Fibonacci calculator
Enter n to find the nth Fibonacci number. Shows the sequence up to your value.
F(
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Fibonacci sequence
F(0) = 0, F(1) = 1, then each number is the sum of the two before it: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610...
The golden ratio
The ratio F(n+1)/F(n) approaches φ = (1+√5)/2 ≈ 1.6180339887... as n grows. This "golden ratio" appears in art, architecture, and nature.
Fibonacci in nature
Flower petals often come in Fibonacci numbers (3, 5, 8, 13, 21). Sunflower seed spirals, pinecone scales, and nautilus shells all follow Fibonacci patterns.
Closed formula (Binet's)
F(n) = (φⁿ − ψⁿ)/√5 where φ = (1+√5)/2 and ψ = (1−√5)/2. This gives exact values without computing the whole sequence.
Popular Fibonacci numbers
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