Math Tools
Fibonacci Calculator
Calculate Fibonacci sequence numbers, find the Nth Fibonacci number, generate sequences, and explore the golden ratio. Perfect for mathematics, nature patterns, and programming.
Use Fibonacci Calculator to get instant results without uploads or sign-ups. Everything runs securely in your browser for fast, reliable output.
Your results will appear here.
About this tool
The Fibonacci sequence is a famous mathematical pattern where each number is the sum of the two preceding ones: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34... This sequence appears throughout nature, art, architecture, and finance.
Our Fibonacci Calculator generates any position in the sequence, shows the progression, calculates golden ratio relationships, and provides real-world examples. Used by mathematicians, students, programmers, traders, artists, and nature enthusiasts.
Usage examples
10th Fibonacci
F(10) = 55
Sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55
Golden Ratio
F(13)/F(12) ≈ 1.618
233/144 = 1.618... (phi)
Nature Example
Sunflower seeds
Spiral patterns follow Fibonacci (34, 55, 89 spirals)
Large Number
F(50)
50th Fibonacci number = 12,586,269,025
Trading Levels
Fibonacci retracement
F(8) = 21, used in technical analysis
How to use
- Enter position (N) in sequence
- Click Calculate
- View Fibonacci number, sequence, and golden ratio
- Explore real-world patterns
Benefits
- Calculate any Fibonacci number
- Generate sequences
- Golden ratio calculation
- Real-world examples
- Fast computation
- Free to use
FAQs
What is the Fibonacci sequence?
The Fibonacci sequence starts with 0 and 1. Each subsequent number is the sum of the previous two: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144... Formula: F(n) = F(n-1) + F(n-2), where F(0) = 0 and F(1) = 1.
What is the golden ratio?
The golden ratio (phi, φ) ≈ 1.618 is the limit of F(n+1)/F(n) as n approaches infinity. As Fibonacci numbers get larger, consecutive ratios approach 1.618. This ratio appears in art, architecture (Parthenon, pyramids), nature (nautilus shells, flower petals), and design.
Where does Fibonacci appear in nature?
Fibonacci appears everywhere in nature: (1) Flower petals (3, 5, 8, 13, 21, 34...), (2) Pinecone spirals, (3) Sunflower seed patterns, (4) Nautilus shell spirals, (5) Tree branch patterns, (6) Pineapple scales, (7) Hurricane spirals. Nature optimizes growth using Fibonacci ratios!
How is Fibonacci used in trading?
Fibonacci retracement levels (23.6%, 38.2%, 61.8%, 100%) predict stock price support/resistance. Formula: key level = high - (high - low) × Fibonacci ratio. Many traders use Fibonacci to identify entry/exit points. However, effectiveness is debated—not a guaranteed strategy.
What is the formula for the Nth Fibonacci number?
Binet's formula: F(n) = (φⁿ - ψⁿ) / √5, where φ = (1+√5)/2 ≈ 1.618 (golden ratio) and ψ = (1-√5)/2 ≈ -0.618. This closed-form formula calculates F(n) directly without recursion. Our calculator uses iterative method for accuracy with large numbers.
Can you calculate very large Fibonacci numbers?
Yes! Our calculator uses efficient iteration to compute large Fibonacci numbers. F(100) = 354,224,848,179,261,915,075. JavaScript can accurately compute up to F(78) before losing precision. For n > 78, we show approximations. Fibonacci grows exponentially—F(n) ≈ φⁿ/√5.
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