What is Fibonacci retracement?

Fibonacci retracement is a tool used in financial trading. It identifies potential support and resistance levels. After a significant price move (up or down), the price will often 'retrace' or pull back a percentage of that move before continuing in the original direction. The key levels traders watch are 23.6%, 38.2%, 50%, and 61.8%.

What is the Golden Ratio?

The Golden Ratio (Phi or Φ) is an irrational number approximately equal to 1.6180339. In the Fibonacci sequence, dividing any number by the one before it (e.g., 89/55) gets you very close to the Golden Ratio. This ratio is found in nature, art, and is the basis for the Fibonacci retracement levels (e.g., 61.8% and its inverse 38.2%).

Fibonacci Calculator (Sequence & Retracement)

A 2-in-1 tool. Use the **Sequence Calculator** for math or the **Retracement Calculator** for financial trading (stocks, forex).

Fibonacci Sequence Calculator (Math)

Find the n-th number in the Fibonacci sequence and see the full list.

Find Fibonacci Number at position (n):

F(n) Result

Golden Ratio (Φ) Approx.

Sequence up to F(n):

Enter a number (0-150) and click Calculate.

Fibonacci Retracement Calculator (Trading)

Calculate support and resistance levels for a financial asset (stock, forex, crypto) based on its high and low price.

1. Select Trend Direction

2. Low Price

3. High Price

The Two Types of "Fibonacci Calculator"

The term "Fibonacci" is used in two very different fields: mathematics and financial trading. This page provides tools for both.

1. The Fibonacci Sequence (Mathematics)

The Fibonacci sequence is a set of numbers where each number is the sum of the two preceding ones, starting from 0 and 1. It is a fundamental concept in mathematics.

Fₙ = Fₙ₋₁ + Fₙ₋₂
Sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...

The "Golden Ratio" (Phi, or $\Phi$) is a special number approximately equal to 1.618. As the Fibonacci sequence progresses, the ratio between one number and the previous one (e.g., 34/21) gets closer and closer to $\Phi$.

2. Fibonacci Retracement (Financial Trading)

In finance, traders use Fibonacci ratios to identify potential support (pullback) and resistance (extension) levels. After a significant price move (an "uptrend" or "downtrend"), the price will often "retrace" (pull back) to one of these key levels before continuing in the original direction.

The key ratios are derived from the Golden Ratio:

61.8% (0.618): The Golden Ratio ($\Phi$ - 1)
38.2% (0.382): 1 - 0.618
23.6% (0.236): 0.382 * 0.618
50% (0.500): A common-sense middle level.

Frequently Asked Questions (FAQ)

What is the 10th number in the Fibonacci sequence?

Using the sequence F₀=0, F₁=1... the 10th number (F₁₀) is 55. Our calculator can find any number in the sequence up to F₁₅₀.

How do you calculate Fibonacci retracement?

First, identify a High and Low price for a trend. Then, find the difference (the "Range"). For a downtrend, you subtract (Range × Ratio) from the High price to find support. For an uptrend, you add (Range × Ratio) to the Low price to find resistance.

Example (Downtrend): High=$150, Low=$100. Range = $50.
The 38.2% retracement level is: $150 - ($50 * 0.382) = $150 - $19.10 = $130.90.