Fibonacci Retracement: Where Pullbacks Tend to Pause

After a strong move, price rarely runs straight on. Fibonacci retracement gives traders a map of the levels where a pullback might stop.

Where the numbers come from

Leonardo of Pisa, known as Fibonacci, brought the number sequence 1, 1, 2, 3, 5, 8, 13… to Europe in his 1202 book Liber Abaci, although Indian mathematicians had described it earlier. Each number is the sum of the two before it. Divide any number by the next one and the result settles near 0.618, the inverse of the golden ratio. Fibonacci never studied markets. The link came much later, largely through the wave theory of R. N. Elliott in the 1930s and 1940s, and then through charting software that put the tool on every screen.

Where the Fibonacci ratios come from The sequence 3, 5, 8, 13, 21, 34, 55, 89. Dividing 55 by 89 gives 0.618, 34 by 89 gives 0.382, and 21 by 89 gives 0.236. 3 5 8 13 21 34 55 89 55 ÷ 89 = 0.618, the 61.8% level 34 ÷ 89 = 0.382, the 38.2% level 21 ÷ 89 = 0.236, the 23.6% level
Figure 1. Dividing by the next number, or by the one two or three places ahead, gives the key ratios.

The levels on a chart

Dividing a number by the one two places ahead gives about 0.382, and three places ahead gives about 0.236. Most platforms add 50%, which is not a Fibonacci ratio but reflects the old market idea that a move often retraces about half. Some also add 78.6%, the square root of 0.618. In an uptrend the price of each level is high − (high − low) × ratio. With a low of 100 and a high of 150, the 61.8% level is 150 − 50 × 0.618 = 119.1.

How to draw it

  1. Pick a clear swing low and the swing high that followed it. In a downtrend, use the swing high and the swing low that followed it.
  2. Drag the Fibonacci retracement tool from the start of the move to its end. The platform draws the levels.
  3. Watch how price behaves as it falls back toward the 38.2%, 50% and 61.8% levels, and look for confirmation such as a hammer candle, a rise in volume or a turn in momentum.
Illustrative Fibonacci retracement Price rises from 100 to 150, pulls back to about 119, which is the 61.8 percent level, then rises above the previous high. 0% 150.0 23.6% 138.2 38.2% 130.9 50% 125.0 61.8% 119.1 78.6% 110.7 100% 100.0 Swing low 100 Swing high 150 Pullback holds near 61.8%
Figure 2. Illustrative data. The shaded band marks the 38.2% to 61.8% zone.

Using it with care

There is no solid statistical proof that price respects these exact levels, and different traders choose different swings, which changes the lines. With so many levels on the chart, price will often be near one of them by chance. Part of their effect may simply be that many traders watch them. Treat the levels as zones, not exact prices, and trust them more when they coincide with other evidence, such as an earlier support or resistance, a moving average or a trend line. Always decide where you will exit if the level fails.

Educational content only. It is not investment advice, and trading involves risk of loss.

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