Fibonacci Calculator (Sequence & Retracement)

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

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.

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.

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