Gann Fan

The Gann Fan is one of W.D. Gann's most accessible and widely-used tools. It projects nine fixed angles from a single pivot point: 82.5° (8×1), 75° (4×1), 71.25° (3×1), 63.75° (2×1), 45° (1×1), 26.25° (1×2), 18.75° (1×3), 15° (1×4), and 7.5° (1×8). Each angle represents a specific ratio of price to time movement on an arithmetic-scaled chart.

Gann considered the 1×1 (45°) angle the most important line in all of technical analysis. In a correctly balanced trend, price hugs the 1×1 line. A break below it (in an uptrend) or above it (in a downtrend) signals a potential change in the trend's character. Gann wrote extensively about angle breaks in "How to Make Profits in Commodities" (1942), calling the 1×1 "the line of natural vibration" and stating that a break of the 1×1 was the single most important reversal signal in his entire methodology.

The theory behind the fan is that markets move in geometric progression. If a market is rising at a rate of 1 unit of price per day (1×1), it is in perfect balance. If it accelerates to 2 units per day (2×1), it is becoming more bullish. If it slows to 1 unit per 2 days (1×2), it is becoming more bearish. Each transition from one angle to another represents a change in the market's vibrational frequency — Gann's central concept. The fan provides a "speedometer" for the trend.

The Gann Fan is a two-anchor drawing tool. The first click sets the pivot point — a major swing high or low. The second click sets the direction and scale of the 1×1 angle. From these two anchors, all nine rays are drawn automatically from the pivot point.

The fan rays are drawn as follows: the 1×1 line connects the pivot to the second click point and extends beyond it. The other eight rays are drawn at fixed angular offsets from the 1×1 line, radiating from the pivot point. Above the 1×1 are the steeper angles (2×1, 3×1, 4×1, 8×1), and below are the shallower angles (1×2, 1×3, 1×4, 1×8). Each ray extends from the pivot to the chart edge, creating a fan-shaped pattern. The horizontal (0°) and vertical (90°) lines serve as reference boundaries but are not typically drawn as fan rays.

The fan can be drawn for both uptrends (pivot at low, 1×1 sloping up) and downtrends (pivot at high, 1×1 sloping down). In an uptrend fan, price above the 1×1 is strong; below it is weak. In a downtrend fan, the interpretation is inverted: below the 1×1 is strong (bearish continuation), above it is weak and suggests a potential reversal.

1. 1
   Set the pivot point

   Click on a significant swing high (for a downtrend fan) or swing low (for an uptrend fan). This is the origin of all nine rays. The pivot must be a clear structural turning point.
2. 2
   Set the 1×1 direction

   Click a second point in the direction of the trend. The 1×1 (45°) line runs through this point. The other eight rays are drawn automatically at their fixed geometric offsets from the 1×1.

On an arithmetic chart with equal price and time scaling (square grid), the Gann angles are fixed by their ratio of price units to time units:

• Price often rides along individual angle lines for extended periods. If price is hugging the 2×1 line for weeks, the trend is operating at that slope — stay in the trend until that specific angle breaks.
• A break from one angle to the next (e.g., falling from 2×1 to 1×1) signals a trend deceleration. This is Gann's primary method for identifying trend aging. Each step down reduces the trend's velocity.
• Each broken angle reverses its role: broken support becomes resistance and vice versa. A 1×1 that was supporting an uptrend becomes resistance after being broken from above. This role reversal is key for retest entries.
• The 7.5° and 82.5° lines are rarely touched outside of extreme conditions. They mark the outer boundaries of the fan. Any move beyond these lines is statistically very unusual and likely represents a market in panic or euphoria.
• When price crosses the 1×1 line with a large candle and volume, the trend character has changed. This is the single most actionable signal in Gann Fan analysis. Do not ignore it.

Angle bounce (trend-following): In an uptrend, wait for price to pull back to the 1×1 line and bounce. Enter long with a stop below the 1×1 by 0.5–1.0%. Target the 2×1 line above. This is the simplest and most reliable Gann Fan strategy — buy the equilibrium, sell the overextension.

Angle break (reversal): When price closes below the 1×1 line in an uptrend (or above in a downtrend), the trend character has changed. Enter in the direction of the break. A retest of the 1×1 from the opposite side confirms the flip is genuine. This is Gann's primary reversal signal and the foundation of his trading methodology.

Angle-to-angle (momentum scaling): When price accelerates from a shallower angle to a steeper one (e.g., 1×2 → 1×1 → 2×1 → 3×1), add to the position at each successful hold. This pyramiding strategy follows Gann's approach of "adding to winners." Conversely, each deceleration to a shallower angle is a warning — reduce exposure at each step down.

A stock rallies from $100 to $130 over 60 days. A Gann Fan is placed at the $100 low. The 1×1 line runs through a point approximately $130 in 60 days (slope = $0.50/day). Over the next 30 days, the stock reaches $145. The 1×1 line is now at $100 + 0.50×90 = $145. The stock is exactly on the 1×1 — in balance. If the stock then rallies to $160 in the next 10 days, it has accelerated to the 2×1 line ($100 + 1.0×100 = $200 target at day 100, but price is above the linear 2×1 path). This acceleration to 2×1 momentum signals a very strong trend. A break below $145 (the 1×1) would be the first warning sign of trend weakening.

The Gann Fan works synergistically with other geometric and momentum tools:

• Gann Box: Overlay the fan on a Gann Box from the same origin. The fan's 1×1 and the box's 1×1 should align. Discrepancy indicates a chart scaling issue or incorrect origin selection.
• Fibonacci retracements: When a Fibonacci retracement level coincides with a Gann angle intersection, the price zone is doubly significant. For example, the 61.8% retracement at the 2×1 line is a powerful confluence.
• Volume: Decreasing volume as price approaches an angle suggests the trend is losing momentum and the angle is likely to hold. Increasing volume through an angle confirms the break is genuine.
• Moving averages: When a key moving average (e.g., 50-day SMA) aligns with the 1×1 line, the angle is reinforced by time-domain analysis. Conversely, when the MA diverges from the 1×1, one of them is "wrong."
• MACD / RSI: Divergence at a Gann angle break is a high-conviction trade signal. A bearish RSI divergence at the 2×1 line followed by a break below 1×1 is triple-layered confirmation of a reversal.

The Gann Fan requires precise angle computation given the pivot point and the chart's arithmetic scaling. The implementation must ensure consistent angle geometry across all nine rays.

Angle computation: Given pivot point (x₀, y₀) and the 1×1 direction point (x₁, y₁), compute the baseline slope S = (y₁ − y₀) / (x₁ − x₀). On an arithmetic chart, the nine Gann angles have fixed trigonometric slopes relative to the 1×1 line: 8×1 has slope S × 8, 4×1 has S × 4, 3×1 has S × 3, 2×1 has S × 2, 1×1 has slope S, 1×2 has S / 2, 1×3 has S / 3, 1×4 has S / 4, 1×8 has S / 8. Each ray passes through (x₀, y₀) and extends to the chart edge: ray(x) = y₀ + slope × (x − x₀).

Angle rotation monitoring: On each bar, compute the price position relative to each angle. Track which two adjacent angles price is currently between. The angle pair (e.g., 1×1 and 2×1) defines the current "velocity channel." When price crosses from one channel to another (e.g., from 1×1–2×1 to 2×1–3×1), it signals acceleration. When price crosses downward through channels (e.g., from 2×1–1×1 to 1×1–1×2), it signals deceleration. Count the number of channels crossed in the last 20 bars as a "velocity change index" — values above 3 indicate significant trend velocity changes.

Break detection with confirmation: A Gann angle break requires a close beyond the angle by more than 0.3× ATR. Generate a "break alert" when this condition is met. Generate a "confirmed break" alert when the next bar closes on the same side of the angle (no false breakout). The confirmed break is the actionable signal. For the 1×1 angle specifically, require 0.5× ATR penetration and confirmation — the 1×1 is too important to trade on marginal breaks.

The Gann Fan's nine rays provide a natural framework for progressive risk management. Each angle transition should trigger a specific adjustment in position size and stop placement.

Angle channel position sizing: When price is between the 1×1 and 2×1 lines (the acceleration channel for an uptrend), maintain full position size (1.0× base). This is the "normal acceleration" zone where the trend is healthy. When price enters the 2×1 to 3×1 channel (strong acceleration), reduce to 0.75× base. When price enters the 3×1 to 4×1 channel (extreme), reduce to 0.5× base. When price exceeds the 4×1 line (parabolic), reduce to 0.25× base. This channel-based sizing ensures maximum exposure at sustainable velocities and minimum exposure at extreme, unsustainable velocities.

Angle-based stop placement: Place the stop at the next angle below the current channel (for an uptrend). If price is in the 1×1–2×1 channel, place the stop at the 1×1 line minus 0.5× ATR. If price is in the 2×1–3×1 channel, place the stop at the 2×1 line minus 0.3× ATR (tighter because steeper angles break more violently). If price falls to the 1×2 or 1×3 zone, the stop is placed at the 1×1 line minus 1.0× ATR (wider because slower trends have more noise). Each angle has a distinct stop characteristic that accounts for the velocity regime.

Reverse-angle entry sizing: When trading a reversal (1×1 break from above in an uptrend → short entry), use 0.5× base position size. The 1×1 break is a significant signal, but the market may retest the broken 1×1 before continuing in the reversal direction. The smaller initial position allows adding on the retest to reach full size. The initial stop for a reversal trade is 1.0× ATR beyond the broken angle, providing room for the optional retest before the main move.

The Gann Fan's multiple angles create a tendency to over-interpret every price movement. The psychological discipline to focus primarily on the 1×1 line and ignore the majority of angle interactions is essential.

The "angle clutter" confusion: With nine rays on the chart, there is always an angle near any price level. This creates the illusion that every reversal is "predicted" by an angle — a form of confirmation bias. The discipline required: mentally disable all angles except the 1×1. Only examine steeper or shallower angles for confirmation of the 1×1's signal, not as independent triggers. The 1×1 is the signal; the other angles are context. If you cannot focus on the 1×1 alone, hide the other eight rays and trade with only the 1×1 line.

The "angle is always right" dogma: When a 1×1 break fails (price breaks below the 1×1 but immediately reverses back above it), traders often refuse to accept the false signal and stay in the reversal trade, believing "the 1×1 break is always right." The 1×1 break is a high-probability signal, not a certainty. A false 1×1 break that reverses within 2 bars must be respected as a false signal. Exit the trade and wait for the next setup. Clinging to a failed 1×1 break is Gann's equivalent of "hoping" — and it destroys accounts as surely as any other form of hope-based trading.

The Gann Fan can be extended and customized for specific analytical requirements. Several variations build on the core nine-angle structure.

Sub-degrees (micro angles): For intraday trading, add intermediate angles between the standard nine. For example, add a 1.5×1 angle (midway between 1×1 and 2×1) and a 1×1.5 angle (midway between 1×1 and 1×2). These micro-angles provide finer granularity for shorter-term moves. On a 15-minute chart, the standard nine angles may be too widely spaced to capture meaningful trend changes — the micro-angles fill the gaps. Use caution: each additional angle increases chart clutter and the risk of over-interpretation.

Angle-weighted regression: Instead of treating each angle independently, use the fan as the basis for an angle-weighted regression model. At each bar, compute which angle price is closest to and use that angle's slope as the predicted trend velocity for the next N bars. The regression model produces a "fan forecast" — a projected price path based on the current dominant angle. The forecast is updated on each bar as price transitions between angles. This turns the Gann Fan from a passive observation tool into an active forecasting model with measurable accuracy.

A Gann Fan on the monthly chart defines the secular trend. The weekly fan defines the cyclical trend. The daily fan defines the trading trend. All three fans should be consistent — the daily fan's angles should all fall within the weekly fan's outer angles, and the weekly fan's angles should fall within the monthly fan's outer angles.

Fan hierarchy: The monthly fan provides the macro trend direction (bullish or bearish). The weekly fan provides the entry timing (pullback or breakout). The daily fan provides the precise stop and target levels. Trade in the direction of the monthly fan, enter on the weekly fan's signals, and manage risk with the daily fan.

Angle stacking: When the same angle level (e.g., 1×1) is broken on both the daily and weekly charts within the same week, the reversal signal is confirmed at both degrees of trend. This "angle stacking" is a high-conviction signal. If only the daily 1×1 is broken but the weekly 1×1 holds, the signal is weaker and may be a false alarm.

The Gann Fan's fixed angles interact differently with different market regimes. The interpretation of angle breaks depends on the market's velocity and volatility structure.

Trending with consistent velocity: The 1×1 line accurately represents equilibrium. Price oscillates around it with regular touches. Angle breaks (from 1×1 to 1×2 or from 1×1 to 2×1) are meaningful and produce reliable reversals. This is the textbook regime for Gann Fan analysis and produces the clearest signals.

Accelerating trend: The 1×1 line becomes a support that is quickly left behind as price moves to the 2×1 or 3×1 zone. In this regime, the 2×1 line becomes the effective equilibrium. Trade the 2×1 line as if it were the 1×1: buy pullbacks to the 2×1 line in an accelerating uptrend. The 1×1 line is "too slow" for the current market velocity. Recognize this regime change and adjust which angle you treat as equilibrium.

Decelerating / range-bound: The 1×1 line is frequently broken in both directions. No angle acts as reliable support or resistance. In this regime, the Gann Fan loses its predictive power. Reduce fan usage and switch to range-bound tools. The fan's angles become too steep or too shallow for the market's actual velocity, and all signals become noise.

• 1.How to Make Profits in Commodities — W.D. Gann (1942)
• 2.Gann Angles — StockCharts ChartSchool
• 3.Gann Fan drawing tool — TradingView Help
• 4.Gann's Scientific Methods Unveiled — Betty Long
• 5.The Gann Fan — understanding the angles — Optuma Knowledge Base
• 6.Technical Analysis of Financial Markets — John J. Murphy (1999)