Square Of Nine Explained

One of the most innovative things that W.D. Gann ever came up with, and quite frankly one of the most mysterious is the Square of Nine. Here is how it works. Take a piece of graph paper with 1/4” squares. Right in the middle of the paper write the number 1. In the square directly to the left of this write the number 2. In the square above the 2, write 3. To the right write 4, then 5. Below the 5 write 6 then 7. To the left of the 7 write 8 then 9.

You now have a 3×3 matrix containing the numbers 1 through 9. Continue this process until you have a large square with numbers arranged like this:

Starting from the 1 and moving to the lower left, we see that the numbers are all squares of odd numbers: 9, 25, 49, 81 and so on. Starting at the 4 and moving to the upper right we see that the numbers are all squares of even numbers: 4, 16, 36, 64 and so on. If you take the square root of a number anywhere on the grid, add 2 and square it, you will get the next number out on the grid. If you subtract 2 from the square root and square it, you will get the next number in.

To the mathematically inquisitive mind all of this is truly amazing, but what use is it? Much, in every way. According to Gann, every market has vibrations. When you add 2 to the square root to get the next number out on the grid, you have effectively gone right around the grid, or 360 degrees. Some markets vibrate at 360 degrees, some at 45, some at 15 and so on. When you find out how your market vibrates, you can predict future support and resistance levels this way.

Many Forex technical analysts have difficulty applying this to currency prices, due to the relatively low magnitude of the exchange rates. For example, if you take a typical wheat price of say 530, and you subtract 45 degrees from it, you will get 518 which is a reasonable price you may expect the market to reach in a reasonable time. But if you take a typical EUR/USD price of say, 1.0822 and you subtract 45 degrees from it, you will get 0.6246, a price which we may not see in our lifetime. So what is the solution? If we subdivide 360 degrees in thirds and quarters until we get reasonable prices, we will be using tiny increments such as 3.75 degrees which are both counter-intuitive, and give bad results. The solution lies in measuring prices in cents rather than dollars just like they do with commodities. 1.0822 is really 108.22 cents. Subtract 45 degrees and we get 103.08, just 500 pips away.

Practically speaking, how do you calculate squares of nine? Do you draw a giant square of nine on the wall? No, there is an easier way. To add 360 degrees to a number you simply take the square root, add 2 and square it. For any division of 360 degrees you add the appropriate number: 1 for 180 degrees, 0.5 for 90 degrees etc. Subtract the number from the square root to subtract the degrees. You must experiment with your market to find out what works best. With EUR/USD, 15 and 30 degrees work well for position trades, while 7.5 degree increments work well intra-day. Other markets may vibrate differently.

Use the calculator below to find support and resistance levels above and below any swing top or bottom.

Square Of Nine
Calculator
Price: 
Increment (degrees): 

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