How to use Fibonacci Calculator
- Enter n, the position in the sequence.
- Read F(n) and the golden-ratio approximation.
- Optionally list the first terms.
About this tool
The Fibonacci sequence starts 0, 1, 1, 2, 3, 5, 8 and each term is the sum of the two before it. The ratio of consecutive terms approaches the golden ratio, about 1.618034. This calculator uses big-integer arithmetic so even F(1000), which has 209 digits, is exact.
Positions are counted from F(0) = 0.
Frequently Asked Questions
- Does the sequence start at 0 or 1?
- This tool uses the modern convention F(0) = 0 and F(1) = 1.
- Where do Fibonacci numbers appear?
- In growth patterns of plants, algorithm analysis, and as the basis of the Fibonacci retracement used in trading.
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