The Square of 9, and what it actually computes
On this page
- Square of 9 levels and time cycles, step by step
- What the Square of 9 is
- The formula
- Worked example: a price of 100
- Why 144 and 64 are not coincidences
- The levels are not evenly spaced
- Root units per rotation — the one convention
- Support and resistance are labels, not forces
- Anchoring to swing points
- Time cycles
- Worked example: time projections
- Price interval and scale
- What this calculator cannot do
- Common mistakes
- Limitations
- Frequently asked questions
Square of 9 levels and time cycles, step by step
It computes Gann Square of 9 price levels from a starting price, and Gann time cycles from a starting date, showing the formula and every intermediate step so that any figure can be checked by hand.
It is a drawing tool for a method, not a forecast. That distinction runs through the whole page and is worth stating at the top: nothing here uses market data, nothing here models price behaviour, and nothing here claims that a price will do anything at any of these levels.
Not a trading signal. Every number on this page is derived from the one price you typed in. If you are studying Gann's methods, this gives you the construction computed correctly. If you are looking for a prediction, there isn't one here.
What the Square of 9 is
A spiral of numbers. Start at the centre and wind outward, and the values arranged around the spiral have a property that is the whole point of the thing: moving a fixed angle around it corresponds to a fixed change in the square root of the value, not in the value itself.
Everything else follows from that. Because the relationship is on the root rather than the price, the same angular step produces a small price move near the centre and a large one further out — which is why the levels widen as price rises, and why the method behaves differently on an instrument priced at 40 than on one priced at 40,000.
Unlike most of the rule-sensitive calculators on this site, the arithmetic here is not proprietary. There is no hidden formula being guessed at. The Square of 9 is a published geometric construction, and this page implements it directly rather than asking you to supply it.
The formula
level = ( √price ± units × scale × angle ÷ 360 ) ²
Take the square root of the starting price. Add or subtract a fraction of a rotation. Square it again. That is the entire calculation, and the page prints it with your own numbers substituted, along with the square root, the adjustment and the squared result for every level.
units is how much a full 360-degree rotation adds to the root. scale multiplies that, and stays at 1 for the standard construction. Both are discussed below.
Worked example: a price of 100
A starting price of 100, whose square root is exactly 10, with the standard two root units per rotation. At 45 degrees the adjustment is 2 × 45 ÷ 360 = 0.25, so the upward level is (10 + 0.25)² = 10.25² = 105.0625.
| Angle | Root adjustment | Downward level | Upward level |
|---|---|---|---|
| 45° | 0.25 | 95.0625 | 105.0625 |
| 90° | 0.50 | 90.25 | 110.25 |
| 135° | 0.75 | 85.5625 | 115.5625 |
| 180° | 1.00 | 81 | 121 |
| 270° | 1.50 | 72.25 | 132.25 |
| 360° | 2.00 | 64 | 144 |
Every one of those can be checked in a second: take the root adjustment, add it to 10 or subtract it, and square the result.
Why 144 and 64 are not coincidences
Look at the 180-degree and 360-degree rows. They land on 81, 121, 64 and 144 — all perfect squares, with no decimals anywhere.
That is the construction showing its hand. With two units per rotation, a half rotation adds exactly 1 to the square root and a full rotation adds exactly 2. Starting from a root of 10, those take you to roots of 9, 11, 8 and 12 — and the squares of whole numbers are whole numbers.
This is the property that made the Square of 9 appealing in the first place. Whole rotations from a perfect square land on other perfect squares, and the sequence 64, 81, 100, 121, 144 is just 8², 9², 10², 11², 12². Whether that has any bearing on markets is an entirely separate question, and not one this page takes a position on.
The levels are not evenly spaced
This surprises people, and it is the most important practical feature of the method. The progression table shows the step between each neighbouring pair:
| From | To | Step |
|---|---|---|
| −135° (85.5625) | −90° (90.25) | 4.6875 |
| −45° (95.0625) | start (100) | 4.9375 |
| start (100) | +45° (105.0625) | 5.0625 |
| +135° (115.5625) | +180° (121) | 5.4375 |
| +270° (132.25) | +360° (144) | 11.75 |
The same 45-degree step is worth 4.69 on the way down and 5.44 on the way up. The widening is not an artefact — it is what squaring a root does, and it is the reason a fixed percentage grid and a Square of 9 grid are different things.
Note also that the 270-to-360 step is 11.75 rather than roughly 5. That is because those two angles are 90 degrees apart, not 45. The progression table lists whatever angles you selected, so the steps reflect your own choices rather than a uniform grid.
Root units per rotation — the one convention
Almost everything on this page is definitional. This setting is not.
How much a full rotation adds to the square root is a convention practitioners choose. Two is the common choice and the default here, because it makes a half rotation add exactly 1 and produces the clean perfect-square behaviour above. One is also used, and gives a much tighter grid: from 100, a full 360-degree rotation then reaches 121 and 81 rather than 144 and 64.
Rather than pick one and stay quiet about it, the page offers both and prints the active value in the formula line above the level table. If you are following a particular source, check which convention it uses before comparing numbers — this is the single most common reason two Gann calculators disagree.
Support and resistance are labels, not forces
The level table has columns headed support and resistance. Those are conventional names for "below the starting price" and "above it", and that is all they are.
Nothing in the arithmetic makes a price stop at either. The construction has no knowledge of volume, order flow, news, or anything else that actually moves a market. It computed those numbers from one price and a square root.
The page uses the conventional labels because that is what the method calls them and renaming them would make it harder to follow alongside other material. It states what they are here so the labels are not mistaken for a claim.
Anchoring to swing points
The construction is anchored entirely to whatever price you give it, which means an arbitrary starting price produces an arbitrary set of levels. Practitioners generally anchor to a significant swing high or swing low instead.
Enter either or both and the page adds a second table: levels projected up from the swing low and down from the swing high. From a swing low of 80, the 45-degree level upward is 84.535; from a swing high of 120, the 45-degree level downward is 114.585.
Neither of those is a round number, which is a useful reminder. The tidy figures in example 1 came from starting at 100, a perfect square. Real swing points rarely are.
Time cycles
Gann's framework treats price and time on the same scale, so the same angles are read as counts of days. Ninety degrees becomes ninety days.
Give the page a starting date and it projects a date for each angle, and pairs it with the price level produced by the same angle. That pairing is the price-time combination the method is built around. The page presents the coordinates; it makes no claim that anything happens at them.
Worked example: time projections
Calendar days, so every day counts:
| Angle | Days | Date | Price at the same angle |
|---|---|---|---|
| 45° | 45 | Sun 15 Feb 2026 | 105.0625 |
| 90° | 90 | Wed 1 Apr 2026 | 110.25 |
| 135° | 135 | Sat 16 May 2026 | 115.5625 |
| 180° | 180 | Tue 30 Jun 2026 | 121 |
| 270° | 270 | Mon 28 Sep 2026 | 132.25 |
| 360° | 360 | Sun 27 Dec 2026 | 144 |
Two of those land on a weekend, which matters if you are looking at an instrument that does not trade then. Switch the day basis to trading days and the same 45 degrees becomes 45 trading days — Thursday 5 March 2026 rather than 15 February, because nine weekends have been skipped along the way.
Ninety trading days lands on Thursday 7 May, and 135 on Thursday 9 July. They are all Thursdays because each of those angle counts is a multiple of five, and five trading days is exactly one week.
Public holidays are not modelled. They differ by exchange and by year, and building a holiday calendar into the page would be an assumption made silently on your behalf. Trading-day projections will therefore run slightly early against a real exchange calendar, and the page says so beside the table.
Price interval and scale
Two settings for making the output usable rather than changing what it means.
Price interval rounds every level to a multiple of the value you give. Set it to 5 and the levels from 100 become 95 and 105, 90 and 110, 85 and 115, 80 and 120, 70 and 130, 65 and 145. Useful for instruments that only trade in fixed increments; leave it at 0 and the levels stay exact.
Scale multiplies the root adjustment. It exists because some practitioners scale the construction to an instrument's typical range. Leave it at 1 for the standard construction — and if you change it, the formula line above the level table shows it applied, so the output never quietly means something different from what it says.
One more presentational note: the number of decimals shown follows the size of the price. A level from a starting price of 100 shows three decimals; one from a price of 0.0842 shows six, because rounding it to two would erase the level entirely.
What this calculator cannot do
It is worth being explicit, because pages of this kind are frequently presented as something they are not.
- It cannot predict a price. There is no forecasting model here of any kind.
- It has no market data. No prices, no history, no volumes. Every figure comes from the number you typed.
- It offers no evidence that the levels matter. The page does not claim prices respect them, because it has nothing to support such a claim.
- It cannot tell you whether to buy or sell anything. It is arithmetic, and arithmetic has no opinion about your money.
What it can do is compute a documented construction correctly, show its working, and be honest about which parts are definitional and which are convention. For someone studying the method, that is worth more than a confident-looking answer with no visible reasoning.
Common mistakes
Comparing against a calculator using the other convention
One unit per rotation versus two produces completely different levels — 121 against 144 from the same starting price. Check which is in use before concluding that anything disagrees.
Anchoring to an arbitrary price
The construction is entirely determined by its starting point. A meaningless anchor gives meaningless levels, tidily formatted.
Reading the labels as predictions
Support and resistance here mean below and above. Nothing more.
Forgetting that trading-day projections ignore holidays
They will run early against a real exchange calendar, by roughly the number of holidays in the period.
Using two decimals on a small-priced instrument
The page adjusts precision automatically, but if you copy levels elsewhere, keep the decimals. At a price of 0.0842 the first upward level is 0.291786, and rounding it to 0.29 loses most of the information.
Limitations
The construction is implemented; its usefulness is not asserted. This page takes no position on whether Gann analysis works. It computes the geometry.
Only the Square of 9 and the day-count time cycles are covered. Gann's wider body of work includes angles drawn on charts, seasonal cycles and much else that is not here.
No holiday calendar. Trading-day projections skip weekends only.
No market data of any kind. Nothing on this page is connected to a price feed, and the current-price field is used only to show distances.
Nothing is stored. Everything runs in your browser and is gone when the tab closes.
Frequently asked questions
What is the Gann Square of 9?
A geometric construction that arranges numbers in a spiral around a centre, so that moving a fixed angle around the spiral corresponds to a fixed change in the square root of the value. In calculation terms, a level at angle t is the square of the starting price's square root plus t/360 of a rotation. It is arithmetic on square roots rather than on prices, which is why the levels spread further apart as price rises.
What is the actual formula used here?
Level = (square root of the starting price, plus or minus units × angle ÷ 360) squared. The page prints that formula with your own numbers substituted, and the working panel shows the square root, the adjustment and the result for every level, so you can reproduce any figure by hand.
Why is the number of units per rotation a setting?
Because it is a convention rather than part of the construction. Two is the most common choice — it makes a half rotation add exactly one to the square root — but one is also used. Rather than hard-code a preference, the page offers both and states which is active on the result.
Why are the levels not evenly spaced?
Because the construction works on square roots. From a price of 100 the first 45-degree step upward is about 5 points, while the step from 270 to 360 degrees is nearly 12. That widening is the defining property of the method, not an error, and it is why the same angle produces a much larger price move at higher prices.
What do the support and resistance columns mean?
They are simply the levels below and above your starting price at each angle. Downward rotations produce the lower set and upward rotations the upper set. Calling them support and resistance is conventional labelling; nothing in the arithmetic makes a price stop at either.
How does the time projection work?
Gann time cycles read the angle as a count of days, so 90 degrees becomes 90 days from your starting date. Choose calendar days and the count runs straight through the week; choose trading days and weekends are skipped, so the same 90 lands considerably later. Public holidays are not modelled, because they vary by exchange.
What are the price-time combinations?
The table pairs each angle's price level with the date produced by the same angle, which is the point of the exercise in Gann's framework — the idea that price and time are measured on the same scale. The page presents the pairing; it makes no claim that anything happens at those coordinates.
Does this predict where a price will go?
No, and nothing on this page should be read that way. It computes a geometric construction from a number you supplied. There is no forecasting model here, no market data, and no evidence offered that prices respect these levels. Treat the output as a drawing tool for a method you are studying, not as a signal.
What should I use as the starting price?
Practitioners generally use a significant swing high or swing low rather than an arbitrary price, because the construction is anchored to whatever you give it and a meaningless anchor produces meaningless levels. The page accepts swing high and swing low as separate inputs so you can see both sets of levels from one entry.
Why does the calculator reject a starting price of zero?
Because the construction takes a square root and works outward from it. A price of zero has a root of zero, so every downward level would be clamped at zero and the upward ones would ignore the starting point entirely. There is nothing meaningful to construct from it.
Disclaimer
This is an educational and analytical tool. It is not financial advice, investment advice, or a recommendation to buy or sell any instrument. Nobody involved in this site is a licensed financial adviser, and nothing here is a substitute for one.
No prediction is made anywhere on this page. The levels are a geometric construction computed from a single number you entered. There is no market data behind them, no model of price behaviour, no back-testing, and no evidence offered that prices respect them. Any page presenting Gann levels as forecasts is making a claim this one does not.
Technical analysis is contested. Gann's methods in particular are interpretive, are applied differently by different practitioners, and have no established predictive validity. Treat the output as a drawing of a method, not as evidence about a market.
Trading and investing carry a real risk of losing money. Leveraged instruments can lose more than the amount deposited. Past movements do not indicate future ones. Please do not commit money on the basis of a level produced by this or any similar calculator, and if you are considering it, speak to a licensed professional in your own jurisdiction first.
The arithmetic here is transparent and can be checked by hand, which is the only thing this page guarantees. What the numbers mean, and whether they mean anything at all, is not something a calculator can tell you.