Fibonacci Calculator
Calculate Fibonacci retracement and extension levels for stocks, forex, and crypto or generate any term in the sequence up to F(1,000) with exact precision. Results update as you type.
Swing high โ peak of the uptrend
Swing low โ base of the uptrend
End of pullback โ where retracement reversed
Enter Custom to see extension levels
Enter High and Low to see Fibonacci levels
What is the Fibonacci Sequence?
The Fibonacci sequence is a series of numbers where each number is the sum of the two before it. Starting from 0 and 1, the pattern looks like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144... and it continues indefinitely. Every number you see is just the previous two added together.
This sequence was described by the Italian mathematician Leonardo of Pisa (known as Fibonacci) in his 1202 book Liber Abaci, though the pattern itself appeared in Indian mathematics centuries earlier. Today, it shows up in nature, architecture, and most practically for our purposes, in financial trading.
Divide any Fibonacci number by the one before it and you get a ratio that gets closer and closer to 1.618 as the numbers grow. F(20) รท F(19) = 6765 รท 4181 = 1.61803... This is the Golden Ratio (ฯ), and it's the mathematical engine behind every Fibonacci trading level you'll ever use.
The Fibonacci Formula
Sequence Formula
- F(n) = the Fibonacci number at position n
- F(nโ1) = the number one position before it
- F(nโ2) = the number two positions before it
- F(0) = 0, F(1) = 1 = the two starting values
Trading Retracement Formula
For an uptrend (measuring pullback support):
For a downtrend (measuring rally resistance):
Extension Formula
Extension levels need a third point, Custom (C), marking where the retracement ended and the trend resumed:
Uptrend: Level = Custom + (High โ Low) ร Extension Ratio
Downtrend: Level = Custom โ (High โ Low) ร Extension Ratio
- High (H) = swing high price of the trend
- Low (L) = swing low price of the trend
- Custom (C) = end of the retracement move
- Fibonacci Ratio = 0.236, 0.382, 0.500, 0.618, or 0.764
- Extension Ratio = 0.618, 1.000, 1.382, 1.618, 2.000, or 2.618
Step-by-Step Walkthrough
Trading Example: EUR/USD Uptrend
EUR/USD rallied from a swing low of 1.2800 up to a swing high of 1.3500. Price then started pulling back. You want to identify where Fibonacci support zones are before considering a long entry.
Given: H = 1.3500, L = 1.2800
Range = 1.3500 โ 1.2800 = 0.0700
38.2% level = 1.3500 โ (0.0700 ร 0.382) = 1.3500 โ 0.0267 = 1.3233
50.0% level = 1.3500 โ (0.0700 ร 0.500) = 1.3500 โ 0.0350 = 1.3150
61.8% level = 1.3500 โ (0.0700 ร 0.618) = 1.3500 โ 0.0433 = 1.3067
The 61.8% level at 1.3067 is the strongest support zone because it's derived directly from the Golden Ratio. If price pulls back to this area and holds, traders read that as a high-probability long setup.
Adding Extension Levels
The pullback ended at 1.2950 (your Custom point). Now you can project profit targets for when the uptrend resumes:
Custom (C) = 1.2950
100% ext. = 1.2950 + (0.0700 ร 1.000) = 1.3650
138.2% ext. = 1.2950 + (0.0700 ร 1.382) = 1.3917
161.8% ext. = 1.2950 + (0.0700 ร 1.618) = 1.4083
The 161.8% extension at 1.4083 is your primary target. Many traders set their take-profit there and watch for price action signals at the 138.2% level as a partial exit zone.
Sequence Example: Finding F(10)
To find F(10) manually, build the sequence one step at a time from the starting values:
F(0) = 0
F(1) = 1
F(2) = 1 + 0 = 1
F(3) = 1 + 1 = 2
F(4) = 2 + 1 = 3
F(5) = 3 + 2 = 5
F(6) = 5 + 3 = 8
F(7) = 8 + 5 = 13
F(8) = 13 + 8 = 21
F(9) = 21 + 13 = 34
F(10) = 34 + 21 = 55
This calculator handles up to F(1000), a number with over 200 digits, using exact arithmetic.
How to Use This Calculator
Trading Levels Mode
- 1Select Uptrend or Downtrend depending on the direction of the original price move.
- 2Enter the High (H) price. For uptrends, this is the swing high where the rally ended. For downtrends, it's where the decline started.
- 3Enter the Low (L) price. For uptrends, this is where the rally started. For downtrends, it's the swing low at the end of the move.
- 4Retracement levels appear automatically. The gold-highlighted 61.8% row is the Golden Ratio level and carries the most weight.
- 5Enter Custom (C) to unlock extension levels. This is the price where the retracement ended before the trend resumed.
- 6Set Decimal Places to match your asset (4 for forex pairs, 2 for most stocks and indices).
Fibonacci Sequence Mode
- 1Switch to Fibonacci Sequence mode using the toggle at the top.
- 2Enter a position n to find F(n). The sequence starts at F(0) = 0, so F(10) gives you the 11th number.
- 3Adjust the term count to display up to 50 numbers in a scrollable list with their golden ratio convergence.
Frequently Asked Questions
Why is 61.8% considered the strongest Fibonacci level?
Because it comes directly from the Golden Ratio. Take 1 divided by 1.618 and you get 0.618 (61.8%). This ratio appears throughout nature and tends to act as a strong magnet for price action. Traders globally watch this level, and because so many people act on it, it becomes a self-reinforcing support or resistance zone.
What's the difference between retracement and extension levels?
Retracement levels sit between your High and Low. They show you where price might pause or reverse during a pullback before continuing the original trend. Extension levels go beyond your High (for uptrends) or below your Low (for downtrends), giving you forward-looking price targets for when the trend resumes.
Can I use Fibonacci levels for stocks and crypto, not just forex?
Yes, Fibonacci works on any liquid, freely traded market where price charts show trends and pullbacks. Stocks, indices, commodities, and crypto all respond to Fibonacci levels because the underlying crowd psychology is the same. The math doesn't care what you're trading. Adjust your decimal places accordingly: 2 places for stocks, 4 for forex, and 0 to 2 for crypto depending on the price range.
Is 50% actually a Fibonacci number?
No, 50% is not a true Fibonacci ratio. It comes from Dow Theory, which observed that trends frequently retrace half of their previous move. Traders added it to Fibonacci toolsets because it works in practice. Think of 50% as a useful psychological midpoint rather than a mathematical Fibonacci level, which is why this calculator labels it as a "Key Level" rather than "Strong" or "Golden Ratio."
Why does the sequence start at F(0) = 0 instead of F(1) = 1?
It's a convention choice. Some textbooks start the sequence at 1, 1, 2, 3... and some at 0, 1, 1, 2, 3... Modern mathematics typically uses 0 as the starting index (F(0) = 0) to keep the indexing consistent with computer science and combinatorics. This calculator follows the standard F(0) = 0 convention, so if you're matching a textbook that starts at 1, just subtract 1 from your position input.
How large can Fibonacci numbers get and does the calculator handle them?
Fibonacci numbers grow exponentially. F(50) is already over 12 billion, and F(100) has 21 digits. JavaScript numbers lose precision around F(78) because they exceed the maximum safe integer. This calculator uses BigInt arithmetic for the sequence mode, which means F(1000) (a 209-digit number) is calculated exactly, not approximately. The trading calculator uses standard floating-point, which is more than sufficient for price-level work.