembled by later students of his work, and versions differ. ### What are the cardinal and diagonal angles on the Square of 9? The cardinal cross marks 0, 90, 180 and 270 degrees on the wheel, and the diagonal cross marks 45, 135, 225 and 315 degrees. Numbers on these spokes are treated as the strongest candidates. In square-root terms, each 45-degree step corresponds to 0.25 added to or subtracted from the root of the anchor. ### What anchor price should you use for the Square of 9? Practitioners anchor on prices the market itself treated as significant: major swing highs and lows, all-time extremes, contract or listing lows. The choice is the method's biggest degree of freedom; two analysts with different anchors get different ladders, which is a strong reason to log actual reactions rather than trust any single grid. ### Is the Square of 9 the same as Gann angles or Gann fans? No. Gann fans and angles are diagonal lines drawn on the chart at fixed price-per-time slopes, such as the 1x1. The Square of 9 is a numeric wheel that outputs horizontal prices, and dates, from an anchor. They share an author and a fondness for geometry, but the constructions are independent. ## Implementations in the Library - Gann Square of 9 Vibration Levels (LuxAlgo): https://www.luxalgo.com/library/indicator/gann-square-of-9-vibration-levels/ ## Related concepts - Trendline: https://www.luxalgo.com/library/concept/trendline/ - Linear-regression Channel: https://www.luxalgo.com/library/concept/linear-regression-channel/ - Parallel Channel: https://www.luxalgo.com/library/concept/parallel-channel/ - Fan Principle: https://www.luxalgo.com/library/concept/fan-principle/ - Standard-error Channel: https://www.luxalgo.com/library/concept/standard-error-channel/ - Polynomial Regression Band: https://www.luxalgo.com/library/concept/polynomial-regression-band/ - Andrews' Pitchfork: https://www.luxalgo.com/library/concept/andrews-pitchfork/ - Gann Fan & Angles: https://www.luxalgo.com/library/concept/gann-fan-and-angles/ - Gann Box: https://www.luxalgo.com/library/concept/gann-box/ - Speed Resistance Lines: https://www.luxalgo.com/library/concept/speed-resistance-lines/ --- Source: https://www.luxalgo.com/library/concept/gann-square-of-9/ (LuxAlgo Library, the encyclopedia of trading & technical analysis). Free to use with attribution: https://www.luxalgo.com/library/license/