Fibonacci Retracement Explained: The Levels, the Math, and the Evidence

Fibonacci retracement is a tool that marks horizontal levels at which a pullback within a trend might pause or reverse. You draw it between a significant swing low and swing high, and the tool places lines at fixed percentages of that move.

The Levels

The standard levels are:

23.6%, 38.2%, 50%, 61.8%, and 78.6%

(Charting platforms usually add 0% and 100% as the endpoints, and some add extensions like 161.8% for projecting beyond the move.)

Where the Numbers Come From

The levels are derived from the Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89... in which each number is the sum of the two before it. The ratios between numbers in the sequence settle toward fixed values:

• A number divided by the next one approaches 0.618 (for example, 34 ÷ 55 ≈ 0.618). This is the "golden ratio" conjugate and gives the 61.8% level.
• A number divided by the one two places later approaches 0.382 (21 ÷ 55 ≈ 0.382), giving 38.2%.
• A number divided by the one three places later approaches 0.236 (13 ÷ 55 ≈ 0.236), giving 23.6%.

The 50% level is not a Fibonacci ratio. It's included by convention, partly because of an older idea (associated with Dow theory) that markets often retrace about half of a prior move. And 78.6% is the square root of 0.618.

None of this establishes that markets respect these ratios; it's the origin of the numbers, not evidence that they work.

How to Calculate the Levels

In an uptrend, draw from the swing low to the swing high. A retracement level is:

Level = High − (ratio × (High − Low))

Worked example. A stock rises from a low of $100 to a high of $150, a move of $50.

• 23.6% retracement = 150 − (0.236 × 50) = $138.20
• 38.2% retracement = 150 − (0.382 × 50) = $130.90
• 50% retracement = 150 − (0.5 × 50) = $125.00
• 61.8% retracement = 150 − (0.618 × 50) = $119.10
• 78.6% retracement = 150 − (0.786 × 50) = $110.70

In a downtrend, draw from the swing high to the swing low, and the levels are measured upward from the low.

How Traders Use Them

• Potential support or resistance. After a move, price pulls back; traders watch whether it pauses near one of the levels, most often 38.2%, 50%, or 61.8%.
• Gauging pullback depth. A shallow retracement (23.6% to 38.2%) is read as a strong trend; a deeper one (61.8% or more) as a weaker one; a retracement past 100% means the move is fully reversed.
• Combining with other tools. Levels carry more weight, in the traditional view, when they coincide with a moving average, a prior support or resistance level, or a chart pattern.

Why the Evidence Is Thin

Fibonacci retracements are popular, but they're hard to defend empirically:

• Subjectivity in the anchors. Which swing low and swing high to use is a judgment call. Different choices produce different levels.
• Too many levels. With five or more levels, and any pullback of any depth, price will almost always land near one. That makes it easy to see confirmation after the fact.
• Hindsight. Levels where price did reverse get remembered; those that were ignored get forgotten.
• Limited rigorous testing. There isn't a strong body of research showing that Fibonacci levels predict reversals better than chance. See do chart patterns actually work for why technical claims are hard to verify.
• Possible self-fulfilling effect. If many traders watch the same levels, price may react there for that reason alone, but this is an argument about behavior, not about the Fibonacci numbers themselves.

A Fair Way to Think About It

The most defensible use is as a reference grid: a way of marking potential areas of interest and defining risk in advance, not as a predictor. If price falls through a level, that's information; if price holds at one, that's also information; neither means the numbers have special power.

This article is for educational purposes only and is not investment advice.