Gann's Square of Nine — what it is and how to use it

What is the Square of Nine?

The Square of Nine is a spiral grid of integers, anchored at the number 1 in the center, expanding outward one ring at a time. The first ring around 1 contains 2 through 9. The next ring contains 10 through 25. Each subsequent ring adds eight more cells than the last.

That last detail is the entire point. The Square of Nine isn't a number line — it's a way of encoding two things about every value: its magnitude (how far it sits from the center) and its angle (which direction from the center it sits in). Gann claimed price levels at the same angle from a chosen anchor behaved like harmonic resonances of each other.

Why Gann built it

William Delbert Gann (1878–1955) was an American trader who became convinced that markets weren't purely random — that price and time related to each other through geometric and astronomical patterns. He sold an interpretation of those patterns through courses, books, and chart services for the last forty years of his life.

You don't have to buy the cosmology to find the geometry useful. What Gann was really doing with the Square of Nine was building a coordinate system that mapped magnitude and angle simultaneously — exactly the kind of dual representation a chartist needs when picking out support and resistance from a swing low or a swing high. The grid was a way to do that arithmetic on paper, fast, in 1920.

The math, in plain English

Three observations carry most of the weight.

01 — The outer ring of any odd square is exactly that square

The 3×3 grid's outer ring ends at 9 (= 3²). The 5×5 grid's outer ring ends at 25 (= 5²). The 7×7 ends at 49. That's why Gann called it the Square of Nine — the first non-trivial ring ends at 9, and from there the pattern scales.

02 — Diagonals encode multiplicative growth

The south-east diagonal of the diagram above — 1, 9, 25 — is 1², 3², 5². Extend the grid and the next entries are 49 (= 7²) and 81 (= 9²). The north-west diagonal contains the even squares: 4, 16, 36, 64. Every diagonal in the spiral encodes a multiplicative relationship, not just an additive one.

03 — Rotations around the spiral measure angles

Each full ring is 360° of rotation around the center. A quarter ring is 90°. An eighth is 45°. So "move 90° from your anchor on the Square of Nine" is a well-defined arithmetic operation: you start at your anchor price, count outward by the appropriate number of cells, and read off the value at that new angular position. Gann's claim — testable on any chart you like — is that those rotated values often act as future price levels.

How traders use it manually

The classical workflow has three steps.

1. Pick an anchor. Usually a significant low or high — a swing pivot the market clearly respected. The whole projection is relative to this number, so the anchor matters more than any other choice you make.
2. Project rotations. Apply the Square of Nine rotations (45°, 90°, 135°, 180°, …) to the anchor. On paper this means writing out the spiral by hand and reading off the values. Traders who do this professionally use printed Square of Nine sheets or — more often — spreadsheets that mechanize the calculation.
3. Plot the levels. Draw horizontal lines on the chart at each projected price. Watch how price reacts when it reaches them. The harmonic levels are hypotheses, not signals — a level the market ignores is real information too.

The bottleneck is step two. Even with a spreadsheet, retracing the geometry for a new anchor on a new asset takes the better part of an hour if you want it accurate. That's where automation earns its place.

Where the indicator helps

PyraTime publishes a TradingView indicator, Square of Nine Harmonics [SQ9], that does the bookkeeping. You drop a vertical line on your anchor — a low, a high, or any pivot you pick — and the indicator recomputes the Square of Nine rotations against that anchor in real time. Cardinal and diagonal harmonics appear as horizontal levels on the chart. If you move the anchor, every level redraws in seconds.

It doesn't replace the thinking — picking the right anchor still matters, and a level the market ignores is still useful information. What it replaces is the spreadsheet work. The geometry comes for free; the rest is up to you.

Where to go from here

If you're new to Gann, the cheapest thing you can do is print out a paper 9×9 Square of Nine, pick a market you follow, and try to anchor and project a few levels by hand. The grid teaches faster than any explainer.

If you already work with Square of Nine projections and the spreadsheet step is the bottleneck, the SQ9 Harmonics indicator is what we built for you.