# Gann Fan & Angles

Also known as: 1×1, 2×1, 4×1 angles.
A Trend concept (Channels, lines & geometry) in the LuxAlgo Library, with 1 indicator implementation.

## What are Gann Fans & Angles?

Gann angles are lines drawn from a significant pivot at fixed rates of price change per unit of time, and a Gann Fan projects the standard set of them from one anchor. The centerpiece is the 1×1 angle, one price unit per one time unit, which W.D. Gann treated as the balance line between price and time; steeper angles (2×1, 3×1, 4×1, 8×1) and shallower ones (1×2, 1×3, 1×4, 1×8) fan out on either side. Unlike a [trendline](https://www.luxalgo.com/library/concept/trendline/) fitted to actual swing points, Gann angles are pure geometry: the slopes are fixed in advance, and only the anchor is chosen.

The angles come from W.D. Gann (1878-1955), who taught from the 1920s through the 1950s that markets move in proportional relationships of price and time, the 45-degree line marking their balance. How faithfully modern fan tools reproduce what Gann actually did is debated, since his courses are cryptic and his charts were drawn on paper with explicit unit scales. What survives cleanly is the framework of fixed-rate lines radiating from a pivot.

The conventional reading is that a trend holding above the 1×1 is strong, a trend below it is weak, and when price breaks one angle it tends to travel toward the next, so each fan line acts as sloped support or resistance. Successive breaks toward the shallow side of the fan read as the trend losing speed and often precede a fuller [reversal](https://www.luxalgo.com/library/concept/reversal/) attempt; a broken angle is then watched for resistance from the other side.

The unavoidable caveat is scale: one unit of price per one unit of time means nothing until you define how many points equal one bar, so the same fan looks different under different chart scales and zoom levels. Usable implementations fix the price-per-bar ratio explicitly; some modern indicators derive the unit from volatility, scaling the 1×1 to the instrument's typical range per bar. Without a fixed convention, the angles are decorative; traders who want sloped references without a scaling decision often reach for an adaptive line such as an [EMA](https://www.luxalgo.com/library/concept/ema/) instead.

## How to draw a Gann Fan

A fan needs two decisions, the anchor and the price-per-bar scale; everything else is standard.

1. Anchor at a significant pivot: a major swing low for a rising fan, a major swing high for a falling one.
2. Fix the scaling that defines the 1×1, via the platform's points-per-bar setting or a volatility-derived unit; without this the angles are arbitrary.
3. Apply the fan so the 1×1 rises (or falls) at the chosen rate, with the steeper and shallower angles fanning out around it.
4. Sanity-check on history: a well-scaled fan shows past reactions spread across several angles rather than all price action hugging one extreme line.
5. Track which angle currently contains price and watch behavior at each line: respect, break, retest from the far side.

## How it's calculated

A set of rays from a single pivot whose slopes are fixed price-per-time ratios, with the 1×1 line advancing one price unit per bar.

```
1. Anchor the fan at a pivot (t_0, P_0): a major swing low for a rising fan, a major swing high for a falling fan.
2. Fix the scale u, the price value assigned to one bar; at this scaling the 1×1 line is a 45 degree diagonal.
3. Draw each fan line as the ray P(t) = P_0 + s × (p / q) × u × (t - t_0).
4. Use the classic ratio set p:q of 1:8, 1:4, 1:3, 1:2, 1:1, 2:1, 3:1, 4:1, 8:1 (price units : time units), spanning 1 price unit per 8 bars up to 8 price units per bar.
5. The 1×1 ray is the primary trend reference: price holding above a rising 1×1 signals strength, below it weakness.
6. When price breaks one ray, the next ray in the set becomes the expected support or resistance, so the fan acts as a ladder of angled levels.

  t_0: bar time of the anchor pivot
  P_0: price of the anchor pivot
  t: bar time along the ray
  P(t): fan line price at time t
  u: chart scale, the price change assigned to one bar (user-set)
  p: price units in the ratio
  q: time units in the ratio
  s: direction, +1 for a fan rising from a low, -1 for a fan falling from a high
```

The quoted angle degrees (45 for 1×1, out to 82.5 for the steepest and 7.5 for the shallowest ray) hold only at the chosen scale u; rescaling the chart changes every angle.

Labeling conventions conflict: some platforms write price×time (2×1 steeper than 1×1), others time×price (2×1 shallower), so check which set your tool uses.

Unlike an ordinary trendline, a Gann angle is fixed by the anchor and scale alone, not by a second pivot.

## How traders use it

- As sloped support and resistance: watching for reactions where price meets a fan line, and for the line's role to flip once it breaks.
- As a trend-strength gauge: which angle currently contains price (riding above the 1×1 versus sagging into the shallow angles) summarizes how the move measures against Gann's balance line.
- As confluence with horizontal tools: a fan line intersecting a fixed level, such as a prior high or a daily floor pivot, gets more attention than either alone.
- As break-and-target structure: when one angle gives way, the adjacent angle becomes the working reference, a built-in sequence of sloped [breakout](https://www.luxalgo.com/library/concept/breakout/) levels and travel targets.
- As a slope benchmark: comparing a trend's realized climb rate to the 1×1 plays the same role as reading an average's gradient with an [MA slope filter](https://www.luxalgo.com/library/concept/ma-slope-filter/), except the benchmark is fixed geometry, not a smoothed line.

## Gann Fan vs other sloped references

- **Trendline** (https://www.luxalgo.com/library/concept/trendline/): A trendline's slope comes from the market: drawn through actual pivots, every trendline is unique to its chart. Gann angles impose predetermined slopes and let the market choose only the anchor. Trendlines describe what price did; Gann angles test price against a fixed geometric standard.
- **Supertrend** (https://www.luxalgo.com/library/concept/supertrend/): Supertrend builds a trailing line from average true range, so its distance adapts to measured volatility, and it flips sides mechanically. A Gann fan never adapts: its lines are straight, fixed at drawing time, meaningful only under the chosen scale. One is a volatility-aware trailing system; the other a static geometric framework.
- **Dynamic S/R Via MA** (https://www.luxalgo.com/library/concept/dynamic-s-r-via-ma/): Moving-average support and resistance bends with price and requires no scaling decision, at the cost of lagging turns. Fan lines are straight and projected forward from the anchor, so they offer levels ahead of price, but depend entirely on anchor and scale choices that averages avoid.

## FAQ

### What does 1×1 mean on a Gann Fan?

It is the angle that moves one unit of price per one unit of time, plotted at 45 degrees when the chart is scaled so those units are visually equal. A 2×1 angle means two price units per bar (steeper); 1×2 means one price unit per two bars (shallower). The labels describe slope only and carry no probability by themselves.

### Why does my Gann Fan look different on every chart?

Because Gann angles are only defined relative to a chosen price-to-time ratio. Change the vertical zoom, switch between log and linear scale, or move to a different instrument, and the same nominal angle plots differently. Fixing an explicit points-per-bar scaling, and keeping it constant, is the only way to make a fan reproducible across charts and platforms.

### Is the 1×1 line always 45 degrees?

Only when the chart is scaled so one price unit and one time unit occupy equal visual distance. The 1×1 is defined by rate, one price unit per bar, not by screen angle; it renders at 45 degrees under that scaling and at some other visual angle otherwise. This is why careful implementations specify a points-per-bar ratio rather than a degree figure.

### What price-to-time scale should I use for a Gann Fan?

There is no universal answer, which is the tool's central difficulty. Common choices are a round points-per-bar figure that keeps historical swings distributed across the fan, or a volatility-derived unit such as average range per bar so the 1×1 reflects the instrument's typical speed. Keep it fixed per instrument and timeframe so signals are reproducible.

### Do Gann angles have proven predictive power?

There is no rigorous public evidence that fixed price-time angles predict turning points, and the scale-dependence problem makes clean testing hard. Reactions at fan lines certainly occur, but so do reactions at many arbitrary lines. Most disciplined users treat the fan as a way to organize sloped levels and require independent confirmation before trading them.

## Implementations in the Library

- Gann Fan & Angles (LuxAlgo): https://www.luxalgo.com/library/indicator/gann-fan-and-angles/

## 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 Box: https://www.luxalgo.com/library/concept/gann-box/
- Gann Square of 9: https://www.luxalgo.com/library/concept/gann-square-of-9/
- Speed Resistance Lines: https://www.luxalgo.com/library/concept/speed-resistance-lines/

---

Source: https://www.luxalgo.com/library/concept/gann-fan-and-angles/ (LuxAlgo Library, the encyclopedia of trading & technical analysis). Free to use with attribution: https://www.luxalgo.com/library/license/