Fibonacci Calculator
Calculate an exact Fibonacci number and nearby terms using a bounded fast-doubling algorithm.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Use the convention F(0)=0 and F(1)=1. Split the index into halves recursively. Apply the even and odd fast-doubling identities. Display the exact term and neighboring indices.
F(2k)=F(k)[2F(k+1)−F(k)]; F(2k+1)=F(k)²+F(k+1)²
Worked example
F(20)=6765, with F(19)=4181 and F(21)=10946.
Assumptions and input details
Indices from zero to ten thousand are supported. Results use exact integer arithmetic. A large term is displayed as a long integer and is not converted to an approximate scientific-notation count.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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