Fibonacci levels explained

While many would undoubtedly be aware of the Fibonacci sequence, and the technical use of Fibonacci (Fib) levels, here is a complete picture of how they are derived.

(no tricks were used in the making of this post, it uses numbers and basic calculations only)

FIBONACCI SEQUENCE and calculating Fib levels


Virtually everyone uses the 61.8, 50.0 and 38.2 Fib levels many times a day. Lessor known (but equally valid) Fib levels are 33.3, 20.0 etc from above

50% Fib - when applied to a range, is simply an average of that range (a mean price).

A lessor known rule for calculating Fibs (for when you cannot remember) is simply multiply 61.8% by itself (0.618x0.618)x100% = 38.2, and again = 23.6% etc

Now this is where it might get interesting -
More accurately, the primary FIB level of 61.8% is actually 0.618033989 (can see where I got this above at (**)). Add 1 to the primary Fib and you have the Golden Ratio (GR).

Major Fib level = 1/GR = GR - 1

So in order of decreasing Fib levels the actual sequence is -

(retraction levels, applied to a 100% range)
61.80%
50.00% = 1/2 (half) = an average price
38.20%
33.33% = 1/3 (third)
23.61%
20.00% = 1/5 (fifth)
14.59%
etc

Fib projections (beyond a range) simply add 100% to these numbers)
161.8%
150.0%
138.2% etc

Calculating Fib levels from the Fib sequence is simple enough. First create a sequence of divisions of consecutive pairs. Then skip one, and divide every second one. Then skip 2 and divide every third one etc etc.

You will then find each successive Fib level to be itself x 0.618 (rounding off). But linked to the Golden ratio.

Spooky hey? (:o)
Enjoy.

rgds,
pw

Wolfram Mathworld on the Golden Ratio
Wiki on the Golden Ratio

"The golden ratio, also known as the divine proportion, golden mean, or golden section, is a number often encountered when taking the ratios of distances in simple geometric figures such as the pentagon, pentagram, decagon and dodecahedron. "